Ravalli County Curriculum Consortium

Ravalli County Curriculum Consortium Mathematics K-8

(02) Prepared by Marzano Research Laboratory September, 2009

Note to Ravalli: The green highlighting represents either suggestions/comments we have made or additions that we have made to the rubric. Remember that our suggestions are only that, and the final word is up to you!

At times, we did not complete a 2.0 element or task because we had a question on the 3.0 element. Until the 3.0 is set, we cannot write the 2.0 or task.

In some case, when the 3.0 element asks the student to solve something, we suggested using solve simple versions at the 2.0 The intent here is to have the student solve basic or introductory type problems at the 2.0 and then to solve more complicated or complex problems using the skills and procedure learned while solving the simple version. In many cases, you can think of the way that a text presents these – simple non-complicated problems to introduce the concepts, then more complicated problems later. When we used this at the 2.0, we did not write a sample task because it depends on the example we asked you to come up with.

We recommend that grade level examples of the type of problem be put into the element as well as in the sample task. This can be done using an (e.g., ) after the element. The reason for this is that sample tasks can be changed or deleted, the format of the rubric could change according to your needs, etc. and the example should be linked to the element in order to keep it specific.

Ravalli-Mathematics K-8 Version 2 Page 1 Mathematics Measurement Topics K 1 2 3 4 5 6 7 8

Strand: Numbers Sense and Operations Numbers and Equivalent Representations * * * *

Counting * * * *

Addition/Subtraction * * *

Multiplication/Division * * * * * *

Fractions, Decimals, Percents * * * * * * * *

Ratio and Proportion * * *

Scientific Notation * * *

Real Numbers *

Place Value * * * * * * * *

Measurement Units * * * * *

Time and Temperature * * * * *

Strand: Algebraic and Functional Reasoning Symbols and Expressions * * * * * * * * *

Equations * * * * * * * *

Ravalli-Mathematics K-8 Version 2 Page 2 Functions and Relationships * * *

Linear and Non-Linear Equations * * *

Inequalities * *

Patterns * * * * * * * * *

Properties * * *

Strand: Geometric Reasoning Geometric Figures * * * * * * * * *

Congruence and Symmetry * * * * * * * * *

Transformations * * * * * * *

Geometric Properties * * * * * * * * *

Length, Area and Volume * * * * * * * * *

Capacity and Weight * * * * * * * *

Strand: Data Analysis Data Collection, Organization and Display * * * * * * * * *

Analysis * * * * * * * * *

Probability * * * * * * * *

Ravalli-Mathematics K-8 Version 2 Page 3 Numbers Sense and Operations

Ravalli-Mathematics K-8 Version 2 Page 4 Numbers and Equivalent Representations

Ravalli-Mathematics K-8 Version 2 Page 5 Strand: Number Sense and Operations Topic: Numbers and Equivalent Representations Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will state the names of random numbers 3.0  recognizes numbers from 0 -10 (e.g., random order) given to them in various forms (e.g. counters, number The student exhibits no major errors or omissions. cards). 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given a prompt of a number line, students will state 2.0 processes as the student: the name of a given number.  recognizes numbers from 0 – 10 (e.g., numeric order) However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 6 Strand: Number Sense and Operations Topic: Numbers and Equivalent Representations Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  On a number line, student places markers on 3.0  read, write (in standard form), compare and order numbers from 0 – appropriate numbers to indicate understanding. (what 100 are they marking, what sort of understanding?? Be  recognize ordinal positions first through tenth more specific.) The student exhibits no major errors or omissions.  Students form a physical line using ten students and are able to verbalize the an indicated position. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given a picture with 5 objects, students can verbalize 2.0 processes as the student: which object is in first, second, third position etc.  reads, writes, compares and orders numbers from 0-50   identifies ordinal positions first through fifth  recognizes or recalls basic terminology such as: o ordinal position However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 7 Strand: Number Sense and Operations Topic: Numbers and Equivalent Representations Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  On a number line labeled 50 – 70 (maybe increase 3.0  read, write, compare and order numbers 0 – 999 numbers b/c the element says 0-999), circle one  use ordinal position first through twentieth number and have students identify what number comes The student exhibits no major errors or omissions. before the circled number.  Students will be given a task of putting 20 objects in a row and writing the ordinal position under each. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:   reads, writes, compares and orders numbers 0-500  uses ordinal position first through twelfth  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Number Sense and Operations Topic: Numbers and Equivalent Representations Grade: Three

Ravalli-Mathematics K-8 Version 2 Page 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students are given a number (e.g., 0-9,999) in 3.0  read, write, compare and order numbers in expanded form and their standard form and the students write it in word form. word forms from 0 – 9,999 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Students are given a number (e.g., 0-999) in standard  read, write, compare and order numbers in expanded form and their form and the students write it in word form. word forms from 0-999  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Do you want this rubric??

Strand: Number Sense and Operations Topic: Numbers and Equivalent Representations

Ravalli-Mathematics K-8 Version 2 Page 9 Grade: fourth Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Students are given a number (e.g., 999,999) in 3.0  Read, write, compare and order numbers in expanded form and their standard form and the students write it in word form. word forms from 0 – 999,999  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Students are given a number (e.g., 9,999) in standard  read, write, compare and order numbers in expanded form and their form and the students write it in word form. word forms from 9,999   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 10 Counting

Ravalli-Mathematics K-8 Version 2 Page 11 Strand: Number Sense and Operations Topic: Counting Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Verbally count to 20 while moving counters. 3.0  count to 20 by demonstrating one-to-one correspondence using counters The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Verbally count to 10 while moving counters. 2.0 processes as the student:  counts to 10 by demonstrating one-to-one correspondence using counters However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 12 Strand: Number Sense and Operations Topic: Counting Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Verbally count to 100 by 2’s. 3.0  use number patterns and models to count by 2’s, 5’s, and 10’s to 100 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Verbally count to 50 by 5’s. 2.0 processes as the student:  uses number patterns and models to count by 2’s, 5’s, and 10’s to 50  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 13 Strand: Number Sense and Operations Topic: Counting Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Identify missing numbers on a number line. 3.0  use number patterns to skip count (skip count by what and to what number?? Be more specific to differentiate from grade 1) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 14 Strand: Number Sense and Operations Topic: Counting Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve by using repeated addition: 3.0  use multiplication and division as repeated addition or subtraction 3 x 2 = and 2 + 2 + 2 = The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Solve by using repeated addition with counters: 2.0 processes as the student: 3 x 2 = and 2 + 2 + 2 =  models multiplication and division as repeated addition or subtraction  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 15 Addition/Subtraction

Ravalli-Mathematics K-8 Version 2 Page 16 Strand: Number Sense and Operations Topic: Addition/Subtraction Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  10 – 8 = ___ 3.0  add and subtract one- and two- digit numbers without regrouping  Recall 20 out of 40 facts in one minute (e.g., 0+1=1,  solve addition facts using addends 0, 1 and 2 1+1=2, 2+2=4, etc.). The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Circle the correct answer: 8 or 5 2.0 processes as the student:  add and subtract one digit numbers without regrouping 7 - ____ = 2  solves addition facts using addends 0 and 1  recognizes or recalls basic terminology such as:  Recall 15 out of 40 facts in one minute (e.g., o 0+1=1, 1+1=2, etc.). However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Number Sense and Operations

Ravalli-Mathematics K-8 Version 2 Page 17 Topic: Addition/Subtraction Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 23+28=51 3.0  add and subtract two and three digit numbers with and without  Recall 40 addition and subtraction facts in one regrouping minute.  solve addition and subtraction facts using all addends The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Circle the correct answer: 28 or 34 2.0 processes as the student:  add and subtract 2 digit numbers with or without regrouping 23 + _____ = 51  solves addition and subtraction facts using addends 3s, 4s and 5s  recognizes or recalls basic terminology such as:  Recall 20 out of 40 addition and subtraction facts in o one minute. However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 18 Strand: Number Sense and Operations Topic: Addition/Subtraction Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 699-234= 465 3.0  add and subtract three and four-digit whole and monetary numbers Solve: 7403 + 271 = 7674 with and without regrouping The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Solve : 422-311=111 2.0 processes as the student:  add and subtract three digit whole and monetary numbers without regrouping  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 19 Multiplication/Division

Ravalli-Mathematics K-8 Version 2 Page 20 Strand: Number Sense and Operations Topic: Multiplication/Division Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Recall 20 multiplication facts in one minute (e.g., 3.0  solve multiplication facts with products to 81 (e.g.,1s-9s)) 1*4, 3*3, 7*6, 9*9) The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Recall 10 facts in one minute (e.g., 1*5, 2*5, 5*5). 2.0 processes as the student:  solves multiplication facts (e.g., 1s,2s,5s)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 21 Strand: Number Sense and Operations Topic: Topic: Multiplication/Division Grade: Four Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 37 x 4 = 148 3.0  multiply and divide multi-digit numbers by a one-digit whole number with regrouping  use multiplication and corresponding division facts (products to 144, (1s-12s)) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and Solve: 9/4=2 R1 2.0 processes as the student:  multiplies and divides, with remainders, one digit by one digit numbers  identifies multiplication and corresponding division facts (products to 81)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 22 Strand: Number Sense and Operations Topic: Multiplication/Division Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 25 x 12 = 3.0  perform double digit (2-digit by 2-digit) multiplication and division  Solve: 78 13 = The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Solve: 25 x 6 =  multiplies and divides 2-digit by one digit numbers  Solve: 48÷3 =  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 23 Strand: Number Sense and Operations Topic: Multiplication/Division Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve: 3.0  divide numbers with decimals (up to the thousandths place)  849.875 ÷ 106.25 = The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student: Solve :  divides numbers with decimals (up to the hundredths place)  123.25÷11.34 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 24 Strand: Number Sense and Operations Topic: Multiplication/Division Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Evaluate the following numbers: 3.0  multiply up to four digits with decimals 83.4 x 8 = The student exhibits no major errors or omissions. Answer: 667.2 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student: Did we reverse these two (6 and 7) rubrics?  multiplies up to two digits with decimals  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 25 Strand: Number Sense and Operations Topic: Multiplication/Division Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Solve: 3.0  solve using order of operations 2 (18) – 1 + 3 ÷ 2 = The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  ask students to list the steps of the order of 2.0 processes as the student: operations  recognizes or recalls the steps to the order of operations  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 26 Fractions, Decimals, and Percents

Ravalli-Mathematics K-8 Version 2 Page 27 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given pictures of whole and part objects, ask the 3.0  distinguish between parts of and whole objects student to circle the whole objects and to place a The student exhibits no major errors or omissions. square around the part objects. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  ask the student to produce or identify definitions to  given terms  recognizes or recalls basic terminology such as: o whole, part However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 28 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Shade in ½ of the following rectangle. (where’s the 3.0  use the unit fractions1/2, 1/3, 1/6, 1/8 and ¼ as equal parts of a whole rectangle?) or sets of objects could we model these fractions at this grade level?  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 29 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Shade in 1/3 of a rectangle. 3.0  use all unit fractions as equal parts of a whole or sets of objects

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Tell how many parts are shaded.  use the unit fractions1/2, 1/3, 1/6, 1/8 and ¼ as equal parts of a whole or sets of objects could we model these fractions at this grade level?

 recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 30 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: Four Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 5/8+1/8= 6/8 3.0  add and subtract fractions with like denominators using models and drawings

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Circle the fractions with like denominators:  recognizes fractions with like denominators using models and drawings a) 4/12  recognizes or recalls basic terminology such as: b) 5/12 o c) ¾ However, the student exhibits major errors or omissions regarding the more d) 2/6 complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 31 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 7/8 – ½ = (7/8 – ½ = 3/8) 3.0  add, subtract, multiply and divide fractions with like and unlike denominators The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Solve: 8/12 – 3/12 = 2.0 processes as the student:  add, subtract, multiply and divide fractions with like denominators  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 32 Strand: Number Sense and Operations Topic: Fractions, Percents and Decimals Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Order the following from least to greatest part of the 3.0  order fractions, decimals, and percents unit. 1.1, 7/10, 99% (7/10, 99%, 1.1) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Which ordered pair is correct?  recognizes equivalent fractions, decimals and percents a) .3 35% 4/5  recognizes or recalls basic terminology such as: b) .9 30% 1/2 o c) .7 80% 1/10 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 33 Strand: Number Sense and Operations Topic: Fractions, Decimals and Percents Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  .84 = 21/25 .006=3/500 34% = 17/50 3.0  write fractions and decimals as percents in simplest form  write percents as fractions and decimals in simplest form The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Match the following:  recognizes examples of fractions and decimals as percents in simplest 1. .84 A. 3/500 form 2. 34% B. 21/25  recognizes examples of percents as fractions and decimals in simplest 3. .006 C. 17/50 form  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 34 Strand: Number Sense and Operations Topic: Fractions, Decimals and Percents Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: Five is what percent of 8?  3.0  use percent proportion to solve problems 5/8 = P/100 5x100=8 x P 500 = 8P The student exhibits no major errors or omissions. 500/8 = 8P/8 62.5 = P So, 5 is 62.5% of 8

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   use percent proportion to solve simple problems (give an example of a basic or introductory problem using this skill)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 35 Ratio and Proportion

Ravalli-Mathematics K-8 Version 2 Page 36 Strand: Number Sense and Operations Topic: Ratios and Proportion Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Simplify the following ratio: 5 kg to 30 kg 3.0  write and apply ratios in mathematical and practical problems 1/6 or 1:6 involving measurement and monetary conversions The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes ratios in mathematical and practical problems  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 37 Strand: Number Sense and Operations Topic: Ratio and Proportions Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Determine whether the following ratios and 3.0  solve equations with ratios and proportions proportions are equivalent. 6:8 and 36:48? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   solves simple equations with ratio and proportion (please give example of a basic or introductory type problem)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 38 Strand: Number Sense and Operations Topic: Ratio and Proportions Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  a/25 = 52/100 a x 100 = 25 x 52 100a/100 = 3.0  use ratios and proportions to solve practical problems 1300/100 a = 13 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   use ration and proportion to solve simple practical problems (please give example)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 39 Scientific Notation

Ravalli-Mathematics K-8 Version 2 Page 40 Strand: Number Sense and Operations Topic: Scientific Notation Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  The Mariana Trench is 36,000 feet deep. 3.0  write and evaluate numbers in scientific notation and standard form Write the depth in scientific notation. 3.6 x 104 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Which is greater or = to 1, but less than 10?  recognizes numbers in scientific notation and standard form (same as a) 338x105 grade 7, give examples here to differentiate) b) 19,800  recognizes or recalls basic terminology such as: c) 46,000 o d) 6.98 x 15 e) 7 However, the student exhibits major errors or omissions regarding the more 8.06 x 10 complex ideas and processes. None of the answers is correct!

Ravalli-Mathematics K-8 Version 2 Page 41 Strand: Number Sense and Operations Topic: Scientific Notation Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Taking three scientific notated numbers, order them 3.0  write, evaluate and order numbers in scientific notation and standard from least to greatest. form The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Match the scientific notation with the standard form.  recognizes numbers in scientific notation and standard form (same as grade 6, give examples here to differentiate)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 42 Strand: Number Sense and Operations Topic: Scientific Notation Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  (4x104)+(8x103)+(3x102)+(9x101)+(6x100)= 3.0 In standard form: 48,396  use scientific notation to express numbers in standard form and Students are either given the equation and asked to expanded form (e.g., (4x104)+(8x103)+(3x102)+(9x101)+(6x100)) give the number in standard form or given the number Suggest: simplify complex problems involving scientific notation (e.g., ) and asked to give the equation.

Then you could use simpler examples at the 2.0?

We prefer to put the example in both places because the sample task could always change!

The student exhibits no major errors or omission.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student: Given the following problem: which is the correct  recognizes whether a problem is in standard or expanded form (same as answer? (4x104)+(8x103)+(3x102)+(9x101)+(6x100)= lower grades) Suggest: simplify simple problems involving scientific a) 48,396 4 3 notation (e.g., 2x10 +3x10 ) b) 4,839  recognizes or recalls basic terminology such as: c) 483,960 o The task doesn’t measure the element. The element is

Ravalli-Mathematics K-8 Version 2 Page 43 However, the student exhibits major errors or omissions regarding the more asking the student to identify whether the problem is in complex ideas and processes. standard or expanded. A task for that would look like : label the following as either standard or expanded form We also try to avoid using multiple choice as the 2.0 for a solving element because the student still needs to solve in order to recognize the answer.

Ravalli-Mathematics K-8 Version 2 Page 44 Real Numbers

Ravalli-Mathematics K-8 Version 2 Page 45 Strand: Number Sense and Operations Topic: Real Numbers Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Create a Venn Diagram to compare all of the sets of 3.0  compare numbers in the real number system numbers to which each real number belongs. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Ask the student to list components of the real number  recognizes components of numbers in the real number system system to which a number belongs  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 46 Measurement Units

Ravalli-Mathematics K-8 Version 2 Page 47 Number Sense and Operations Topic: Measurement Units Grade: K Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will be able to match hours with time, inches with 3.0  explain hours, inches, pounds and the situations in which each unit is distance and pounds with weight and give examples of the appropriate best situations to use each measurement The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Students will match hours with time, inches with distance 2.0 processes as the student: and pounds with weight when prompted by a teacher. I.E, “Which one of these would you measure a fish with? How  recognizes examples of the situation in which hours, inches and pounds are would you measure how long until recess?” used  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Ravalli-Mathematics K-8 Version 2 Page 48 Number Sense and Operations Topic: Measurement Units Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will be able to measure the length of a pencil in 3.0  use non-standard, standard and metric units (e.g., length (inches and inches and centimeters. centimeters), time and temperature) The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Students will recognize an inch on a ruler, low and high 2.0 processes as the student: degree on a thermometer and tell time on an analog and digital clock.  recognizes a centimeter and inch on a ruler, a degree on a thermometer and tells time However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 49 Strand: Number Sense and Operations Topic: Measurement Units Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will use a foot, and yard to measure the length of 3.0  measure in standard units (e.g., inches, feet and yards) the bookcase to the nearest whole unit.  measure in metric units (e.g., centimeter, meter)  Students will use a meter to measure the length of the room The student exhibits no major errors or omissions. to the nearest whole unit.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Students show teacher, when given a ruler or a yardstick,  recognizes a foot and yard as a unit of measure what the distance of a foot or a yard is.  describes appropriate situations to use metric units of meter, centimeter and  Students describe situations in which he or she would use a kilometer centimeter, meter or kilometer to measure.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 50 Strand: Number Sense and Operations Topic: Measurement Units Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Measure the length of an identified object using a ruler to 3.0  measure in standard and metric units as a whole and in parts (e.g., ¼, ½ inch) the inch and half-inch. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Students will identify and show one inch and one-half inch 2.0 processes as the student: on a ruler.  recognizes standard and metric units as a whole and in parts  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Strand: Number Sense and Operations Topic: Measurement Units

Ravalli-Mathematics K-8 Version 2 Page 51 Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Provide either metric and standard yard sticks or measuring 3.0  perform conversions within the standard and metric systems to the nearest one- tapes. Have students measure the length and width of the fourth inch or millimeter class room and record the measurements in feet and parts of The student exhibits no major errors or omissions. an inch (1/2 or 1/4) for standard measurement and millimeters, centimeters and meters for metric measurement. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Students will be able to recognize and show one-fourth of 2.0 processes as the student: an inch on a standard ruler and millimeter on a meter stick.  recognizes one-fourth inch and millimeter  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 52 Time and Temperature

Strand: Number Sense and Operations Topic: Time and Temperature Grade: K Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 53 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will name objects that are hot and objects that are 3.0  distinguish between items and events which are hotter and colder cold.  tell time on the hour (on an analog or digital clock?)  Students will tell time on the hour.  order events by time  Students will order a triad of pictures. The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  When presented with a pair of pictures of an item/event 2.0 processes as the student: they will be able to identify the relative temperature.  defines the terms hotter and colder (doesn’t measure element the element asks for a definition,  recognizes the hour hand on a clock not identifying objects that are hotter or colder)  defines the terms first and last  Students identify the hour hand on a clock. However, the student exhibits major errors or omissions regarding the more  Students will order a pair of pictures. (doesn’t measure complex ideas and processes. element, it asks for a definition of first and last)

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 54 Topic: Time and Temperature Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will demonstrate telling time by the hour and the 3.0  tell time on the hour and the half-hour on an analog and digital clock half-hour using an analog and digital clock.  distinguish between hotter and colder on a thermometer  When a student is given a thermometer he/she will be able The student exhibits no major errors or omissions. to identify if it is hot or cold.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  When given several analog pictures, the student will be  recognizes the hour hand/position and the minute hand/position on an analog able to match them correctly with the digital time to the and digital clock hour and the half-hour.  identifies the terms: thermometer, hotter, colder  When a student is given several seasonal pictures he/she However, the student exhibits major errors or omissions regarding the more will be able to match the picture with the thermometer. complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Number Sense and Operations Topic: Time and Temperature Grade: 2 Ravalli-Mathematics K-8 Version 2 Page 55 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will demonstrate telling time by the hour, half- 3.0  tell time on the hour, half-hour and quarter hour (on analog and digital clocks) hour and quarter hour using an analog and digital clock.  state the temperature in Fahrenheit on a thermometer  When a student is given a picture of a thermometer, he/she The student exhibits no major errors or omissions. will tell the degree of temperature.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  When given several analog pictures, the students will be 2.0 processes as the student: able to match it correctly with the digital time to the hour,  recognizes the hour hand and the minute hand on an analog and digital clock half-hour and quarter hour. (same element in grade 1)  When a student is given several seasonal pictures, he/she  identifies the terms: thermometer Fahrenheit scale and degree will be able to match the picture with the Farenheit scale in However, the student exhibits major errors or omissions regarding the more degrees. complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Number Sense and Operations Topic: Time and Temperature Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught. 

Ravalli-Mathematics K-8 Version 2 Page 56 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success.

Score The student will:  Read the temperature on a thermometer in Celsius. 3.0 Identify on a thermometer degrees, Fahrenheit and Celsius The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content

Score There are no major errors or omissions regarding the simpler details and processes as the  When a student is given several seasonal pictures, he/she 2.0 student: will be able to match the picture with the Farenheit scale in  identifies the terms: thermometer Fahrenheit scale and degree degrees.   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content

Score With help, a partial understanding of some of the simpler details and processes and some of the more 1.0 complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Place Value

Ravalli-Mathematics K-8 Version 2 Page 57 Strand: Number Sense and Operations Topic: Place Value Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 58 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Children work with a partner to make groups of 10, 3.0  recognize the value of 2-digit numbers (1s and 10s) using objects that stack easily such as, blocks, books, The student exhibits no major errors or omissions. and boxes. (not sure how this measures the element)  Students are given a 2-digit number and are able to tell the position of the digit and its value. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 59 Strand: Number Sense and Operations Topic: Place Value Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given the number 127, ask students to tell the value 3.0  determine place value positions of a given digit in the 1’s, 10’s and of the tens place? Ones place? 100’s The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:  determines place value positions of a given digit in the 1s and 10s  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 60 Strand: Number Sense and Operations Topic: Place Value Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given the number 106,543, ask students to tell the 3.0  determine place value positions of a given digit in the 1’s, 10’s, 100’s, value of the hundred thousand’s place? 1000’s place? 1000’s, 10,000’s and 100,000’s 100’splace? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given the number 7, 345, determine the value of 2.0 processes as the student: thousand’s place.  determine place value up to 1000’s  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 61 Strand: Number Sense and Operations Topic: Place Value Grade: Four Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given the number 1,256,643, ask students to tell the 3.0  determine place value positions of whole numbers to one million digit of the Millions, Hundred Thousands, Ten The student exhibits no major errors or omissions. Thousands? Thousands place? Tens place? Ones place? 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  What is the place value of 6 in the following number:  recognize place value positions of whole numbers to one million 56,643  recognizes or recalls basic terminology such as: a) Tens o b) Ones However, the student exhibits major errors or omissions regarding the more c) thousands complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 62 Strand: Number Sense and Operations Topic: Place Value Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given the number 56.643, ask students to tell the 3.0  determine place value positions of whole numbers and decimals to digit in the Thousandths, Hundredths place? Tenths thousandths place? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Given the number 43.56, ask students to identify the  recognizes place value positions of whole numbers and decimals to place value of 6. thousandths  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 63 Topic: Place Value Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given the number 5.6643, ask students to tell the 3.0  determine place value positions of millions to millionths digit in the Ten Thousandths? Thousandths place? The student exhibits no major errors or omissions. Tenths place? bump up the task to match the expectationof the element 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Identify the following place value: 3,785 2,325 2.0 processes as the student:  recognizes place value positions to ten thousandths  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 64 Algebraic and Functional Reasoning

Ravalli-Mathematics K-8 Version 2 Page 65 Properties

Ravalli-Mathematics K-8 Version 2 Page 66 Strand: Algebraic and Functional Reasoning Topic: Properties Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 7(3+2) = 35 3.0  solve simple problems using the Distributive Property  Tell what property is used in the following problem:  use order of operations to evaluate expressions and solve one-step 47 + (89 + 13) equations (can these really be done together, doesn’t order of operations imply more than one step?) They will be asked to solve in another topic The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Circle the problems that show the Distributive  recognizes examples of simple problems that use the Distributive Property: Property a) 5(4+7) =  recognizes or recalls basic terminology such as: b) 2 x 3 = o Distributive Property c) 5 + 7 = However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated.

Ravalli-Mathematics K-8 Version 2 Page 67 0.0 Strand: Algebraic and Functional Reasoning Topic: Properties Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Which property is used in the following equation? 3.0  use the following properties: Commutative Property of Addition and 6(9+3) = 6(9) + 6(3) (Distributive Property) Multiplication, Associative Property of Addition and Multiplication, Additive (this is not measuring “using,” more of an and Multiplicative Identity, Multiplicative Property of Zero, Distributive Property identifying task) Write a task that asks the student The student exhibits no major errors or omissions. to simply and equation using the properties 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Match the following:  recognizes the following properties: Commutative Property of Addition and 1. 6(9+3) = 6(9) + 6(3) a. Associative Property Multiplication, Associative Property of Addition and Multiplication, Additive 2. 6 + (2+7) = (6+2) +7 b. Distributive Property and Multiplicative Identity, Multiplicative Property of Zero, Distributive Property  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 68 Strand: Algebraic and Functional Reasoning Topic: Properties Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: 2 + (5 +10) = (2+ 5) + ____ 3.0  use Associative, Commutative, and Distributive Properties to simplify  Solve: 3 + 5 + 7 = 7 + 5 + 3 algebraic expressions (same as grade 7??) You can use more complex  Solve: 5 (x + 3) = problems as an example to differentiate between 7 and 8 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  State which of Name the following problems is the as 2.0 processes as the student: Associative, Communicative, or Distributive  recognizes the Associative, Commutative, and Distributive Properties Properties: (same as grade 7) a. 2 + (5 +10) = (2+ 5) + ____  recognizes or recalls basic terminology such as: b. 3 + 5 + 7 = 7 + 5 + 3 o c. 5 (x + 3) = However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated 0.0

Ravalli-Mathematics K-8 Version 2 Page 69 Symbols and Expressions

Ravalli-Mathematics K-8 Version 2 Page 70 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a set of manipulatives, break them into two 3.0  create sets of objects with unequal amounts, describing them as greater groups with different number in each group. than or less than Describe each set as greater than or less than. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given two groups of objects, student will point 2.0 processes as the student: to the group that is greater than.  recognizes sets of objects with unequal amounts, describing them as greater than or less than  recognizes or recalls basic terminology such as: o “greater than” o “less than” However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 71 Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a set of manipulatives, break them into two 3.0  create and describe sets of objects as greater than, less than, or equal to groups with different number in each group. The student exhibits no major errors or omissions. Describe each set as greater than, less than, or equal to. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given two groups of objects, student will 2.0 processes as the student: describe the group that is greater than, less  recognizes group of objects that is greater than, less than, or equal to another than or equal to. group  recognizes or recalls basic terminology such as: o “greater than” o “less than” o “equal to” However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 72 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given two sets of objects, write a number sentence 3.0  represent mathematical situations using numbers, symbols, and words describing the relationship between the two sets. The student exhibits no major errors or omissions. Example: There are 20 pencils in one group and 13 pencils in the second group. (20 13). 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  completes number sentences with appropriate words and symbols (+, -, and =)  7 ⬚ 4  recognizes or recalls basic terminology such as: o “greater than”, “less than”, “equal to” However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 73 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  complete multi-digit number sentences with appropriate words and symbols (+, - , =,  72 + 38 ⬚ 49 + 28 The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  completes 1 digit number sentences with appropriate words and symbols (+, - , =,  7 + 3 = ⬚, 4 + 2 = ⬚; therefore, 7 + 3 ⬚ 4 + 2  recognizes or recalls basic terminology such as: o “greater than”, “less than”, “equal to”, etc. However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 74 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Four Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  complete multi-digit and multi-operation number sentences with appropriate words and symbols (+, - , =, ) The student exhibits no major errors or omissions.  78 + (15 – 10) ⬚ ( 15 – 10) + 78

 ¾ ⬚ 5/8

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  15 – 10 = ___, 78 + 5 = ___;  completes multi-digit number sentences with appropriate words and symbols (+, - , =, )  recognizes or recalls basic terminology such as: o “greater than”, “less than”, “equal to”, etc. o Parenthesis means “perform this operation first” However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Ravalli-Mathematics K-8 Version 2 Page 75 Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Ravalli-Mathematics K-8 Version 2 Page 76 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  complete number sentences including negative numbers with the  - 8 1 appropriate words and symbols including ≠, ≥, ≤ The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Match a symbol with the appropriate terms. 2.0 processes as the student:  complete number sentences with appropriate words and symbols including ≠, ≥, ≤ recognize or recalls basic terminology such as: o Not equal to, greater than or equal to, less than or equal to However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 77 Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using a word problem, write a simple equation, such 3.0  write expressions and equations using variables to represent as ¼ x = 2/3. Can you give an example of the word mathematical situations problem? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Identify the variable: 2.0 processes as the student: 1/4 x = 2/3 Variable is “x”.  identifies the variables in simple expressions and equations Suggest:  writes simple equations and expressions using variables to represent mathematical situations (please provide example) or writes an equation from a number sentence  recognizes or recalls basic terminology such as: o Variable, expressions, equations However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Algebraic and Functional Reasoning Ravalli-Mathematics K-8 Version 2 Page 78 Topic: Symbols and Expressions Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Write and solve 2 examples of an algebraic 3.0  simplify complex algebraic expressions by combining like terms expression. The student exhibits no major errors or omissions.  Write and solve 2 examples that are not algebraic expressions.  Simplify the following number sentence: 4x2 + 3y + 2x2 + 2xy + 6y - xy 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Combine the following like terms: 2.0 processes as the student:  simplifies simple algebraic expressions 2 x + 3 b + 5 x + 2 b = ( Answer: 7x + 5 b)  recognizes or recalls basic terminology such as: o Like terms However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Algebraic and Functional Reasoning Topic: Symbols and Expressions

Ravalli-Mathematics K-8 Version 2 Page 79 Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Solve: (2y + 5) – (y + 8) 3.0  add and subtract polynomials Does this belong in symbols and expressions? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  1  determines if each expression is a polynomial 5 a2 , x2 + 9  recognizes or recalls basic terminology such as: o Polynomial However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 80 Equations

Ravalli-Mathematics K-8 Version 2 Page 81 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using picture representation, 3 ducks in a box + 3.0  recognize that unknowns, in an addition or subtraction equations, empty box = 5 ducks in a box. How many ducks represent a missing value that will make the statement true (suggest: should there be in the empty box? (Student draws solve simple equations using picture representation) two ducks in the box.) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Using picture representation, 5 dogs in a box - empty 2.0 processes as the student: box = 2 dogs in a box. How many dogs should there  recognizes accurate statements about and examples of unknowns in be in the empty box? (3 dogs in a box, 7 dogs in a equations box)  recognizes or recalls basic terminology such as: o Addition and subtraction symbols  Students identify the variables in a given equation However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 82 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  identify missing operations or missing numbers in completes open  5 5 = 10 number sentences, involving number facts in addition and subtraction, with missing operations or numbers The student exhibits no major errors or omissions.  13 - ⬚ = 8

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  5 5 = 10 Choose from + or - .  selects missing symbols or numbers from multiple choices to complete open number sentences involving addition and subtraction  recognizes or recalls basic terminology such as:  13 - ⬚ = 8 Choose from 5 or 21. o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 83 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  solve open number sentences involving addition, subtraction, and  9 x 5 = n multiplication  n + 40 = 90 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  46 – 13 = n  selects missing symbols or numbers from multiple choices to complete open number sentences  recognizes or recalls basic terminology such as: However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 84 Strand: Algebraic and Functional Reasoning

Topic: Equations Grade: Four Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  The sum of Jana’s age and Kristen’s age is 17. Kristen is one 3.0  solve multiplication and division word problems containing variables year older than Jana. What number represents the product of The student exhibits no major errors or omissions. their ages? (72)  In six years, Alan will be three times as old as he is now. How old will Alan be in six years? (9 years old) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  When n = 7, solve the problems. 2.0 processes as the student: 62 – n  solves multiplication and division expressions containing variables n + (n + 2)  recognizes or recalls basic terminology such as: o product However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and 1.0 some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Ravalli-Mathematics K-8 Version 2 Page 85 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond what was Sample Tasks 4.0 taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  find solutions for equations that contain an unknown number or variable  Find the values of y to complete each table. using whole numbers as a replacement set y = x - 1 The student exhibits no major errors or omissions. x y -1 -2 0 -1 +2 +1 +3 +2 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and processes as 2.0 the student:  x ÷ 8 = 2  selects from multiple choices, the number that would correctly complete the x = 14, x = 16, x = 18 equation  recognizes or recalls basic terminology such as: o Variable, replacement set, value However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some 1.0 of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Ravalli-Mathematics K-8 Version 2 Page 86 0.0

Ravalli-Mathematics K-8 Version 2 Page 87 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  graph simple inequalities with one variable on a number line  3p 27. Graph your answer.  evaluate formulas and algebraic expressions using whole numbers  4x = 24 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  recognizes simple inequalities with one variable  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 88 Strand: Algebraic and Functional Reasoning Topic: Equations Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Thirty two is twice the number increased by eight. 3.0  write algebraic equations/expressions from word problems This is the (32 = 2a + 8) same as symbols and expressions 6th grade. We think it belongs here The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Thirty two is twice the number increased by eight. 2.0 processes as the student: Which is the correct equation represented by this word  recognizes correct algebraic equations/expressions from word problem? problems a. 32 = 8a + 2  recognizes or recalls basic terminology such as: b. 32 = 2a – 8 o c. 32 = 2a + 8 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Algebraic and Functional Reasoning

Ravalli-Mathematics K-8 Version 2 Page 89 Topic: Equations Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  translate verbal sentences into equations (basically the same as grade 7  Write 14 is 12 less than twice the value of x as an and 6th grade symbols and expressions) equation. (14 = 2x – 12) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  14 = 2x – 12, x = 2.0 processes as the student: a. 11  recognizes the correct solution for verbal sentences and equations with b. 13 multiple steps c. 15  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 90 Functions and Relationships

Ravalli-Mathematics K-8 Version 2 Page 91 Strand: Algebraic and Functional Reasoning Topic: Functions and Relationships Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Evaluate a function table to determine a set of 3.0  determine functions from information in tables, sets of ordered pairs, ordered pairs. equations, graphs, and mappings The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   plots ordered pairs  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 92 Strand: Algebraic and Functional Reasoning Topic: Functions and Relationships Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: If you earn $5 per week, make a function table that shows your total earnings 3.0  create an input/output table Make this one more complicated and use a after weeks 1, 2, 3 and 4. simpler version at the 2.0 This task seems to be on the simple side and Input Function Rule Output would make a better 2.0 Week # Multiply by 5 Total Earning The student exhibits no major errors or omissions. 1 1 x 5 2 2 x 5 3 3 x 5 4 4 x 5

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   completes in simple input/output table  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0

Ravalli-Mathematics K-8 Version 2 Page 93 Strand: Algebraic and Functional Reasoning Topic: Functions and Relationships Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Find three solutions: 3.0  find possible solutions that satisfy the given function 2x + 3y = 14 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   finds possible solutions that satisfy a given simple function (need example)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 94 Linear and Non-Linear Equations

Ravalli-Mathematics K-8 Version 2 Page 95 Strand: Algebraic and Functional Reasoning Topic: Linear and Non-Linear Equations Grade: Six Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Graph a set of ordered pairs to determine if the set is 3.0  evaluate a function table to determine linear or non-linear equations linear or non-linear. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given multiple graphs, ask students to identify which 2.0 processes as the student: have ordered pairs that are linear and non-linear.  recognizes graphs with linear and non-linear ordered pairs  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 96 Strand: Algebraic and Functional Reasoning Topic: Linear and Non-Linear Equations Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Model the steps required to solve a two-step linear 3.0  evaluate various one and two step linear equations, algebraic equation with whole number coefficients. expressions, and inequalities The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given a simple, one step, linear equation, ask students 2.0 processes as the student: to solve.  solves simple, one step, linear equations, algebraic expressions and inequalities  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 97 Strand: Algebraic and Functional Reasoning Topic: Linear and Non-Linear Equations Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Model steps to solve multi-step linear and non-linear 3.0  evaluate various linear and non-linear equations (with integer equations. coefficients and solutions) and algebraic expressions (given integer values for variables) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:  solves, one step, linear and non-linear equations and algebraic expressions  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 98 Inequalities

Ravalli-Mathematics K-8 Version 2 Page 99 Strand: Algebraic and Functional Reasoning Topic: Inequalities Grade: Seven Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will: 3.0  write solves equations and inequalities to represent relationships (task  2x + 8 24 What does x equal? (x 8) changes this to solves) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   solves simple equations and inequalities (give examples)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 100 Strand: Algebraic and Functional Reasoning Topic: Inequalities Grade: Eight Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  x/-3 4 3.0  solve inequalities by using the Addition, Subtraction, Multiplication, or -3(x/-3) ≥ -3(4) Division Properties of Inequalities with positive and negative numbers x ≥ -12 The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Ask the student to list the Addition, Subtraction,  recognizes or recalls the Addition, Subtraction, Multiplication, or Multiplication, or Division Properties of Inequalities Division Properties of Inequalities  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 101 Patterns

Ravalli-Mathematics K-8 Version 2 Page 102 Strand: Algebraic and Functional Reasoning Topic: Patterns Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using unifix cubes or pattern blocks, student makes a 3.0  create simple repeating patterns using objects or manipulatives pattern that repeats three times. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Using unifix cubes or pattern blocks, student copies a 2.0 processes as the student: teacher made pattern that repeats three times.  reproduces a simple repeating pattern using objects or manipulatives  recognizes or recalls basic terminology such as: o Pattern However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 103 Strand: Algebraic and Functional Reasoning Topic: Patterns Grade: One Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using unifix cubes or pattern blocks, student makes a 3.0  create growing patterns using symbols, objects or manipulatives pattern that increases. Example: 1 blue, 1 red, 2 The student exhibits no major errors or omissions. blue, 2 red, 3 blue, 3 red, etc. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Using unifix cubes or pattern blocks, student copies a 2.0 processes as the student: teacher-made pattern that increases. Example: 1 blue,  reproduces growing patterns using symbols, objects or manipulatives 1 red, 2 blue, 2 red, 3 blue, 3 red, etc.  recognizes or recalls basic terminology such as: o pattern However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 104 Strand: Algebraic and Functional Reasoning Topic: Patterns Grade: Two Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  On a calendar, predict upcoming odd and even 3.0  predict next item in a pattern using objects and numbers found in tables numbers. (how can you predict with a calendar? Is and number charts this supposed to be a blank calendar?) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  On a calendar, identify the even numbers. 2.0 processes as the student:  recognizes patterns using objects and numbers found in tables and number charts  recognizes or recalls basic terminology such as: o Odd numbers, even numbers However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 105 Strand: Algebraic and Functional Reasoning Topic: Patterns Grade: Three Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a series of numbers, explain the pattern or 3.0  explain patterns and relationships in the number system, including relationship of the numbers within the set. (Ex: 3, 6, arithmetic or geometric sequences 9, 12, 15, 18, Rule—plus 3) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  On a hundreds chart, highlight all the numbers that 2.0 processes as the student: are multiples of three.  recognizes patterns or relationships in the number system, including arithmetic or geometric sequences  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 106 Strand: Algebraic and Functional Reasoning

Topic: Patterns

Grade: Four

Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Name the next two x terms and the next two y 3.0  use patterns to solve problems terms in the pattern (12, 14; 6, 7) The student exhibits no major errors or omissions.

x 2 4 6 8 10 y 1 2 3 4 5

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Name the next two x terms and the next two y terms  recognizes missing numbers in a pattern used to solve a problem in the pattern.  recognizes or recalls basic terminology such as: x 2 4 6 8 10 12 o y 1 2 3 4 5 7 However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 107 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Strand: Algebraic and Functional Reasoning Topic: Patterns Grade: Five Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  What are the next two numbers in the sequence? 3.0  dDescribe or represent patterns and relationships in a number system Describe the sequence. 1, 4, 2, 8, 4, 16, 8,?, ? The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  What are the next two numbers in the sequence? 2.0 processes as the student:  recognizes patterns and relationships in a number system 1, 4, 2, 8, 4, 16, 8,?, ?  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 108 Geometric Reasoning

Ravalli-Mathematics K-8 Version 2 Page 109 Geometric Figures

Ravalli-Mathematics K-8 Version 2 Page 110 Strand: Geometric Reasoning Topic: Geometric Figures Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Recall the names of shapes when provided pictures. 3.0  name shapes to include circle, square, triangle and rectangle  Relate geometric shapes to real world objects. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Point to provided shapes when prompted. 2.0 processes as the student:  recognizes the shapes o circle, square, triangle and rectangle However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 111 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Create a picture using at least one of each shape and 3.0  draw and describe circle, square, triangle and rectangle describe the characteristics of the shape.  recall examples of a diamond, oval, heart and star  Relate geometric figures to real world objects. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Ask the student to match the name to the shape 2.0 processes as the student:  recognizes examples of basic shapes (e.g., circle, square, triangle and rectangle diamond, oval, heart and star, )  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 112 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using the net of a solid figure, trace and label the two- 3.0  describe the difference between solid and plane figures dimensional shapes. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   identifies solid and plane figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 113 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using a geo-board create a triangle. 3.0  describe and model two-dimensional shapes (polygons, circles, and quadrilaterals) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Using cut out manipulatives, sort shapes into specific  classify two-dimensional shapes (polygons, circles, and quadrilaterals) sets. However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 114 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Chart the edges, sides and vertices of three- 3.0  describe and model three-dimensional shapes (spheres, cones, cube, dimensional figures. cylinder, pyramid and prism)  Create a net that can be folded to make a cube, prism, The student exhibits no major errors or omissions. cone, cylinder or pyramid. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Out of a mixed group of 3-demensional shapes  classify three-dimensional shapes (spheres, cones, cube, cylinder, categorize them by number of faces. pyramid and prism) However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 115 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Use a protractor to determine and label a set of angles. 3.0  construct different types of triangles to include right, obtuse, acute, Upon determination also label them as scalene, scalene, equilateral, and isosceles equilateral, or isosceles. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Label a given set of triangles as right, obtuse, acute,  identifies different types of triangles (right, obtuse, acute, scalene, scalene, isosceles, and equilateral. equilateral and isosceles)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 116 Strand: Geometric Reasoning Topic: Geometric Figures Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using solid figures classify two- and three- 3.0  classify two- and three-dimensional figures based on attributes, dimensional figures into appropriate sets. properties and component parts (to include different kinds of triangles)  Draw quadrilaterals and triangles based on given information (this could be a 2.0 element) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Geometric Figures Ravalli-Mathematics K-8 Version 2 Page 117 Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Explain and exemplify how a two-dimensional figure 3.0  analyze geometric relationships between two and three dimensional is a representation of a three-dimensional object. objects

The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   describes characteristics of two and three dimensional objects  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Geometric Figures Grade: 8

Ravalli-Mathematics K-8 Version 2 Page 118 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Explain and model the steps required to construct an 3.0  construct polygons, angles, angle bisectors, perpendicular bisectors, angle bisector. segments and lines The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes polygons, angles, angle bisectors, perpendicular bisectors, segments and lines  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Congruence and Symmetry

Ravalli-Mathematics K-8 Version 2 Page 119 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  3.0  find two equal sets of objects in different spatial arrangements (using objects that are both identical and non-identical) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes like (identical) objects  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 120 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  ask the student to identify objects in the classroom or 3.0  find real life examples of line symmetry school that exhibit line symmetry (e.g., chalkboard, The student exhibits no major errors or omissions. window, etc.) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  ask the student to identify the line of symmetry in  recognizes lines of symmetry on given objects teacher provided objects  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning

Ravalli-Mathematics K-8 Version 2 Page 121 Topic: Congruence and Symmetry Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  3.0  find congruent figures, angles, and line segments in real life situations The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes, from a picture, congruent figures, angles, and line segment  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 122 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Draw the lines of symmetry on a triangle. 3.0  explain basic distinctions between lines of symmetry in triangles, squares, and rectangles, such as number of lines, location of lines  draw a shape that is congruent and similar to another The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Given multiple sets of shapes determine which are  recognizes shapes with lines of symmetry congruent.  recognizes shapes that are congruent and similar  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 123 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Put in examples 3.0  show lines of symmetry of complex figures  describe how to determine whether two quadrilaterals are congruent The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Put in examples  recognizes examples of shapes that are congruent  show all lines of symmetry of basic shapes recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 124 Topic: Congruence and Symmetry Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using grid paper, students will create congruent 3.0  explain ways in which figures are congruent figures and label congruent lines and angles.  describe and create symmetric figures The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Given multiple sets of figures determine which are congruent. Recalls statements about congruent figures  Recognizes examples of symmetric figures  Recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Ravalli-Mathematics K-8 Version 2 Page 125 Topic: Congruence and Symmetry Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  3.0  classify congruent objects by their properties, and explain the characteristics that make two objects congruent The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls examples of congruent figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 126 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  3.0  graph figures that are similar to other figures The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   draws figures that are similar to other figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 127 Strand: Geometric Reasoning Topic: Congruence and Symmetry Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  3.0  explain and model the steps required to draw a figure that is congruent to one another The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   draws congruent figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 128 Transformations

Ravalli-Mathematics K-8 Version 2 Page 129 Strand: Geometric Reasoning Topic: Transformations Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using pattern blocks perform the transformations 3.0  describe reflections, rotations and translations with squares and triangles when prompted. using pattern blocks The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Label the transformation when shown a picture. 2.0 processes as the student:  recognizes when a square or triangle has been reflected, rotated or translated However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 130 Strand: Geometric Reasoning Topic: Transformations Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Draw a specified transformation when given a plane 3.0  demonstrate reflections, rotations and translations with all plane figures figure. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Given a set of figures label them as translation,  recognizes when a plane figure has been reflected, rotated or translated reflection, or rotation. However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 131 Strand: Geometric Reasoning Topic: Transformations Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Draw and label a specified transformation when given 3.0  show the results of a reflection, rotation or translation of various a complex figure. geometric figures  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Put in example  Recognizes when a complex figure has been reflected, rotated or translated.  However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Ravalli-Mathematics K-8 Version 2 Page 132 Topic: Transformations Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Sketch a prediction of a given reflection, rotation, 3.0  Perform a reflection, rotation or translation of various geometric figures translation from coordinates. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Identify a given picture as either a rotation, translation,  Identify the difference between reflection, rotation or translation of or reflection. various geometric figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Transformations

Ravalli-Mathematics K-8 Version 2 Page 133 Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Sketch a prediction of a given reflection, rotation, 3.0  explain and model the steps required to draw a translation, reflection, translation from coordinates and describe some and rotation of a give shape relationships between both figures. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls accurate statements about and examples of translations, reflections and rotations  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Transformations Grade: 7

Ravalli-Mathematics K-8 Version 2 Page 134 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Explain and model the steps required to graph a 3.0  graph transformations of quadrilaterals on the Cartesian plane by transformation of a given quadrilateral on the plotting vertices Cartesian plane. (switch this to element and element to The student exhibits no major errors or omissions. task) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls accurate statements about and examples of transformations of quadrilaterals However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Transformations Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks Ravalli-Mathematics K-8 Version 2 Page 135 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using a sheet of paper, have students trace the outline 3.0  explain and model the steps required to draw a dilation of a given figure of their body on the paper. Then measure dimensions. The student exhibits no major errors or omissions. Use the information obtained to dilate the outline of the body and re-draw beside the original outline. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls accurate statements about and examples of dilations  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 136 Geometric Properties

Ravalli-Mathematics K-8 Version 2 Page 137 Strand: Geometric Reasoning Topic: Geometric Properties Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using bear manipulatives follow verbal cues asking 3.0  name the position of an place objects relative to a closed figure students to place the bears in appropriate locations. (example: above, below, inside, outside, beside or over) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Ask students “what is above the door,” “what is under 2.0 processes as the student: the chalk board,” etc.  recognizes objects relative to a closed figure  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 138 Strand: Geometric Reasoning Topic: Geometric Properties Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given pictures of triangles, squares and rectangles, 3.0  recognize a side and vertex on simple geometric shapes (triangle, square color the sides red, circle the vertices mauve. and rectangle) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls accurate statements about sides and vertices on simple geometric shapes  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Ravalli-Mathematics K-8 Version 2 Page 139 Topic: Geometric Properties Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Label the sides and vertices of plane figures. 3.0  determine the number of sides and vertices of plane figures  State the number of sides and vertices of a given shape The student exhibits no major errors or omissions. when prompted (written or verbal). 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls accurate statements about sides and vertices of plane figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Geometric Properties Grade: 3

Ravalli-Mathematics K-8 Version 2 Page 140 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Count the number of sides, faces and vertices of a 3.0  determine the number of sides, faces and vertices of solid geometric given solid figure when prompted (written or verbal). figures (cube, rectangular prism, cone, pyramid, triangular prism).  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Count the number of sides on a cube.  Identifies sides, vertices and faces of three dimensional figures (solid geometric figures)   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Geometric Properties Grade: 4 Ravalli-Mathematics K-8 Version 2 Page 141 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Name the geometric solid represented by a net. 3.0 Recognize a given net as a specific geometric solid. 

The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Name the geometric solid represented by a folded net.   recognizes geometric solids o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 142 Strand: Geometric Reasoning Topic: Geometric Properties Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Farmer Jones needs to build a fence that surrounds 3.0  solve practical word problems involving the perimeter and area of his 216 square foot area. Find possible dimensions geometric figures (more specific, give examples of the geometric (length and width) that Farmer Jones’ fence could be. figures to differentiate from 6) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   solves problems involving the perimeter and area of geometric figures  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 143 Score Even with help, no understanding or skill demonstrated. 0.0

Strand: Geometric Reasoning Topic: Geometric Properties Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  A flag pole stands 30 feet tall. The distance from the 3.0  understand and apply geometric theorems such as the Pythagorean top of the flag pole to Bob’s toe’s measures 35 feet. Theorem in word problems Using the Pythagorean Theorem, calculate the The student exhibits no major errors or omissions. distance from the flag pole to Bob. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  find the hypotenuse of a right triangle when side a is 6 2.0 processes as the student: and side b is 4  uses given geometric theorems to solve set up problems  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 144 Strand: Geometric Reasoning Topic: Geometric Properties Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Create charts to show differences in spatial 3.0  recognize and use appropriate vocabulary when dealing with spatial relationships. relationship (2.0??)  Using pictures of buildings, bridges, and objects in the  use geometry as a means of describing the real world classroom, describe what geometric terms apply to the The student exhibits no major errors or omissions. objects. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 145 Length, Area and Volume

Ravalli-Mathematics K-8 Version 2 Page 146 Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: K Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will be able to measure the length of a desk using 3.0  utilize non-standard measurement units to identify length a self designed measurement tool The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Students will be able to identify the correct length of an 2.0 processes as the student: object( in cubes) when presented with a pre-made measurement tool.  recognizes the length of an object using a pre-made measurement tool However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 147 Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will be able to measure the desk length using 3.0  utilize non-standard, standard and metric units (cubes, inches and centimeters) cubes, inches, centimeters. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  When given a picture of an object next to a ruler, a student  recognizes an inch and centimeter on a ruler will be able to tell its length in inches and centimeters.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 148 Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Students will be able to measure the desk length using 3.0  utilize non-standard, standard and metric units (cubes, inches, feet and cubes, inches, feet and centimeters. centimeters) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  When given a picture of an object next to a ruler, a student  recognizes an inch, foot and centimeter on a ruler will be able to tell its length in inches, feet and centimeter.

However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Length, Area, Volume

Ravalli-Mathematics K-8 Version 2 Page 149 Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using grid paper students will count squares to determine 3.0  Find area and perimeter of squares and rectangles. the area of a rectangle.  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   Define area and perimeter.

o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: 4 Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 150 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Find the area of an image of a house. 3.0  Using irregular plane figures calculate the perimeter and area with grid paper.  The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Count squares on grid paper to find the area of a rectangle. 2.0 processes as the student:  find the area and perimeter of a rectangle and square with grid paper  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 151 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given an example of a prism, use the formula to find the 3.0  find the surface area of a prism surface area.  choose the proper unit of measure for volume and weight The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Find the area of each side separately of the given prism. 2.0 processes as the student:  finds the area of the individual sides of 3 dimensional objects

 recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 152 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given an example of a circle, the student will apply the 3.0  find the circumference and area of a circle correct formulas to find the area and circumference of that circle (ex. using pi (3.14)).  Given an example of a circle, the student will apply the correct formulas to find the perimeter and area of that circle. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given the radius, diameter, and pi find the circumference 2.0 processes as the student: and area of a circle.  given dimensions and formulas. calculates the circumference and area of a circle  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Geometric Reasoning Topic: Length, Area, Volume Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 153 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given either an actual object or illustration the student will 3.0  calculate the perimeter and area of irregular polygons use the given measurements to calculate the perimeter and The student exhibits no major errors or omissions. area of each described surface(s). 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given the measurements and formulas on each polyhedral, 2.0 processes as the student: calculate the perimeter and area of each described surface(s).  calculates the area and perimeter of polyhedrals, given measurements and formulas  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 154 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given an example of a specific polyhedron, the student will 3.0  calculate surface area of polyhedrons (ex: cones, pyramids and cylinders) use the correct processes and formulas to calculate the  calculate volume of polyhedrons (ex: cones, pyramids and cylinders) surface area and volume of that object. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Given the dimensions, the student will use the correct 2.0 processes as the student: formula to calculate surface area and volume.  chooses correct formula and calculates surface area and volume of polyhedrons  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 155 Capacity and Weight

Strand: Geometric Reasoning Topic: Capacity and Weight Grade: Kindergarten Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 156 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students will identify if a cup will fit in a box or a thimble. 3.0  recognize an object’s relative capacity by comparing it to a variety of  When students are presented with a picture of a kitten and a containers hoppy (?) they will be able to identify which one would  identify distinguish between representations of lighter and heavier objects weigh more. The student exhibits no major errors or omissions.

2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  When a student compares a jar and a teacup, they can 2.0 processes as the student: identify which holds more.  defines the terms more and less  Students will hold a paper clip and a rock and identify the  identifies between recognizes lighter and heavier objects and objects that hold lighter object. more or less However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Geometric Reasoning Topic: Capacity and Weight Grade: First Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 157 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  When a student is given a glass he/she will be able to 3.0  describe the differences of full or empty explain the difference between full or empty.  distinguish between representations of several objects with different weights  When a student is presented with 3 pictures of objects The student exhibits no major errors or omissions. (paper clip, book, house) he/she will be able to identify their relative weights in order from the lightest to the heaviest. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  When a student looks at a glass he/she will be able to tell if  recognizes examples of a container that is full and empty it is full or empty.  recognizes the heaviest and lightest of several objects  When a student is given a textbook, pencil and a full However, the student exhibits major errors or omissions regarding the more backpack; he/she will be able to tell the order the objects complex ideas and processes. from lightest to heaviest.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Geometric Reasoning Topic: Capacity and Weight Grade: Second Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 158 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  When a student is given a container he/she will be able to 3.0  describe the differences between full, half-full a third full or empty describe what it would look like if it is full, half-full, a third  Identify determine if a container would be measured by cups or gallons full or empty.  weigh an item using customary and non-customary measurements  When a student looks at a container he/she will determine if The student exhibits no major errors or omissions. it is better measured by cups or gallons.  Students will weigh a water bottle and determine if its weight is less than a pound, pound or more than a pound. (how does this relate to customary and non-customary measurements? Measures score 2.0 element more closely) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  When a student looks at a jar he/she will be able to tell if it 2.0 processes as the student: is full, half-full, a third full or empty.  recognizes examples of full, half-full a third full and empty  When a cup or gallon is placed on a table the student will  recognizes a cup or gallon be able to tell if it is a cup or gallon.  recognizes an object’s weight as less than a pound about a pound or more  Students will use pictures of an object on a scale to tell if than a pound an the object is less than a pound, about a pound or more However, the student exhibits major errors or omissions regarding the more than a pound. complex ideas and processes.

1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. Ravalli-Mathematics K-8 Version 2 Page 159 0.0

Ravalli-Mathematics K-8 Version 2 Page 160 Strand: Geometric Reasoning Topic: Capacity and Weight Grade: Third Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will :  Given a variety of objects, students determine how many 3.0  Convert measurements (cups, pints, quarts and gallons) cups, pints, quarts and gallons would be needed to fill the The student exhibits no major errors or omissions. objects (given a gallon jug of milk, how many pints would fill the jug? (answer: 8 pints) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes 1.0 and some of the more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Geometric Reasoning

Ravalli-Mathematics K-8 Version 2 Page 161 Topic: Capacity and Weight Grade: Fourth Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Students demonstrate equal volumes using a variety of 3.0  estimate, measure and investigate capacity and weight measuring tools (ex. Digital scales, various metric and The student exhibits no major errors or omissions. standard volume measures such as a cup, quart or liter). 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Tell how many cups are in a quart. 2.0 processes as the student:  Convert measurements (cups, pints, quarts and gallons)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 162 Topic: Capacity and Weight Grade: Fifth Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a picture of a three dimensional object, use the 3.0  apply concepts of capacity and weight for both standard and metric units provided formula to find volume (ex. V=l*w*h). The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  Weigh different objects in the classroom. 2.0 processes as the student:  Estimate, measure and investigate weight and capacity  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Capacity and Weight Grade: Sixth Ravalli-Mathematics K-8 Version 2 Page 163 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  3.0  Does not apply. Review and use in support of other mathematical operations. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Geometric Reasoning Topic: Capacity and Weight Grade: Seventh Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 164 Score In addition to Score 3.0, in-depth inferences and applications that go beyond  4.0 what was taught. 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  3.0  Does not apply. Review and use in support of other mathematical operations. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and  2.0 processes as the student:   recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 165 Data Analysis

Ravalli-Mathematics K-8 Version 2 Page 166 Data Collection, Organization and Display

Ravalli-Mathematics K-8 Version 2 Page 167 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Group different colored objects by color and describe 3.0  sort real objects into a set the groups that result. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   Sort real objects into sets with help (“with help” is reserved for score 0.5. suggest: describes basic characteristics of given sets)  recognizes or recalls basic terminology such as: o set o sort However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 168 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Ask the students the question: Do you have a dog, cat, 3.0  generate simple question for data collection both or neither. Tally the results. Have the students  create a simple graph with appropriate labels use the results tallied to create a simple graphic The student exhibits no major errors or omissions. display with appropriate labels. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes that “What is your favorite color?” is an example of a simple questions used for data collection. recognizes examples of simple questions used for data collection (e.g., “what is your favorite color?”)  labels a simple graph using terms from a word bank  recognizes or recalls basic terminology such as: o label o graph However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis

Ravalli-Mathematics K-8 Version 2 Page 169 Topic: Data Collection, Organization and Display Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Create and label a bar graph to display the number of 3.0  create and label displays for a given set of data using pictographs, tally students with birthdays from January to June. charts, bar graphs, and Venn diagrams The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   competes a teacher set up pictograph, tally chart, bar graph and Venn diagram  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Data Analysis

Ravalli-Mathematics K-8 Version 2 Page 170 Topic: Data Collection, Organization and Display Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given random information about two sisters, students 3.0  collect and organize data using bar graphs and diagrams will create a Venn Diagram about two sisters The student exhibits no major errors or omissions. differences and commonalities. The task should ask the student to collect data and create a bar graph or diagram 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   Put data on a provided graph  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 171 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Explain and model (Tally-chart) how to record the 3.0  collect, organize, and display data using line graphs. results of an informal survey about number of siblings The student exhibits no major errors or omissions. of classmates. Using this information create a bar graph. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Have students graph number of birthdays in each  completes a line-graph with given data month.  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated. 0.0 fi

Ravalli-Mathematics K-8 Version 2 Page 172 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Explain and model (Tally-chart) how to record the 3.0  display data in an organized fashion using graphs, data charts, and results of an informal survey about number of pets of frequency tables classmates. Using this information create a data chart. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Ask peers what their favorite cookie is and record on a  collect, organize, and display data using line graphs line graph. o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks

Ravalli-Mathematics K-8 Version 2 Page 173 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Have students measure each others height in 3.0  collect data and choose an appropriate type of graph to represent the centimeters. Record the results. Students can then use information to include double bar graphs, line plots, stem and leaf plots, the data to create a stem and leaf plot or line graph to and frequency tables display the heights of classmates from smallest to  understand and identify the four quadrants of the coordinate graph and largest. their relationships The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   displays data on a given graph (bar graphs, line plots, stem and leaf plots and frequency tables)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 174 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using the given test scores of 71, 85, 95, 88, 62, 51 3.0  collect data and choose an appropriate type of graph to represent the and 25. Have students find the median, upper/lower information to include circle graphs, scatter plots, and box and whisker quartile, maximum and minimum. Display the plot information in a box and whisker plot. (not measuring The student exhibits no major errors or omissions. “collecting data” and if they are given the type of graph they aren’t “choosing” either.) (this could be the score 2.0 task) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   displays data on a given graph (circle graphs, scatter plots and box and whisker plots)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis Topic: Data Collection, Organization and Display Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 175 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using the given test scores of 71, 85, 95, 88, 62, 51 3.0  collect data and choose an appropriate type of graph to represent the and 25. Have students find the median, upper/lower information to include histograms quartile, maximum and minimum. Display the The student exhibits no major errors or omissions. information in a histogram. (not measuring “collecting data” and if they are given the type of graph they aren’t “choosing” either.) (could be the score 2.0 task) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   display data on a given graph (histograms)  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 176 Analysis

Ravalli-Mathematics K-8 Version 2 Page 177 Strand: Data Analysis Topic: Analysis Grade: Kindergarten Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Ask students to answer questions about a graph that 3.0  interpret data from a given graph has been previously created. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes or recalls basic terminology such as: o group o set However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 178 Strand: Data Analysis Topic: Analysis Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Have each student pick their favorite candy bar from a 3.0  interpret data from a given and created graph created as a class group of three, create a graph as a class, and then have (interpreting graphs that are given is in kinder.) students answer question from the information The student exhibits no major errors or omissions. presented. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognize that there is information on a graph (if the students are interpreting data at kinder. They already know there is data on graphs. Suggest: )  recognizes or recalls basic terminology such as: o list o graph However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 179 Strand: Data Analysis Topic: Analysis Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Graph the weather Monday-Thursday, predict what 3.0  interpret data and make predictions from a given and created graph the weather will be like on Friday. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   describes what information is contained on a given graph  recognizes or recalls basic terminology such as: o tally However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 180 Strand: Data Analysis Topic: Analysis Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a graph of favorite pets, determine how many 3.0  interpret data and solve problems using a given or created graph more students prefer one specific pet over another The student exhibits no major errors or omissions. (cats vs. dogs ex.) 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes data from a given or created graph  recognizes or recalls basic terminology such as: o data o bar graph However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 181 Topic: Analysis Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using a graph, solve a problem that involves the 3.0  formulate and solve problems that involve collecting and analyzing data addition or deletion of data. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Answer questions using data from a completed graph.  recognizes information from a specified graph or tally chart  recognizes or recalls basic terminology such as: o survey o tally chart o pictograph However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 182 Topic: Analysis Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a set of numbers, (heights of students) 3.0  compute or determine the mean, median, mode, and range for data sets determine the mean, median and mode of that set of  evaluate different representations of the same data data. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Find the average of the number of siblings per family  identifies the steps required to determine mean, median, mode, and in classroom. range  recognizes or recalls basic terminology such as: o mean o median o mode o range However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis Topic: Analysis

Ravalli-Mathematics K-8 Version 2 Page 183 Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a range of test scores, students will determine 3.0  select the most appropriate measure (mean, median, mode, and range) the most appropriate measure for determining central for a given set of data tendency.  explain, model and interpret information depicted by a graph  explain the function and purpose for a graph as it relates to real world situations The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   compute or determine the mean, median, mode, and range for data sets  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 184 Strand: Data Analysis Topic: Analysis Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Given a range of test scores, students will determine 3.0  compute measures of central tendency and the range using a given set the most appropriate measure for determining central of data or graphs then create a graph, including histograms, frequency tendency. Then use the information to create tables and stem/leaf plots frequency tables, histograms, and stem and leaf plots.  describe the effects of outliers of mean, median and mode The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognizes accurate statements about central tendency and range  recognizes accurate statements about outliers of mean, median and mode  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 185 0.0 Strand: Data Analysis Topic: Analysis Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Using a set of temperatures, find the mean, median 3.0  compute various measures of central tendency and using a given set of and mode. Then calculate the upper quartile and lower data or graphs including histograms, frequency tables and stem/leaf quartile. Use this information to create a box and plots whisker plot.  analyze and represent data with a box-and-whisker plot The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 186 Probability

Ravalli-Mathematics K-8 Version 2 Page 187 Strand: Data Analysis Topic: Probability Grade: 1 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Tallying the number of times a coin lands on heads 3.0  perform and record (with tally marks) simple probability experiments involving 2 possibilities The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   identifies the possible outcomes of a simple probability experiment  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 188 Strand: Data Analysis Topic: Probability Grade: 2 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Tallying the number of times a spinner lands on a 3.0  explain and predict basic reasons why one event is more likely/less color using an unequally divided spinner. Ask the likely than another student to explain and predict why one spinner section  perform and record results of simple probability experiments involving is more likely to come up than the others more than 2 possibilities The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:   recognize or recall accurate statements about the reasons one event is more likely than another and the possible outcomes of a simple probability experiment involving more than 2 outcomes  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis

Ravalli-Mathematics K-8 Version 2 Page 189 Topic: Probability Grade: 3 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Determine the likelihood of outcomes from a spinner 3.0  explain and model basic ways to determine how likely an outcome with 2 blues, 1red, and 1 yellow. might appear in future experiments (e.g., certain, likely, unlikely or  impossible) The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  From a given circle graph show which is impossible.

 recognizes or recalls basic terminology such as: o certain, likely, unlikely or impossible However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 190 Topic: Probability Grade: 4 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Record the sum of two dice, rolled at the same time, 3.0  summarizes results of probability experiments (e.g., certain, likely, for a specified number of rolls, to determine the unlikely or impossible) number of times six appears as the sum. Write a  summary of the results using certain, unlikely, likely The student exhibits no major errors or omissions. or impossible to describe the probability of a sum of six appearing 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  ask the student o answer forced choice or fill in the  recognizes or recalls accurate statements about the results of a blank type questions about the results of a probability probability experiment experiment  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 191 Strand: Data Analysis Topic: Probability Grade: 5 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Determine the probability of rolling two dice with a 3.0  determine and represent probabilities as fractions or decimals between 0 sum of six or eight. Express the results in fraction or and 1 decimal form. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Determine the probability of pulling out a red marble  Determine simple probabilities of outcomes in fractions or decimal form in a sack with 4 red marbles and 3 blue.  recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 192 Strand: Data Analysis Topic: Probability Grade: 6 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Determine the sample space of a jar containing 20 3.0  determine the probability of an event and the probable outcome of dimes, 15 nickels, and 5 pennies and determine the independent events as a ratios and the probable outcome of independent probability of picking a nickel at random represented events ?? as a ratio and decimal. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:  Given a jar with 25 quarters and 15 nickels, what is  determines the probability of picking one item given 2 possibilities the probability of picking a nickel? Represent the  recognizes or recalls basic terminology such as: answer in the form of a ratio and decimal o However, the student exhibits major errors or omissions regarding the more complex ideas and processes. 1.5 Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content Score With help, a partial understanding of some of the simpler details and processes and some of the 1.0 more complex ideas and processes. 0.5 With help, a partial understanding of the 2.0 content but not the 3.0 content

Score Even with help, no understanding or skill demonstrated. 0.0 Strand: Data Analysis Topic: Probability Grade: 7 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught. 

Ravalli-Mathematics K-8 Version 2 Page 193 3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student:  Determine the theoretical probability of an equally 3.0  Understand sample spaces, experimental probability and theoretical divided spinner landing on one of four colors. probability (if the student doesn’t understand sample spaces until grade  Determine the experimental probability of landing on 7 then the element and task at grade 6, score 3.0 is too difficult) one color eight times. The student exhibits no major errors or omissions. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

Ravalli-Mathematics K-8 Version 2 Page 194 Strand: Data Analysis Topic: Probability Grade: 8 Score In addition to Score 3.0, in-depth inferences and applications that go beyond Sample Tasks 4.0 what was taught.  3.5 In addition to score 3.0 performance, in-depth inferences and applications with partial success. Score The student will:  Determine the probability of complimentary events, 3.0  determine the probability of complementary events, mutually exclusive mutually exclusive events, and dependent and events, and dependent/independent events independent events through modeling and The student exhibits no major errors or omissions. representation graphs. 2.5 No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content Score There are no major errors or omissions regarding the simpler details and 2.0 processes as the student:    recognizes or recalls basic terminology such as: o complementary events, mutually exclusive events, and dependent/independent events However, the student exhibits major errors or omissions regarding the more complex ideas and processes.

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