Mathematics CCSS Pacing Guide

Pojoaque Valley Schools Mathematics CCSS Pacing Guide Grade 1

*Skills adapted from Kentucky Department of Education Math Deconstructed Standards ** Evidence of attainment/assessment, Vocabulary, Knowledge, Skills and Essential Elements adapted from Wisconsin Department of Education and Standards Insights Computer-Based Program

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1 Pojoaque Valley Schools Math Common Core Pacing Guide Introduction

The Pojoaque Valley Schools pacing guide documents are intended to guide teachers’ use of Common Core State Standards (CCSS) over the course of an instructional school year. The guides identify the focus standards by quarter. Teachers should understand that the focus standards emphasize deep instruction for that timeframe. However, because a certain quarter does not address specific standards, it should be understood that previously taught standards should be reinforced while working on the focus standards for any designated quarter. Some standards will recur across all quarters due to their importance and need to be addressed on an ongoing basis.

The Math pacing guides are grounded in four key components: the key fluency expectations for each grade level, the critical areas designated in the CCSS Math Standards, the Common Core Standards for Mathematics and the integration of the Standards for Mathematical Practice. In planning instruction it is important that math teachers incorporate the 8 mathematical practices for mathematics to ensure that the Common Core standards are mastered by all students.

The Math CCSS pacing guides contain the following elements:  Grade Level: Identify the grade level of the intended standard  Standard with code: Defines the knowledge and skills for students. The code contains the grade level, domain and standard number.  Domain: Larger groups of related standards. Standards from different domains may sometimes be closely related.  Cluster: Summarize groups of related standards.  Skills and Knowledge: Identified as subsets of the standard and appear in one or more quarters. Define the skills and knowledge embedded in the standard to meet the full intent of the standard itself.

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2 Version 2 of the Pojoaque Valley School District Pacing guides for Reading Language Arts and Mathematics are based on the done by staff and teachers of the school district using the Kentucky model, and a synthesis of the excellent work done by Wisconsin Cooperative Educational Service Agency 7 (CESA 7) School Improvement Services, Green Bay, WI. (2010), Standards Insight project. Standards Insight was developed to give educators a tool for in depth investigation of the Common Core State Standards (CCSS). The CCSS are “unpacked” or dissected, identifying specific knowledge, skills, vocabulary, understandings, and evidence of student attainment for each standard. Standards Insight may be used by educators to gain a thorough grasp of the CCSS or as a powerful collaborative tool supporting educator teams through the essential conversations necessary for developing shared responsibility for student attainment of all CCSS. . . . serves as a high-powered vehicle to help educators examine the standards in a variety of ways. The Version 2 Pojoaque Valley School District Pacing guides present the standard with levels of detail and then the necessary skills by quarter based on the Kentucky model. On the second page for each standard, the synthesis of the Standards Insight project is presented in a way that further defines and refines the standard such that teachers may use the information to refine their teaching practices. Based on this synthesis of work and the purpose for the unpacking, the following fields were selected as most helpful to aid in understanding of the Common Core Standards that will lead to shifts in instruction:

1. Evidence of Student Attainment: “What could students do to show attainment of the standard?” 2. Vocabulary: “What are key terms in the standard that are essential for interpretation and understanding in order for students to learn the content?” 3. Knowledge: “What does the student need to know in order to aid in attainment of this standard?” 4. Skills and Understanding: “What procedural skill(s) does the student need to demonstrate for attainment of this standard?”, and “What will students understand to attain the standard?” The following fields are included in Version 2: Evidence of Student Attainment: This field describes what the standard may look like in student work. Specific expectations are listed in performance terms showing what students will say or do to demonstrate attainment of the standard.

Standards Vocabulary: This field lists words and phrases specific to each standard. Shared interpretation and in depth understanding of standards vocabulary are essential for consistent instruction across and within grade levels and content areas.

Knowledge: The knowledge field lists what students will need to know in order to master each standard (facts, vocabulary, definitions).

Skills and Understanding: The skills field identifies the procedural knowledge students apply in order to master each standard (actions, applications, strategies), as well as the overarching understanding that connects the standard, knowledge, and skills. Understandings included in Standards Insight synthesize ideas and have lasting value.

Instructional Achievement Level Descriptors: This field lists, by level what a teacher can expect to see in a student who achieves at a particular level. Additionally teachers can use this filed to differentiate instruction to

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3 provide further growth for student’s in moving from one level to another. This field can be used to provide specific teaching approaches to the standard in question.

A Note About High School Standards: The high school standards are listed in conceptual categories. Conceptual categories portray a coherent view of high school instruction that crosses traditional course boundaries. We have done everything possible, with teacher input, to link individual standards to the appropriate pacing guides,

References to Tables: References to tables within the standards in the Standards Insight tool refer to Tables 1- 5 found in the glossary of the Mathematics Common Core State Standards document found at www.corestandards.org. Quarterly View of Standards 1 st Grade Mathematics Pacing Guide

1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.3 Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 3 Students need not use formal terms for these properties. 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = * – 3, 6 + 6 = * . 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.2abc Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used Quarter Version 3 2015-2016

4 1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. 4Students do not need to learn formal names such as “right rectangular prism.” 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

CCSS Math Pacing Guide Grade 1

Grade Level: 1st Standard with code: 1.OA.1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2 See Common Core State Standards Glossary, Table 1. Domain: Operations Cluster: Represent and solve problems involving addition and subtraction. and Algebraic Version 3 2015-2016

5 Thinking Quarter 1: Quarter 2: Quarter 3: Use a symbol for an unknown number in an addition or subtraction problem Use a symbol for an unknown number in within 20 an addition or subtraction problem within 20 Solve word problems using addition and subtraction within 20 Solve word problems using addition and Interprets situations to solve word problems with unknowns in all positions subtraction within 20 within 20 using addition and subtraction Interprets situations to solve word Determines appropriate representations for solving word problems involving problems with unknowns in all positions different situations using addition and subtraction within 20 using addition and subtraction

Determines appropriate representations for solving word problems involving different situations using addition and subtraction Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the reasoning tools them. of others. strategically.

Evidence of Student Vocabulary K Skills Attainment/Assessment n o w le d g e Students: See glossary for problem types. S Students understand that/are able to: Given a variety of tu Represent quantities and operations (addition & addition and subtraction d subtraction) physically, pictorially, or symbolically, word problems within 20, e Strategically use a variety of representations to solve Explain and justify nt addition and subtraction word problems, solutions and solution s Use informal and mathematical language to communicate paths using connections k the connections among addition and subtraction contexts among a variety of n and related physical, pictorial, or symbolic representations (e.g., o representations, objects, drawings, and w Accurately compute sums and differences, equations with a symbol : Use symbols to represent unknown quantities in for the unknown A equations. number). d Addition is both putting together and adding to,

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6 di Subtraction is taking apart, taking from, and comparisons, ti Mathematical problems can be solved using a variety of o strategies, models, and representations, n Variables in the form of blanks, boxes, or letters, a represent unknown quantities when representing n mathematical situations algebraically. d s u bt ra ct io n st ra te gi e s, S tr at e gi e s f o r re p re s e nt in g a n d s ol vi n g p r

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7 o bl e m s w it h al l a d di ti o n a n d s u bt ra ct io n c o nt e xt s (t a bl e 1 ).

Grade Level: 1st Standard with code: 1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Domain: Operations Cluster: Represent and solve problems involving addition and subtraction. and Algebraic

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8 Thinking Quarter 1: Quarter 2: Quarter 3: Know how to add three whole numbers whose sum is less than or equal to 20.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20

Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and critique mathematics. tools persevere in solving the reasoning of others. strategically. them.

Evidence of Student Vocabulary Kn Skills Attainment/Assessment owl edg e Students: Stu Students understand that/are able to: Given word problems den Efficiently apply strategies for solving multiple addend that call for addition of ts problems, three whole numbers kno whose sum is less than or w: Use symbols to represent unknown quantities in equations, equal to 20, Ch Explain and justify ara Accurately compute sums. solutions and solution cter Efficient application of representations and computation paths using connections isti strategies are based on the numbers in the problems. among a variety of cs representations (e.g., of objects, drawings, and add equations with a symbol itio Version 3 2015-2016

9 for the unknown n number). con text s, Str ate gie s for sol vin g pro ble ms inv olv ing mo re tha n two add end s.

Grade Level: 1st Standard with code: 1.OA.3 Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 3 Students need not use formal terms for these properties. Domain: Operations Cluster: Understand and apply properties of operations and the relationship between addition and subtraction. and Algebraic Thinking Quarter 1: Quarter 2: Quarter 3: Explain how properties of operation Explain how properties of operation strategies work. strategies work.

Apply strategies using properties of operations to solve addition and Apply strategies using properties of subtraction problems. operations to solve addition and subtraction problems. Version 3 2015-2016

10 Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the reasoning tools them. of others. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Commutative property of addition St Students understand that/are able to: Given single digit addition ud Associative property of addition Strategically and efficiently apply properties of addition in and subtraction problems, ent order to find sums. Use informal language of s kn The order in which addends are joined doesn't change the properties to justify their sum, sums and differences (e.g., ow "I already figured out that : Numbers may be composed or decomposed in a variety of 8 + 3 = 11, and 3 + 8 is Co ways. just the turnaround of that m so it must be 11, too."). mu tati ve an d ass oci ati ve pr op ert ies Version 3 2015-2016

11 of ad dit ion (in for ma l lan gu ag e to de scr ibe pr op ert ies not the ter ms ) an d rol e of zer o in ad dit ion .

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12 CCSS Math Pacing Guide Grade 1

Grade Level: 1st Standard with code: 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that Domain: Operations Cluster: Understand and apply properties of operations and the relationship between addition and subtraction. and Algebraic Thinking Quarter 1: Quarter 2: Quarter 3:

Identify the unknown in a subtraction problem Identify the unknown in a subtraction problem Solve subtraction problems to find the missing addend. Solve subtraction problems to find the Explain the relationship of addition and subtraction. missing addend.

Explain the relationship of addition and subtraction.

Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriat persevere in critique the reasoning e tools solving them. of others. strategicall y.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Addend St Students understand that/are able to: Given a subtraction ud Use symbols such as blanks, boxes, or letters to represent Version 3 2015-2016

13 problem with an unknown en unknown quantities in equations, difference, ts Use mathematical language to communicate the Use a pictorial or physical kn o connections between an unknown difference problem and model to explain the the related unknown addend problem, connection between the w: subtraction problem and St Use the inverse relationship between addition and the related unknown rat subtraction to find differences, addend equation. eg Choose and apply addition and subtraction strategies to ies accurately determine sums and differences within 20. fo Given addition and Addition and subtraction have an inverse relationship that r subtraction problems can be used to solve problems, within 20, fin di Efficient application of computation strategies are based Be able to use an efficient ng on the numbers in the problems strategy (e.g., recall, su doubles, counting on or m back 1 or 2, make a ten, s close to doubles, etc.) to an name the sum or d difference. dif fer en ce s, Su btr ac tio n is th e in ve rs e of ad dit io n.

Grade Level: 1st Standard with code: 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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14 Domain: Operations Cluster: Add and subtract within 20. and Algebraic Thinking Quarter 1: Quarter 2: Quarter 3:

Know how to count on and count back.

Explain how counting on and counting back relate to addition and subtraction.

Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and critique mathematics. tools strategically. persevere in the reasoning of others. solving them.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Given addition and ud Effectively communicate justifications for sums and subtraction problems, en differences by relating the symbolic problems (equations) Use modeling strategies ts to appropriate models. (e.g. number lines, kn o Counting can be used to find solutions in addition and counting objects) to justify subtraction situations, solutions (both counting w: Version 3 2015-2016

15 on and counting back) and St A variety of models and tools can be used to communicate to show the relationship rat justifications for mathematical ideas and solutions. between counting, eg Counting can be used to find solutions in addition and addition, and subtraction. ies subtraction situations, fo r A variety of models and tools can be used to communicate m justifications for mathematical ideas and solutions. od eli ng ad dit io n an d su btr ac tio n on nu m be r lin es an d wi th ph ys ic al ob je cts , H o w to co un t on Version 3 2015-2016

16 or co un t ba ck fr o m a gi ve n nu m be r.

Grade Level: 1st Standard with code: 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = Domain: Operations Cluster: Add and Subtract within 20. and Algebraic Thinking

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17 Quarter 1: Quarter 2: Quarter 3:

Add fluently within 10. Add fluently within 10.

Subtract fluently within 10. Subtract fluently within 10.

Apply strategies to add and subtract within 20. Apply strategies to add and subtract within 20.

Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in critique the reasoning tools solving them. of others. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Fluency St Students understand that/are able to: Given any two addends ud Use addition and subtraction thinking strategies efficiently whose sum is less than or en based on the values in the problems. equal to ten, ts kn Efficient application of computation strategies is based on Use an efficient strategy the numbers in the problems, their relative sizes, and the (e.g., recall, doubles, o w: relationship of the desired sum or difference to known derived facts, counting on 1 sums and differences. or 2, close to doubles) to Th name the sum. in Efficient application of computation strategies is based on ki the numbers in the problems, their relative sizes, and the ng relationship of the desired sum or difference to known Given two whole numbers sums and differences. less than or equal to ten, str ate Use an efficient strategy gi Version 3 2015-2016

18 (e.g., counting on with es tracking, counting back to, for derived facts) to name the fin difference in the two di numbers. ng su ms an d dif fer en ce s.

Grade Level: 1st Standard with code: 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. Domain: Domain: Cluster: Work with addition and subtraction equations. Operations and Algebraic Thinking Quarter 1: Quarter 2: Quarter 3:

Explain the meaning of an equal sign (the quantity on each side of the equality symbol is the same).

Compare the values on each side of an equal sign.

Determine if the equation is true or false.

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19 Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Equation St Students understand that/are able to: Given mathematical ud Partition equal groups of numbers in different ways, statements with quantities en and/or single operation ts Efficiently apply strategies for determining the value of phrases (addition or kn simple addition and subtraction mathematical phrases, subtraction) on each side of o Use strategies for comparing quantities less than 20, the equal sign, w: (including using relational thinking to show equality or Justify the truth of each Str inequality of mathematical phrases). statement using ate When equal groups of objects or numbers are partitioned mathematical justification. gi in different ways, the total amount stays the same, es The equal sign represents a relationship of balance for between numerical expressions rather than performing an fin operation, di ng Equalities contain expressions that represent the same th amount on each side of the equal sign. e va lu e of si m pl e ad dit io n an Version 3 2015-2016

20 d su btr act io n m at he m ati cal ph ras es, Str ate gi es for co m pa rin g qu an titi es be tw ee n 0 an d 20 , in cl ud in g usi ng rel ati on Version 3 2015-2016

21 al thi nk in g, Str ate gi es to sh o w eq ua lit y or in eq ua lit y of m at he m ati cal ph ras es (e. g., 7 +9 = 8+ 10 is fal se be ca us e if Version 3 2015-2016

22 yo u ch an ge 7 int o 8 th en yo u m ust su btr act 1 fro m th e ni ne so thi s eq ua tio n is fal se be ca us e 8 + 8 is no t 8 + 10 ).

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Grade Level: 1st Standard with code: 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. number that makes the equation true in each of the equations 8 + ? = 11, 5 = * – 3, 6 + 6 = * . Domain: Operations Cluster: Work with addition and subtraction equations. and Algebraic Thinking Quarter 1: Quarter 2: Quarter 3:

Recognize part-part- Recognize part-part- whole relationships whole relationships of three whole of three whole numbers numbers Example: Example: + 5 = + 5 = 8 8 5 = -3 5 = -3 In each instance the 3 In each instance the 3 and 5 represent the and 5 represent the parts and the 8 would parts and the 8 would be representative of be representative of the whole. the whole.

Determine the Determine the missing value in an missing value in an addition or addition or subtraction equation subtraction equation by using a variety of by using a variety of strategies. strategies.

Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and mathematics. tools strategically. persevere in solving critique the reasoning of them. others.

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24 Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Equation St Students understand that/are able to: Solve single operation ud Efficiently apply strategies for solving simple equations addition/ subtraction en with one unknown, ts equations containing a Justify solutions for single unknown equations. single unknown (e.g., 8+? kn = 11, 5= __ -3, 6+6 = ___). o Equalities contain expressions that name the same amount w: on each side of the equal sign. Str ate gi es for sol vi ng si m pl e eq ua tio ns wi th on e un kn o w n.

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Grade Level: 1st Standard with code: 1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. Domain: Numbers Cluster: Extend the counting sequence and Operations in Base Ten Quarter 1: Quarter 2: Quarter 3:

Write numerals up to 120.

Represent a number of objects up to 120 with a written numeral.

Count (saying the number sequence) to 120, starting at any number less than 120.

Read the numerals up to 120.

Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in critique the reasoning tools solving them. of others. strategically.

Evidence of Student Vocabulary Knowledge Common Core Essential Elements Attainment/Assessment Version 3 2015-2016

26 Students: Students know: EE1.NBT.1.a. Count by ones. Use the pattern and regularity Number - numeral correspondence (from 0-120) EE1.NBT.1.b. Count as many as 10 objects and represent the in the counting sequence to Strategies for counting sets of objects. recognize the position of any quantity with the corresponding numeral. number between 1 and 120 and then continue counting in sequence from the given number.

Given a number orally or a quantity of objects (from 0- 120), Write the corresponding numeral.

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Grade Level: 1st Standard with code: 1.NBT.2abc Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Domain: Number Cluster: Understand place value. and Operations in Base Ten Quarter 1: Quarter 2: Quarter 3:

Explain what each digit of a two-digit number represents

Identify a bundle of 10 ones as a “ten”.

Represent numbers 11 to 19 as composed of a ten and correct number of ones.

Represent the numbers 20, 30, 40, 50, 60, 70, 80, and 90 as composed of the correct number of tens.

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29 Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Given any two-digit ud Use place value models or mental strategies to decompose number, en numbers. Use a variety of ts kn The two digits of a two-digit number represent amounts of representations (e.g., tens and ones. symbolic: 10+8; pictorial: o one line and 8 dots; w: Ten things can be represented as one ten or as ten ones. physical: place value N blocks, bundles of sticks, u or groups of fingers, etc.) m to show and explain the be decomposition of the r number into groups of 10 se and ones. qu en ce to 10 .

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Grade Level: 1st Standard with code: 1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols Domain: Number Cluster: Understand place value. and Operations in Base Ten Quarter 1: Quarter 2: Quarter 3:

Identity the value of each digit represented in the two-digit number.

Know what each symbol represents >, <, and =.

Compare two two-digit numbers based on meanings of the tens and ones digits.

Use >, =, and < symbols to record the results of comparisons.

Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and mathematics. tools persevere in critique the reasoning of strategically. solving them. others.

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31 Evidence of Student Vocabulary Knowledge Common Core Essential Elements Attainment/Assessment Students: < less than, = Students know: EE1.NBT.3. Compare two groups of 10 or fewer items when Given two 2-digit numbers equal, > Meanings of mathematical symbols: <, =, >. the quantity of items in each group is similar. Use place value terminology greater than and concepts, to explain and justify the use of <, =, > to compare the numbers and create true equalities and inequalities.

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Grade Level: 1st Standard with code: 1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Domain: Number Cluster: Use place value understanding and properties of operations to add and subtract. and Operations Quarter 1: Quarter 2: Quarter 3:

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33 Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in critique the reasoning tools solving them. of others. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Multiple of 10 St Students understand that/are able to: Given a situation in which ud Model addition problems using appropriate tools, addition is useful with the en sum being not greater than ts Record strategies for solving addition problems, 100 (including the kn Communicate the relationship between models and particular cases of adding o symbolic (numeric) representations of solutions to addition a two-digit number and a w: problems. one-digit number, and Us Relationships between models of addition problems and adding a two-digit number e symbolic recordings of those models can be used to justify and a multiple of 10), of solutions, Generate correct answers, to Two-digit numbers are made up of tens and ones. Explain their reasoning ols using concrete models or for drawings, or using m strategies based on place od value, properties of eli operations, and/or the ng relationship between ad addition and subtraction. dit io Justify the correctness of n the answer and the pr strategy used, including ob relating the strategy used le to a written method ms (symbolic and numeric , recording of the steps used). Str ate

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34 gi es an d m et ho ds for sy m bo lic all y (n u m eri cal ly) re co rdi ng str ate gi es for sol vi ng ad dit io n pr ob le ms .

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Grade Level: 1st Standard with code: 1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used Domain: Number Cluster: Use place value understanding and properties of operations to add and subtract. and Operations in Base Ten Quarter 1: Quarter 2: Quarter 3:

Identify the value of each digit in a number within 100.

Apply knowledge of place value to mentally add or subtract 10 to/from a given two digit number.

Explain how to mentally find 10 more or 10 less than the given two-digit number.

Make sense of Reason abstractly and Construct viable Model with Use

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36 problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the reasoning tools them. of others. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: When presented with a ud Use patterns and regularity in counting sequences and two-digit number orally, en understandings of place value to add or subtract a "ten", ts Can efficiently find 10 Communicate reasoning and solution strategies. more or 10 less than the kn given number and then o The two digits of a two-digit number represent amounts of explain their mental w: tens and ones, strategies. Pl Patterns in the place value system can be used to mentally ac compute sums and differences. e va lu e pa tte rn s in th e co un tin g se qu en ce,

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37 Pl ac e va lu e vo ca bu lar y: te ns, on es.

CSS Math Pacing Guide Grade 1

Grade Level: 1st Standard with code: 1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Domain: Number Cluster: Use place value understanding and properties of operations to add and subtract. and Operations in Base Ten Quarter 1: Quarter 2: Quarter 3:

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38 Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the reasoning tools them. of others. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment n o w le d g e Students: Multiple St Students understand that/are able to: When presented with a u Use models and strategies to find and record solutions to multiple of 10 in the range d problems where a multiple of 10 is subtracted from a of 10-90, e second multiple of 10, and then explain their strategies. Use strategies efficiently to nt s Patterns in the place value system can be used to mentally subtract a second multiple compute sums and differences. of ten from the first, and k explain their strategies. n o w : Pl a c e v al u e m Version 3 2015-2016

39 o d el s fo r a d di n g a n d s u bt ra ct in g n u m b er s le ss th a n 1 0 0, St ra te gi es fo r a d di n g a Version 3 2015-2016

40 n d s u bt ra ct in g m ul ti pl es of 1 0.

Grade Level: 1st Standard with code: 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Version 3 2015-2016

41 Domain: Cluster: Measure lengths indirectly and by iterating length units. Measurement and Data Quarter 1: Quarter 2: Quarter 3:

Make sense of Reason abstractly Construct viable Model with Use problems and and quantitatively. arguments and critique mathematics. appropriate persevere in the reasoning of others. tools solving them. strategically .

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Given three objects of ud Use direct and indirect comparison to order objects by different lengths, en length. Use reasoning skills and ts kn Measurable attributes of objects can be used to describe direct comparison to order and compare the objects. them by length. o w: Given two objects in St rat Version 3 2015-2016

42 different orientations, eg Use a third object to ies indirectly determine which fo of the first two objects is r longer and which is po shorter. sit io ni ng a thi rd ob je ct in co rre ct le ng th or de r to tw o ob je cts w hi ch ha ve alr ea dy be en or de re d s m all Version 3 2015-2016

43 to lar ge .

Grade Level: 1st Standard with code: 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. by a whole number of length units with no gaps or overlaps. Domain: Cluster: Measure lengths indirectly and by iterating length units. Measurement and Data Quarter 1: Quarter 2: Quarter 3:

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44 Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and critique mathematics. tools strategically. persevere in solving the reasoning of others. them.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Accurately measure length ud Accurately measure length using non-standard units (to the using non-standard units en nearest whole unit). ts (e.g., paper clips, The length of the object is expressed as the count of unit Cuisenaire rods). kn o lengths needed to cover the same distance (end-to-end and w: with no gaps or overlaps). M ea su ra bl e att rib ut es Version 3 2015-2016

45 of ob jec ts, sp eci fic all y le ng th, Str ate gi es for m ea su rin g le ng th usi ng no nst an da rd un its.

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Grade Level: 1st Standard with code: 1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Domain: Cluster: Tell and write time. Measurement and Data Quarter 1: Quarter 2: Quarter 3:

Make sense of Reason abstractly and Construct viable Model with Use Version 3 2015-2016

47 problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the reasoning tools them. of others. strategically.

Evidence of Student Vocabulary Knowledge Common Core Essential Elements Attainment/Assessment Students: Students know: EE1.MD.3.a. Demonstrate an understanding of the terms Tell and write time in hours Symbolic representations for times. “tomorrow, yesterday, and today.” and half-hours using analog EE1.MD.3.b. Name a day of the week for tomorrow and and digital clocks. yesterday. EE1.MD.3.c. Identify activities that come next, before, and after. EE1.MD.3.d. Demonstrate an understanding that telling time is the same every day.

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Grade Level: 1st Standard with code: 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Domain: Cluster: Represent and interpret data. Measurement and Data Quarter 1: Quarter 2: Quarter 3: Recognize different methods to organize data

Recognize different methods to represent data

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55 Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and critique the mathematics. tools strategically. persevere in solving reasoning of others. them.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Organize and represent ud Choose and apply appropriate strategies for organizing and data with up to three en recording data, categories using physical ts kn Read and interpret graphical representations (physical objects, tally charts, graphs, tally charts, pictographs, and bar graphs) of data, pictographs, or bar graphs, o w: Communicate and defend solutions and solution paths. Interpret the data by asking and answering Str Questions concerning mathematical contexts can be questions about the total ate answered by collecting and organizing data. number of data points, gi how many in each es category, or how many for more or less are in one co category than in another. lle cti ng , or ga ni zi ng , an d re co rdi ng Version 3 2015-2016

56 da ta (e. g., or ga ni zi ng ph ysi cal ob jec ts; cr eat in g tal ly ch art s, pi ct og ra ph s, an d ba r gr ap hs ), Str ate gi es for co un tin g an Version 3 2015-2016

57 d co m pa rin g qu an titi es.

Grade Level: 1st Standard with code: 1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Version 3 2015-2016

58 Domain: Geometry Cluster: Reason with shapes and their attributes. Quarter 1: Quarter 2: Quarter 3:

Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and critique mathematics. tools strategically. persevere in solving the reasoning of others. them.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Defining attribute St Students understand that/are able to: Given a variety of ud Non defining attribute Use defining characteristics to build/draw and identify examples and non- en basic shapes. examples of basic shapes Closed ts (triangles, rectangles, kn Shapes may be sorted by many sets of attributes, but their squares, circles), o geometric classification is based on certain defining attributes. Identify and label the w: examples using defining D attributes of shapes to efi justify their choices, ni Build and draw examples ng and non-examples of basic ch ar Version 3 2015-2016

59 shapes and justify their ac creations using the ter defining attributes of ist shapes. ics of ba sic sh ap es (tr ia ng les , re ct an gl es, sq ua re s, cir cl es ).

Grade Level: 1st Standard with code: 1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

4Students do not need to learn formal names such as “right rectangular prism.” Version 3 2015-2016

60 Domain: Geometry Cluster: Reason with shapes and their attributes. Quarter 1: Quarter 2: Quarter 3:

Make sense of Reason abstractly and Construct viable Model with Use problems and quantitatively. arguments and mathematics. appropriate persevere in solving critique the tools them. reasoning of others. strategically.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: Trapezoid St Students understand that/are able to: Compose 2D shapes from ud Use shape manipulatives to create composite shapes. Right rectangular prism en smaller 2D shapes (e.g., Both 2D and 3D shapes can be composed and use two right triangles to Right circular cone ts kn decomposed. make a square or two Right circular cylinder squares to make a o Composite shape rectangle), w: Compose 3D shapes from Vi smaller 3D shapes (e.g., su use two cubes to make a al rectangular prism or two ch triangular prisms to make ar a rectangular prism). ac ter ist Version 3 2015-2016

61 ics of ba sic sh ap es (re ct an gl es, sq ua re s, tra pe zo id s, tri an gl es, ha lf- cir cl es, qu art er- cir cl es, cu be s, rig ht re ct an gu lar pri s Version 3 2015-2016

62 m s, rig ht cir cu lar co ne s, an d rig ht cir cu lar cy lin de rs) .

Grade Level: 1 Standard with code: 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Domain: Geometry Cluster: Reason with shapes and their attributes. Quarter 1: Quarter 2: Quarter 3:

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63 Make sense of Reason abstractly Construct viable Model with Use appropriate problems and and quantitatively. arguments and mathematics. tools strategically. persevere in solving critique the reasoning of them. others.

Evidence of Student Vocabulary K Skills Attainment/Assessment no wl ed ge Students: St Students understand that/are able to: Given circles and/or ud Decompose circles and rectangles into halves and fourths, rectangles, en ts Communicate the size of pieces using the appropriate Cut or draw lines to divide fraction terminology, the shapes into two and four kn equal shares, o Communicate the relative size of halves and fourths by w: reasoning about the number of shares created Describe the whole as cut into halves, fourths, and St Fractional parts of a whole are equal-sized portions of that quarters, rat whole, eg Decomposing into more equal shares creates smaller Describe a set of like pieces ies shares. as halves, fourths, quarters, fo Describes a single piece as r half of, fourth of, or quarter de of when compared to the co whole, m po Version 3 2015-2016

64 Describe the whole as two si of, or four of the shares, ng Explain that cutting the sh shape into more shares ap creates smaller pieces. es int o eq ua l sh ar es (h al ve s an d fo urt hs ), Fr ac tio n vo ca bu lar y: ha lv es, fo urt hs, qu art er s, ha lf of, fo urt h Version 3 2015-2016

65 of, qu art er of, w ho le.

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