Township of Union Public Schools s7

TOWNSHIP OF UNION PUBLIC SCHOOLS

Grade 5 Mathematics Accelerated Curriculum Guide 2014/2015 Board Members

Francis “Ray” Perkins, President

Richard Galante, Vice President

David Arminio

Susana Cooley

Thomas Layden

Vito Nufrio

Guy Francis

Lois Jackson

Angel Salcedo TOWNSHIP OF UNION PUBLIC SCHOOLS Administration

Acting Superintendent …………………………………………………………………...…………………….... Mr. Gregory Tatum

Assistant Superintendent ……………………………….………………………….……………………………… Dr. Noreen Lishak

Director of Student Information/Technology ………………………………..………………………….…………. Ms. Ann M. Hart DEPARTMENT SUPERVISORS

Nicole Ahern School Counseling Jason Killian Special Services: PreK - 8 Joseph Seugling Special Services: 9 - 12 Donna Wozniak Special Services: PreK - 8

10-Month Maureen Corbett English: PreK - 2, Social Studies: PreK - 2 Deborah Ford Mathematics: 3 - 5, Science: 3 - 5 Libby Galante Social Studies: 6 - 12, Business Robert Ghiretti English: 3 - 5, Social Studies: 3 - 5 Maureen Guilfoyle Science: 6 - 12 Yvonne Lorenzo Career Ed, World Lang., ESL, Computers, G&T Mary Malyska English: 6-12, Library/Media Theresa Matthews Mathematics: PreK - 2, Science: PreK - 2 Jason Mauriello Mathematics: 6-12 Ron Rago Art, Music Mathematics Grade 5

Curriculum Committee:

Ashley DelValle

Kristin Nunes Table of Contents

Title Page

Board Members

Administration

Department Supervisors

Curriculum Committee

Table of Content

District Mission/Philosophy Statement

District Goals

Course Description

Recommended Texts

Course Proficiencies

Curriculum Units

Appendix: New Jersey Core Curriculum Content Standards Mission Statement

The Township of Union Board of Education believes that every child is entitled to an education designed to meet his or her individual needs in an environment that is conducive to learning. State standards, federal and state mandates, and local goals and objectives, along with community input, must be reviewed and evaluated on a regular basis to ensure that an atmosphere of learning is both encouraged and implemented. Furthermore, any disruption to or interference with a healthy and safe educational environment must be addressed, corrected, or when necessary, removed in order for the district to maintain the appropriate educational setting.

Philosophy Statement

The Township of Union Public School District, as a societal agency, reflects democratic ideals and concepts through its educational practices. It is the belief of the Board of Education that a primary function of the Township of Union Public School System is to formulate a learning climate conducive to the needs of all students in general, providing therein for individual differences. The school operates as a partner with the home and community. Statement of District Goals

 Develop reading, writing, speaking, listening, and mathematical skills.  Develop a pride in work and a feeling of self-worth, self-reliance, and self discipline.  Acquire and use the skills and habits involved in critical and constructive thinking.  Develop a code of behavior based on moral and ethical principals.  Work with others cooperatively.  Acquire a knowledge and appreciation of the historical record of human achievement and failures and current societal issues.  Acquire a knowledge and understanding of the physical and biological sciences.  Participate effectively and efficiently in economic life and the development of skills to enter a specific field of work.  Appreciate and understand literature, art, music, and other cultural activities.  Develop an understanding of the historical and cultural heritage.  Develop a concern for the proper use and/or preservation of natural resources.  Develop basic skills in sports and other forms of recreation. Course Description

The fifth grade curriculum is aligned with the Common Core State Standards for mathematics: 5.OA Operations and Algebraic Thinking 5.NBT Number and Operations in Decimals 5.NF Number and Operations - Fractions 5.MD Measure and Data 5.G Geometry 6.RP Ratios and Proportional Relationships 6.NS The Number System

The content emphases for this grade level are:  Developing an understanding of and fluency with addition, subtraction, multiplication, and division of decimals  Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions  Describing two- and three-dimensional shapes and analyzing their properties, including area and volume

These focal points will be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations. The purpose is “to enable all of New Jersey’s children to acquire the mathematical skills, understandings and attitudes that they will need to be successful in their careers and daily lives” Recommended Textbooks: Houghton Mifflin Harcourt/GO MATH Grade 5 Houghton Mifflin Harcourt/GO MATH Grade 6

Resources:

5th Grade CCSS Resource Packet

Course Proficiencies

Students will be able to…

5.OA Operations and Algebraic Thinking  Communicate understanding of math concepts  Use manipulatives and/or models effectively  Apply appropriate strategies in problem-solving  Write and interpret numerical expressions with grouping symbols  Analyze patterns and relationships

5.NBT Number and Operations in Decimals  Use whole-number exponents to denote powers of 10  Read, write, and compare decimals to thousandths  Use place value understanding to round decimals to any place  Fluently multiply multi-digit whole numbers  Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors  Add, subtract, multiply, and divide decimals to the hundredths

5.NF Number and Operations – Fractions  Add & subtract fractions with unlike denominators  Solve word problems involving addition and subtraction of fractions  Multiply a fraction or whole number by a fraction  Divide unit fractions by whole numbers and whole numbers by unit fractions

5.MD Measurement and Data  Convert like measurement units within a given measurement system  Represent and interpret data  Understand concepts of volume measurement  Solve real world and mathematical problems involving volume

5.G Geometry  Graph points in the first quadrant of the coordinate plane  Interpret coordinate values of points in the context of the situation  Classify two-dimensional figures into categories based on properties

ACCELERATED MATH: 6RP Ratios and Proportional Relationships  Understand ratio concepts and use ratio reasoning to solve problems

6.NS The Number System  Apply and extend previous understandings of numbers to the system of rational numbers Curriculum Units

Unit 1: Operations and Algebraic Thinking

Unit 2: Number and Operations in Decimals

Unit 3: Number and Operations - Fractions

Unit 4: Measurement and Data

Unit 5: Geometry

6 th Grade Unit 1: Ratios and Proportional Relationships

6 th Grade Unit 2: The Number System Pacing Guide

Chapter Introduction Instruction Assessment TOTAL 1 1 day 13 days 2 days 16 th 2 1 day 6 days 2 days 8 - Total days of 5 Grade Instruction: 112 3 1 day 13 days 2 days 16 4 1 day 7 days 2 days 9 - Total days of 6th grade 5 1 day 6 days 2 days 8 Instruction: 33 6 1 day 8 days 2 days 11 -Misc Days/NJASK prep: 35 7 1 day 7 days 2 days 10 8 1 day 4 days 2 days 7 9 1 day 5 days 2 days 8 10 1 day 6 days 2 days 9 11 1 day 7 days 2 days 10 6th Grade Accelerated 33 Chapter Introduction Instruction Assessment TOTAL 3 1 day 10 days 2 days 13 4 1 day 8 days 2 days 11 5 1 day 6 days 2 days 9 Unit 1: 5.OA Operations and Algebraic Thinking Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs)

5.OA.1 & 5.OA.2 5.OA.1 & 5.OA.2 5.OA.1 & 5.OA.2 5.OA.1 & 5.OA.2 Numerical Expressions Numerical Expressions Numerical Expressions Numerical Expressions

 In what order must SWBAT : operations be evaluated  PEMDAS Hopscotch  Sample SCR Item: …to find the solution to a  Use the order of Emma has eleven fish in problem?...when there operations to evaluate  Order of Operations her aquarium. She buys are parentheses within numerical expressions Bowling four more. Write the parentheses? including those that expression that matches contain parentheses,  Create your own the situation numerically.  How can you use a brackets, and braces. PEMDAS acronym (Ans: 11 + 4) numerical expression to saying describe a situation?  Write numerical Sample MC Item: Solve expression to describe a  Exponents Dice Game 3² + 6 ÷ (9 - 2) situation. a. 3 *b. 2 c. 5. d. 4 Cross Curricular Counting on Frank – MATH  Sample ECR Item: Who & ENGLISH is Right? Ms. Robertson put the following expression on the board. She asked all students to solve the problem on their own and explain the solving process.

32 + 4 × 9 – 10

Kayla said the correct answer is 107. Bill said the correct answer is 35. - Solve the problem and show your work. - Who is correct? -If Kayla is wrong, what was the mistake? Explain.

Unit 2: 5.NBT Number and Operations in Decimals

Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs) 5.NBT.1 – 5.NBT.4 5.NBT.1 – 5.NBT.4 5.NBT.1 – 5.NBT.4 5.NBT.1 – 5.NBT.4 Place Value System Place Value System Place Value System Place Value System

 How can you describe SWBAT:  Place value number line  Sample SCR Item: the relationship between What’s the error? Matt 2 place value positions?  Recognize the 10 to 1  Place Value Snakes wrote five million two relationship between 2 hundred thousand seven  How do you read, write, place value positions.  Take a Chance! hundred eighty four as and represent whole 5,025,784. What’s wrong numbers through  Read and write whole  Place Value and write it correctly in hundred millions and numbers through Communicators standard form. decimals through hundred millions and (Ans: 5,205,784) thousandths? decimals through  Decimal War thousandths.  Sample SCR Item:  How can you use an  Decimal Shuffle 103  101 10n exponent to show  Write and evaluate What is the value of n. powers of 10 repeated factors in  Decimal: I Have…You (Ans: 2) exponent form. Have Matching Game  How can you use a basic  Sample MC Item: fact and a pattern to  Use basic fact and a  Dueling Duos multiply by a 2- digit #? pattern to multiply mentally by multiples of 4.85 □ 4.8  How can you use place 10,100, and 1,000. value to compare, order , *a. > b. < c. = and round decimals?

 Compare, order, & round Performance Assessment decimals to thousandths Representing Decimals using place value. Match Chart Cut and Paste

Exemplar Exemplars Gr3-5 Pg 199-206 5.NBT.5 – 5.NBT.7 5.NBT.5 – 5.NBT.7 5.NBT.5 – 5.NBT.7 5.NBT.5 – 5.NBT.7 Operations with Decimals Operations with Decimals Operations with Decimals Operations with Decimals Sample SCR Item: Four  How can you use SWBAT:  Conquering Division friends have three brownies properties of operations Dueling Digits left over from a party. They to solve problems?  Use properties of would like to split them operations to solve  McDonald’s Rhyme equally. How much should  How do you multiply by problems. each of them receive? 1- and 2- digit numbers?  Decimal Squares (Answer: 75% or 0.75 or ¾  Multiply by 1- and 2- digit (manipulative) of a brownie)  How is multiplication numbers. used to solve a division  Decimal Magic Squares Sample SCR Item: A gallon problem?  Use multiplication to contains 128 ounces. Paul solve division problems.  Decimal War wants to divide three gallons  How can you divide of apple cider equally among whole numbers?  Divide -3 and 4- digit  Base Ten Block the two dozen friends at his dividends by 1- and 2- (manipulative) party. How much apple cider  How can you use digit divisors. will each friend receive? compatible numbers to  Fraction People (Answer: 16 oz.) estimate quotients?  Estimate quotients using compatible numbers. Sample MC Item: Debbie  How can you estimate has a $5.00 bill. She wants decimal sums and  Make reasonable to purchase a notebook for differences? estimates of decimal $0.75 and a pen for $0.50. sums and differences. How much money will  How can you use base Debbie have after purchasing the notebook ten blocks to model  Model decimal addition and the pen? (Answer: decimal addition and and subtraction using $3.75) subtraction? base ten blocks. a. $1.25 b. $2.75 c. *$3.75 d. $4.25  How can you add and  Add and subtract subtract decimals? decimals using place Sample MC Item: How value. many numbers between 20  How can you use and 50 have no remainder addition or subtraction to  Identify, describe, and when divided by 6? describe a pattern or create numeric patterns a. 3 b. 4 * c. 5 d. 6 create a sequence with with decimals. decimals?  Solve decimal Sample SCR Item: Paula’s  How can you solve multiplication problems tractor holds 3 liters of decimal multiplication using place value. gasoline. Tom’s tractor holds problems? 2.4 liters. How much more  Divide decimals by whole does one tractor hold than  How can you divide number and decimal the other? decimals by whole divisors. (Answer: 0.6 liters) numbers and decimal divisors?  Place the decimal point Exemplar in decimal multiplication Exemplars Gr3-5  What strategies can you or division. pg133-142 use to place a decimal point in a  Divide decimals by whole product/quotient? number and decimal divisors.  How can you estimate decimal products and  Estimate decimal quotients? products and quotients.

 When do you write a  Write a zero in the zero in the dividend to dividend to find a find a quotient? quotient.

Unit 3: 5.NF Number and Operations - Fractions

Essential Questions Instructional Objectives/ Activities Assessments Skills and Benchmarks (CPIs)

5.NF.1 & 5.NF.2 5.NF.1 & 5.NF.2 5.NF.1 & 5.NF.2 5.NF.1 & 5.NF.2 Add/Subtract Fractions Add/Subtract Fractions Add/Subtract Fractions Add/Subtract Fractions

 How can you add and SWBAT:  Fraction Man Sample ECR Item: Joe had subtract fractions and a pizza party. He ordered 8 mixed numbers with  Use equivalent fractions  Equivalent Fraction Pizza pizzas, each cut into 8 unlike denominators? to add and subtract Activities slices. When his friends fractions and mixed went home, he had ¼ of a  How can you use numbers.  Calculators – Fractions pepperoni pizza, 5/8 of a renaming to find the (manipulative) mushroom pizza, ½ of a difference of two mixed  Rename to find the cheese pizza, and 1/8 of a numbers? difference of two mixed  The Game of veggie pizza left over. How numbers. Concentration Match much pizza was left over in  How can you make Game all? reasonable estimates of  Make reasonable 1 Show one way to get fraction sums and estimates of fraction  Fraction Strips the answer to this problem. differences? sums and differences. (manipulative) Explain your method. 2 Show another way to  Fraction Tiles get the answer to this (manipulative) problem. Explain your method.  Dry Erase Board Fraction Sample SCR Item: A fifth- Problems (manipulative) grade class will perform an act for the spring talent show. Two-thirds of the  Fraction Dice class of 24 students wants to (manipulative) perform a skit. The rest of the students in the class  Fractions: True or False want to sing a song. The Game teacher decided that 3/4 of the students must agree on  Fractions: I Have…You an act before the decision Have Game will be final. How many more students would have to choose a skit before ¾ of the  Sip of Spring students agree on it? (Answer: 2 students) Cross Curricular History of M&Ms Candies – Performance Assessment MATH & SS Add/Subtract Fractions Match Cut and Paste

Exemplar Exemplars Gr3-5 pg153-162

5.NF.3 – 5.NF.7 5.NF.3 – 5.NF.7 5.NF.3 – 5.NF.7 Multiply/Divide Fractions 5.NF.3 – 5.NF.7 Multiply/Divide Fractions Multiply/Divide Fractions Multiply/Divide Fractions  How do you multiply SWBAT:  Fraction War  Sample SCR Item: fractions? Mary cuts 5 pans of  Multiply fractions.  Recipes brownies into eighths.  How do you multiply How many 1/8 size mixed numbers?  Multiply mixed numbers.  Dividing Fractions Song brownie pieces does show have now?  How can you use a unit  Use a model to multiply (Ans: 40) tile to find the area of a two mixed numbers and rectangle with fractional find the area of a  Sample SCR Item: Five side lengths? rectangle. cats each ate a quarter of food. How much food did  How does a fraction  Interpret a fraction as they eat altogether? represent division? division and solve whole (Ans: 1 ¼ ) number division  How can problems that result in a Performance Assessment fraction or mixed Grandma’s Favorite you divide a whole number number. Cupcakes by a fraction and divide a fraction by a whole number?  Divide a whole number Exemplar by a fraction and divide a Exemplars Gr3-5 fraction by a whole pg123-131 number.

Unit 4: 5.MD Measurement and Data

5.MD.1 & 5.MD.2 5.MD.1 & 5.MD.2 5.MD.1 & 5.MD.2 5.MD.1 & 5.MD.2 Convert Measurements Convert Measurements Convert Measurements Convert Measurements

 How can a line plot help SWBAT:  Measure Man Sample MC Item: If these you find an average with fractions were graphed on data given in fractions?  Make and use line plots  Metric Number Line the number line, which of with fractions to solve Communicator them would be closest to  How can you compare problems. zero? and convert customary  Conversions: The Game a. 3 b. 1 c. 3 * d. 1 units of length, capacity,  Compare, contrast, and of Concentration 5 4 20 10 and weight? convert customary units of length, capacity, and  Customary Units of Sample SCR Item: State a  How can you compare weight. Measure Match number that is between 1/3 and convert metric units? and 0.36.  Compare, contrast, and  Conversions: I Have / Acceptable answers would convert metric units. You Have include various representations of Real  Guess My Unit Numbers between 1/3 and . 36 (e.g., 0.34, 0.334, 0.35, 7/20, etc.)

Sample ECR Item: On the number line in your answer folder, plot points for the following numbers. 4/5, 0.6 1 Label each point. 2 Name two different rational numbers that are greater than 0.6 and less than 4/5. (Write one of your numbers in fractional form and write the other number in decimal form.) 3 Explain how you know that each of your numbers is greater than 0.6 and less than 4/5.

Sample ECR Item: Two students measured the same book shelf. Debbie said the measurement is 3. Tim said the measurement is 36. How can both students be correct? Explain your reasoning.

Sample ECR Item: Carol measured her height to be 1.5. How can this be possible? Explain your reasoning.

Performance Assessment Conversions Match Chart Cut and Paste

Exemplar Exemplars Gr3-5 pg143-152

5.MD.3 – 5.MD.5 5.MD.3 – 5.MD.5 5.MD.3 – 5.MD.5 5.MD.3 – 5.MD.5 Geometric Measurement Geometric Measurement Geometric Measurement Geometric Measurement  What is a unit cube and SWBAT:  Cereal Box  Sample MC Item: Find how can you use it to the volume. build a solid figure?  Understand unit cubes  Volume Stations and how they can be  How can you find the used to build a solid  Investigation: Unit Cubes volume of a rectangular figure. and Volume prism using the  Find the volume of formula/using unit rectangular prisms using  Volume Playing Cards cubes? the formula and unit cubes.  Measuring Volume a. 80 ft³ b. 90 ft²  How can you use an Activity c. 80 ft² *d. 90 ft³ everyday object to  Estimate the volume of a estimate the volume of a rectangular prism.  Sample SCR Item: Patty rectangular prism? built a rectangular prism with unit cubes. The base has 12 cm cubes. If the prism was built with 108 cm cubes, what is the height of the prism? (Ans: 9 cm cubes)

Unit 5: 5.G Geometry

5.G.1 & 5.G.2 5.G.1 & 5.G.2 5.G.1 & 5.G.2 5.G.1 & 5.G.2 Coordinate Plane Coordinate Plane Coordinate Plane Coordinate Plane

 How can you identify and SWBAT: Sample SCR Item: Three plot points on a  Super Bowl Graph vertices of a parallelogram coordinate grid?  Graph and name points are at the points (0, 0), (2, on a coordinate grid  River Riding Plot the 4), and (6, 0). What are the  How can you use a using ordered pairs. Picture coordinates of the fourth coordinate grid to display vertex? data collected in an  Collect and graph data  A.I Plot the Picture (Answer: (8,4) or (-4,4) or (4, experiment? on a coordinate grid. -4). Although not expected to find either of the answers out  How can you use a line  Analyze and display data Cross Curricular of the first quadrant, a graph to display and in a line graph. Treasure Map Grid – MATH student would not be analyze real-world data? & SS penalized for finding such a  Understand and apply vertex.) the concepts of congruence and symmetry (line and rotational).

5.G.3 & 5.G.4 5.G.3 & 5.G.4 5.G.3 & 5.G.4 Two-Dimensional Figures Two-Dimensional Figures Two-Dimensional Figures 5.G.3 & 5.G.4 Two-Dimensional Figures  How can you identify and SWBAT:  Polygon Song Sample ECR Item: Describe classify polygons? the similarities and  Identify and classify  Pattern Block differences between the  How can you classify polygons. (manipulatives) following polygons. triangles? quadrilaterals? - Compare and contrast an  Classify and draw  Toothpick Triangles isosceles triangle and an triangles/quadrilaterals equilateral triangle. using their properties.  Geometry Scavenger -Compare and contrast a Hunt rectangle and a parallelogram.  I Have/You Have

 Geoboard (manipulatives)

Cross Curricular Teaching Tangrams – MATH & ENGLISH 6 th GRADE ACCELERATED Unit 1: Ratios and Proportional Relationships

Unit 1: 6.RP Ratios & Proportional Relationships

6.RP.1 & 6.RP.2 6.RP.1 & 6.RP.2 6.RP.1 & 6.RP.2 6.RP.1 & 6.RP.2 Ratios & Proportional Ratios & Proportional Ratios & Proportional Ratios & Proportional Relationships Relationships Relationships Relationships

 What are ratios and how SWBAT: Sample SCR Item: can they be used to If it took 7 hours to mow 4 solve real life problems?  Understand the concept  Modeling ratios with red lawns, then at that rate, how of a ratio and use ratio and yellow counters many lawns could be mowed  How do you calculate language to describe a in 35 hours? At what rate unit rate and how do you ratio relationship  Utilizing food were lawns being mowed? interpret it in context of a between two quantities. advertisements to find real-world scenario? unit rates, such as cost  Understand the concept per pound of apples of a unit rate a/b associated with a ratio  Converting between rate a:b with b ≠ 0, and use and unit rate to compare rate language in the prices of food. context of a ratio For example, 8 oranges relationship. for $2 and 12 oranges for $3 have the same  Use ratio and rate unit rate of 4 oranges for reasoning to solve real- $1. world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 6 th GRADE ACCELERATED Unit 2: The Number System

Unit 2: 6.NS The Number System

6.NS.5 - 6.NS.8 6.NS.5 - 6.NS.8 6.NS.5 - 6.NS.8 6.NS.5 - 6.NS.8 The Number System The Number System The Number System The Number System

 Understand that positive and  Utilize number lines  Sample MC Item: On What are rational numbers? negative numbers are used (horizontal and February 3, 1996, a together to describe vertical) For example, record low temperature How can you represent quantities having opposite show -50 is less than of -47°F was reached in negative numbers in real life directions or values -5. Another example, Iowa. The temperature and on a number line and interpret –3 > –7 as a the next day was a little coordinate plane?  Understand a rational statement that –3 is warmer. Which could number as a point on the located to the right of have been the How can you find and number line. Extend number –7 on a number line temperature the next interpret the absolute value line diagrams and coordinate oriented from left to day? of rational numbers? axes familiar from previous right. a) -51°F b)-49°F grades to represent points on c) -47°F d)-45°F the line and in the plane with  Comparison of (Answer: D) negative number temperature. coordinates. For example,  Sample MC Item: While  write –3 oC > –7 oC to scuba diving, Amelia  Understand ordering and express the fact that explored the ocean at an absolute value of rational –3 oC is warmer than elevation of -30 feet. numbers. –7 oC. Ricardo was closer to the surface of the water than  Solve real-world and  Account balance Amelia. Which describes mathematical problems by activities. Ricardo’s depth? graphing points in all four For example, a) depth of greater than quadrants of the coordinate recognize that an -30 feet plane. Include use of account balance less b) depth of greater than coordinates and absolute than –30 dollars 30 feet value to find distances represents a debt c) depth of less than 30 between points with the greater than 30 feet same first coordinate or the dollars. d) depth of less than -30 same second coordinate. feet  Real-world scenarios (Answer: C) for absolute value. For example, discuss two people living the same distance from a location but in opposite directions.

 Plotting points on all 4 quadrants that create a picture. Common Core State Standards Mathematics

Operations and Algebraic Thinking

. Write and interpret numerical expressions.

. Analyze patterns and relationships.

Number and Operations in Base Ten

. Understand the place value system.

. Perform operations with multi-digit whole numbers and with decimals to hundredths.

Number and Operations—Fractions

. Use equivalent fractions as a strategy to add and subtract fractions.

. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Measurement and Data

. Convert like measurement units within a given measurement system.

. Represent and interpret data.

. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Geometry

. Graph points on the coordinate plane to solve real-world and mathematical problems.

. Classify two-dimensional figures into categories based on their properties.

6th Grade Unit 1 – Ratios and Proportional Relationships

. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.

. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

6th Grade Unit 2 – The Number System

. Apply and extend previous understandings of numbers to the system of rational numbers.

. Understand a rational number as a point on the number line.

. Understand ordering and absolute value of rational numbers.

. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. New Jersey Scoring Rubric

Rubrics - SCORING STUDENT RESPONSES Holistic Scoring Guide for Mathematics Open-Ended (OE) Items (Generic Rubric)

3 - Point Response The response shows complete understanding of the problem's essential mathematical concepts. The student executes procedures completely and gives relevant responses to all parts of the task. The response contains few minor errors, if any. The response contains a clear, effective explanation detailing how the problem was solved so that the reader does not need to infer how and why decisions were made.

2 - Point Response The response shows nearly complete understanding of the problem's essential mathematical concepts. The student executes nearly all procedures and gives relevant responses to most parts of the task. The response may have minor errors. The explanation detailing how the problem was solved may not be clear, causing the reader to make some inferences.

1 - Point Response The response shows limited understanding of the problem's essential mathematical concepts. The response and procedures may be incomplete and/or may contain major errors. An incomplete explanation of how the problem was solved may contribute to questions as to how and why decisions were made.

0 - Point Response The response shows insufficient understanding of the problem's essential mathematical concepts. The procedures, if any, contain major errors. There may be no explanation of the solution or the reader may not be able to understand the explanation. The reader may not be able to understand how and why decisions were made.