1st Grade MathematicsUnit 2 Curriculum Map:

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ORANGE PUBLIC SCHOOLS

OFFICE OF CURRICULUM AND INSTRUCTION

OFFICE OF MATHEMATICS

Table of Contents

I. Unit Two Overview p. 2

II. MIF Lesson Structure p. 8

III. Transition Lesson Structure p. 10

IV. Unit One Pacing Guide p. 11

V. Pacing Calendar p. 17

VI. Assessment Framework p. 20

VII. Transition Guide References p. 22

VIII. PARCC Assessment Evidence/Clarification Statements

p. 23

IX. Connections To Mathematical Practices p. 25

X. Potential Student Misconceptions p. 27

XI. Chapter Quizzes p. 30

XII. Resources p. 36

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Unit Overview

Unit 2: Chapters 7-8, 12, 13, 14In this Unit Students will learn how to count, read and write numbers within 20. (Chapter 7) learn to recognize the numbers 11 to 20 as 1 group of ten and particular numbers of ones

(Chapter 7) compare numbers using the concepts of greatest and least (Chapter 7) recognize and make increasing and decreasing number patterns (Chapter 7) learn more strategies for addition and subtraction as they solve problems that include numbers

between 10 and 20. (Chapter 8) Use the concepts of place value when they add or subtract by grouping the two-digit number as a

10 and ones. (Chapter 8)

Count, compare and order numbers to 40 (Chapter 12) utilize the standard vertical form for addition and subtraction of numbers to 40 (Chapter 13) use place value charts to correctly align the digits and to record the regrouping process. (Chapter 13) learn and apply strategies to do addition and subtraction mentally (Chapter 14)

Essential Questions

How are number words and numerals connected to the quantities they represent?How do we use place value?How can I apply counting skills to identify the value for a category?What does it look like to count, compare and order numbers to 40?How can a place-value chart help with determining number patterns?What does it mean to align the digits of a number in a place value chart to record regrouping?How can the Associative Property of Addition and number bonds help in adding three 1-digit numbers?Why are doubles facts helpful with mental math?

Enduring Understandings

Pictorial representations of concrete objects can help when counting to 20.The numbers from 10-19 are 1 group of ten and particular number of ones.Strategies for adding and subtracting are grouping into a ten and ones, number bonds, and using doubles facts. Numbers can be compared using words like greater than, more than, less than.Whole numbers can be added and subtracted with or without regrouping.Number bonds help you to add and subtract mentally.

Common Core State Standards

1.NBT.1Count 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.

Count on from a number ending at any number up to 120. Recognize and explain patterns with numerals on a hundreds chart. Understand that the place of a digit determines its value. For example, students recognize that 24

is different from and less than 42.) Explain their thinking with a variety of examples. Read and write numerals to 120.

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Students extend the range of counting numbers, focusing on the patterns evident in written numerals. This is the foundation for thinking about place value and the meaning of the digits in a numeral. Students are also expected to read and write numerals to 120.

l.NBT.2a 10 Can be thought of as a bundle of ten ones – called a “ten.”

Given objects such as counters, linking cubes, or ten frames, students bundle or group 10 ones to make a ten.

Develop vocabulary to refer to a group of 10 as 1 ten. Differentiate between 1 ten (a bundle) and 10 ones.

Students begin to unitize or consider 10 ones as a group or unit called a ten. Rather than seeing 10 individual cubes, they can link those cubes and make a group of 1 ten.

1.NBT.2bThe numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Students build on previous work in kindergarten (K.NBT.A.1) where they composed and decomposed numbers from 11 to 19 into 10 ones and some more ones. This standard expects that students will understand that the 10 ones, from their previous experiences, are now thought of as a bundle or group of 10. It is a unit, that is, 1 ten. Through experiences using a variety of materials such as ten frames, bundling straws, and linking cubes, students see a teen number, such as 16, as 1 ten plus 6 ones. Given a number of objects between 11 and 19, group them into 1 group of ten and some ones. Describe the grouping, using place value language.

1.NBT.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Once students show an understanding of place value for tens and ones, they begin to compare two numbers by determining the number of tens and the number of ones in each number. After experiences with comparing using concrete materials, including ten frames and place value charts, students move to the hundreds chart and number lines. They generalize that the number with the most tens is greater. If the number of tens is the same, the number with more ones is greater. Comparative language including greater than, more than, fewer than, equal to, and same as is developed. When students become facile with using appropriate vocabulary, the mathematical symbols should be introduced.

Use concrete materials such as objects on place value charts, tens frames, hundreds chart, and number lines to compare two 2-digit numbers.

Describe the comparison using terms including greater than, more than, less than, fewer than, equal to, and same as.

Justify their reasoning as they compare numbers. Compare two 2-digit numbers written as numerals. Use the mathematical symbols <, >, and = to represent comparisons symbolically.

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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

Students begin to develop understanding and skill with adding beyond the basic facts through the use of concrete representations. They progress to making generalizations and developing their own strategies for adding one- and two-digit numbers.

Making groups of ten and using place value charts should be extended to working with two addends.

Include problems that provide a context for addition as often as possible. Equations should be written both horizontally and vertically.

Encourage students to make estimates before adding to determine if their answers are reasonable.

It is important to remember that the goal of this standard is to have students develop strategies and make sense of adding one-and two-digit numbers.

Model addition examples with sums to 100 using concrete materials, pictures, and lastly numerals. Use mental computation strategies to develop conceptual understanding and number sense around

adding one-and two-digit numbers.Record addition examples accurately using both vertical and horizontal formats.

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.

This standard builds on students’ work with place value and requires them to understand and apply the concept of ten by mentally finding 10 more or 10 less. Use a variety of materials and strategies to add or subtract 10 from a number in the range of 1 to

100. Explain their reasoning using place value understanding and patterns on the hundreds chart. Mentally calculate to find 10 more or 10 less than a given number.

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 subtractions; relate the strategy to a written method and explain the reasoning used.

The expectation of this standard is for students to subtract multiples of 10 from greater multiples of 10, using understanding of subtraction and a variety of strategies. Connections among concrete, pictorial, and eventually written equations should be explicit. Use a variety of materials and strategies to subtract groups of ten from more tens. Once students

can successfully describe their work with concrete materials, move to pictures and then to words. Look for and describe patterns they find as they work with various representations. Explain their reasoning using place value understanding and patterns on the hundreds chart. Calculate subtracting multiples of 10 from multiples of 10 both mentally and using written

equations.

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1.OA.1Use 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.

Describe what is happening in the problem Represent each problem situation using concrete materials. Explain their reasoning to partners, in small groups, and to the class. Compare and discuss what is similar and what is different in various problems. Represent their thinking using objects, pictures, number lines, hundreds charts, words, and

numbers. Develop appropriate vocabulary to describe less than, fewer than, and more than situations. Use and explain meaningful strategies to add the numbers in the problem including counting on,

counting back, making groups of 10, and finding missing addends. Begin to write equations to represent their work. Identify what they are looking for in each problem situation.

Students explore solutions to problems using materials such as counte3rs and five and te3n frames to model various situations. They develop understanding of each problem situation over time.

1.OA.3 Apply properties of operations as strategies to add and subtract.

Use representations to solve addition and subtraction examples. Describe patterns and make generalizations. Explain their reasoning to others. Write equations for the examples they have modeled. Solve problems that use these properties.

Students explore and use patterns they see to begin to develop an understanding of important properties of addition and subtraction.

Commutative Property of Addition Associative Property of AdditionThe order of the addends does not change the sum.For example, if8 + 2 = 10 is known, then2 + 8 = 10 is also known.

The grouping of the 3 or more addends does not affect the sum.For example, when adding 2 + 6 + 4, the sum from adding the first two numbers first (2 + 6) and then the third number (4) is the same as if the second and third numbers are added first (6 + 4) and then the first number (2). The student may note that 6+4 equals 10 and add those two numbers first before adding 2. Regardless of the order, the sum remains 12.

1.OA.4 Understand subtraction as an unknown-addend problem.

Use representations to model related addition and subtraction facts using objects, pictures, numbers, and words.

Identify parts of addition and subtraction equations using the terms addend, missing addend, and total.

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Explain their reasoning to the teacher and to classmates Use the relationship between addition and subtraction to practice basic facts.

Given change unknown problem situations, students begin to understand the relationship between addition and subtraction. Students often find learning subtraction facts to be more challenging than learning addition facts. Thinking about subtraction as finding a missing addend helps students connect what they don’t know to what they do know and to begin to work with subtraction facts as part of a fact family. This strategy is known as the think addition strategy for learning subtraction facts. Although there are other strategies for learning subtraction facts, the think addition strategy reinforces both addition and subtraction facts.

1.OA.5Relate counting to addition and subtraction

Use a variety of materials to continue to work on counting strategies to find sums and differences of basic facts through sums of 10.

Explain their thinking using a counting strategy for finding the answer to an addition or subtraction fact with sums to 10.

Look for patterns as they use counting strategies, including for which facts counting is efficient.

Counting All (addition): The student counts out fifteen counters. The student adds two more counters. The student then counts all of the counters starting at 1 (1, 2, 3, 4,…14, 15, 16, 17) to find the total amount.

Counting On (addition): Holding 15 in her head, the student holds up one finger and says 16, then holds up another finger and says 17. The student knows that 15 + 2 is 17, since she counted on 2 using her fingers.

Counting All (subtraction): The student counts out twelve counters. The student then removes 3 of them. To determine the final amount, the student counts each one (1, 2, 3, 4, 5, 6, 7, 8, 9) to find out the final amount.

Counting Back (subtraction): Keeping 12 in his head, the student counts backwards, “11” as he holds up one finger; says “10” as he holds up a second finger; says “9” as he holds up a third finger. Seeing that he has counted back 3 since he is holding up 3 fingers, the student states that 12 – 3 = 9.

1.OA.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums

Use a variety of materials to develop understanding of strategies in adding and subtracting numbers with sums to 10.

Explain their strategy for finding the answer to an addition or subtraction fact with sums to 10, using objects, pictures, words, and numbers. Students should use strategies that are efficient and make sense to them. Not all students will use the same strategy.

Demonstrate fluency for addition and subtraction facts with sums to 10. Extend use of strategies to facts with sums to 20, using concrete, pictorial, and symbolic

representations. Explain their thinking for extended facts, using objects, pictures, words, and numbers.

As students become comfortable with counting on strategies they should begin to have opportunities

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to us other strategies so they do not become dependent on counting, which beyond adding or subtracting 1 or 2 is inefficient.Students need experiences with physical counters and ten frames to develop conceptual understanding of strategies prior to skill drill, and practice. Although fluency requires accuracy with reasonable speed (about 3 seconds per fact), it is best reached with a foundation of conceptual understanding and efficient strategies. Premature drill and practice does not produce fluency.

1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false

Transition from the use of concrete objects that represent equations to the use of mathematical symbols including numerals, operational symbols (+, -), and the equal sign (=).

After writing equations, justify their thinking, using concrete materials or words to show that both sides of the equation show the same amount.

Write equations in all orients. Given a variety of correct and incorrect equations, students identify which are true and which are

false and justify their thinking.

In order to determine whether an equation is true or false, First Grade students must first understand the meaning of the equal sign. This is developed as students in Kindergarten and First Grade solve numerous joining and separating situations with mathematical tools, rather than symbols. Once the concepts of joining, separating, and “the same amount/quantity as” are developed concretely, First Graders are ready to connect these experiences to the corresponding symbols (+, -, =). Thus, students learn that the equal sign does not mean “the answer comes next”, but that the symbol signifies an equivalent relationship that the left side ‘has the same value as’ the right side of the equation. When students understand that an equation needs to “balance”, with equal quantities on both sides of the equal sign, they understand various representations of equations, such as:• an operation on the left side of the equal sign and the answer on the right side (5 + 8 = 13)• an operation on the right side of the equal sign and the answer on the left side (13 = 5 + 8)• numbers on both sides of the equal sign (6 = 6)• operations on both sides of the equal sign (5 + 2 = 4 + 3).Once students understand the meaning of the equal sign, they are able to determine if an equation is true (9 = 9) or false (9 = 8).

1.OA.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers

After solving various problems using concrete materials, write equations to represent their work symbolically.

Solve for the unknown in various positions in addition and subtraction equations. Explain how they found the unknown value in an equation.

First Graders use their understanding of and strategies related to addition and subtraction as described in 1.OA.4 and 1.OA.6 to solve equations with an unknown. Rather than symbols, the unknown symbols are boxes or pictures.

M : Major Content S: Supporting Content A : Additional Content

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MIF Lesson StructureLESSON STRUCTURE RESOURCES COMMENTS

Chapter OpenerAssessing Prior Knowledge

The Pre Test serves as a diagnostic test of readiness of the upcoming chapter

Teacher MaterialsQuick CheckPreTest (Assessm’t Bk)Recall Prior Knowledge

Student MaterialsStudent Book (Quick Check); Copy of the Pre Test; Recall prior Knowledge

Recall Prior Knowledge (RPK) can take place just before the pre-tests are given and can take 1-2 days to front load prerequisite understanding

Quick Check can be done in concert with the RPK and used to repair student misunderstandings and vocabulary prior to the pre-test ; Students write Quick Check answers on a separate sheet of paper

Quick Check and the Pre Test can be done in the same block (See Anecdotal Checklist; Transition Guide)

Recall Prior Knowledge – Quick Check – Pre Test

Direct Involvement/EngagementTeach/Learn

Students are directly involved in making sense, themselves, of the concepts – by interacting the tools, manipulatives, each other, and the questions

Teacher Edition5-minute warm upTeach; Anchor Task

TechnologyDigi

OtherFluency Practice

The Warm Up activates prior knowledge for each new lesson

Student Books are CLOSED; Big Book is used in Gr. K

Teacher led; Whole group Students use concrete manipulatives to

explore concepts A few select parts of the task are explicitly

shown, but the majority is addressed through the hands-on, constructivist approach and questioning

Teacher facilitates; Students find the solution

8

DIRECT ENGAGEMENT

PRE TEST

Guided Learning and PracticeGuided Learning

Teacher EditionLearn

TechnologyDigiStudent BookGuided Learning PagesHands-on Activity

Students-already in pairs /small, homogenous ability groups; Teacher circulates between groups; Teacher, anecdotally, captures student thinking

Small Group w/Teacher circulating among groupsRevisit Concrete and Model Drawing; ReteachTeacher spends majority of time with struggling learners; some time with on level, and less time with advanced groupsGames and Activities can be done at this time

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Independent Practice

A formal formative assessment

Teacher EditionLet’s PracticeStudent BookLet’s PracticeDifferentiation OptionsAll: WorkbookExtra Support: ReteachOn Level: Extra PracticeAdvanced: Enrichment

Let’s Practice determines readiness for Workbook and small group work and is used as formative assessment; Students not ready for the Workbook will use Reteach. The Workbook is continued as Independent Practice.Manipulatives CAN be used as a communications tool as needed.Completely IndependentOn level/advance learners should finish all workbook pages.

Extending the Lesson Math JournalProblem of the LessonInteractivitiesGames

Lesson Wrap Up Problem of the LessonHomework (Workbook , Reteach, or Extra Practice)

Workbook or Extra Practice Homework is only assigned when students fully understand the concepts (as additional practice)Reteach Homework (issued to struggling learners) should be checked the next day

End of Chapter Wrap Up and Post Test

Teacher EditionChapter Review/TestPut on Your Thinking CapStudent WorkbookPut on Your Thinking CapAssessment BookTest Prep

Use Chapter Review/Test as “review” for the End of Chapter Test Prep. Put on your Thinking Cap prepares students for novel questions on the Test Prep; Test Prep is graded/scored.The Chapter Review/Test can be completed Individually (e.g. for homework) then

reviewed in class As a ‘mock test’ done in class and doesn’t

count As a formal, in class review where teacher

walks students through the questions

Test Prep is completely independent; scored/gradedPut on Your Thinking Cap (green border) serve as a capstone problem and are done just before the Test Prep and should be treated as Direct Engagement. By February, students should be doing the Put on Your Thinking Cap problems on their own.

GUIDED LEARNINGINDEPENDENT PRACTICE

ADDITIONAL PRACTICE

POST TEST

TRANSITION LESSON STRUCTURE (No more than 2 days) Driven by Pre-test results, Tran

Transition Guide Looks different from the typical daily lesson

Transition Lesson – Day 1

Objective:

CPA Strategy/Materials Ability Groupings/Pairs (by Name)

10

Task(s)/Text Resources Activity/Description

11

MIF Pacing Guide

Activity Description CCSS Time Lesson NotesPre-Test Ch. 7

Count and write numbers 0 to 20

Counting on

45min. Differentiate: Assign instructional groups based on results.

Chapter Opener: Numbers to 20

Big Idea: Count, compare, and order numbers to 20.

1.NBT.11.NBT.2a 1.NBT.2b

45 min.

7.1 Counting to 20

Count on from 10 to 20.

Read and write 11 to 20 in numbers and words.

1.NBT.11.NBT.2a 1.NBT.2b

1 day

7.2 Place Value Use a place-value chart to show numbers up to 20.

Show objects up to 20 as tens and ones.

1.NBT.11.NBT.2a 1.NBT.2b

1 day

7.3 Comparing Numbers

Compare numbers to 20. 1.NBT.2a 1.NBT.2b

1 day

7.4 Making Patterns and Ordering Numbers

Order numbers by making number patterns.

1.NBT.11.NBT.2a 1.NBT.2b

1 day

Chapter 7 Quiz Found on District Math Curriculum Website

45 min.

Put On Your Thinking Cap

Thinking Skill Analyzing patterns

and relationships.Problem Solving Strategy

Look for patterns.

CC.K-12.MP.1 CC.K-12.MP.2CC.K-12.MP.8

45 min.

Review Day: Ch. 1- 4, 7

2 days Math Workstations

Ch. 7Test Prep

45 min.

Ch. 7 Test Prep:Extended Response Questions

45 min. Authentic Assessment Score with the rubric attached below

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Activity Description Common Core Standards

Time Lesson Notes

Pre-Test Ch. 8

Represent addition stories with small whole numbers

Applying the concepts of part-whole and number bonds in the addition and subtraction of numbers to 10

½ day45 min.

Differentiate: Assign instructional groups based on results.

Chapter Opener: Addition and Subtractions Facts to 20

Big Idea: Different strategies can be use dot add and subtract.

1.OA.11.OA.3

½ day45 min.

8.1 Ways To Add Use different strategies to add 1- and 2-digit numbers.

1.OA.6 1.OA.71.OA.8

3 days Day 1: ST: 201-203SW: 197-202Day 2:ST: 204-205SW: 203-204Day 3:ST: 206-208SW: 205-208

8.2 Ways to Subtract

Subtract a 1-digit from a 2-digit number with and without regrouping.

1.OA.4 1.OA.6 1.OA.71.OA.8

2 days Day 1: ST: 209-212

Day 2:ST: 213-214SW: 209-216

Ch. 8 Quiz Found on district math curriculum website

½ day45 min.

8.3 Real World Problems

Solve real-world problems. 1.OA.1 -7

1 day S. Text: 215-220S. Workbook:217-218

Put On Your Thinking Cap

Thinking Skills and Problem Solving Strategies

1.OA.3

1 day

Ch.8 Test Prep ½ day45 min

Math Workstations

Review Day: Ch. 1- 4, 7-8

2 days Math Workstations

Ch. 8 Test Prep: Extended

½ day45 min

Authentic Assessment Scored with rubric

13

Responses Math Workstations

Activity Description Common Core Standards

Time Lesson Notes

Pre-Test Ch. 12

Count and write numbers 1 to 20

Adding and subtracting Making a ten strategy Compare and order

numbers to 20 Number patterns with

numbers up to 20

½ day45 min.

Differentiate: Assign instructional groups based on results.

Chapter Opener: Numbers to 40

Big Idea: Count, compare, and order numbers from 1 to 40.

1.NBT.11.NBT.2

½ day45 min.

12.1 Counting to 40

Count on from 21 to 40. Read and write 21 to 40 in

numbers and word.

1.NBT.1 1.NBT.2a 1.NB.2c 1.OA.5 1.OA.8

1 day

12.2 Place Value Use a place-value chart to show numbers up to 40.

Show objects up to 40 as tens and ones.

1.NBT.11.NBT.2a 1.NB.2c 1.OA.8

1 day

12.3 Comparing, Ordering and Patterns

Compare numbers to 40. Order numbers to 40. Find the missing numbers

in a number pattern.

1.NBT.11.NBT.2a1.NBT.3 1.OA.8

1 day

Ch. 12 Quiz Found on district math curriculum website

½ day45 min.

Put On Your Thinking Cap

Thinking Skills Analyzing parts and whole Sequencing ComparingProblem Solving Strategies Look for patterns Use before-and-after

concepts

½ day45 min.

Ch. 12 Test Prep Reinforce and consolidate chapter skills and concepts

½ day45 min.

Math Workstations

Review Day: Ch. 1- 4, 7-8, 12

2 days Math Workstations

Ch. 12 Test Prep:Extended

½ day45 min.

Authentic Assessment Score with rubric

14

Responses

Activity Description CCSS Time Lesson NotesPre-Test Ch. 13

Represent addition and subtraction stories

Place value: 0 to 40

½ day45 min.

Differentiate: Assign instructional groups based on results.

Chapter Opener: Addition and Subtraction to 40

Big Idea: Whole numbers can be added and subtracted with or without regrouping.

1.OA.6 ½ day45 min.

13.1 Addition Without regrouping

Add a 2-digit number and a 1-digit number without regrouping.

1.NBT.4 1.OA.71.OA.8

1 day

13.2 Addition With regrouping

Add a 2-digit number and a 1-digit number with regrouping.

1.NBT.2.a1.NBT.41.OA.8

2 days Day 1:ST: 94-97

Add two 2-digit numbers without regrouping.

Day 2: ST:98-100SW: 65-68

13.3 Subtraction Without Regrouping

Subtract a 1-digit number from a 2-digit number without regrouping

1.NBT.61.OA.41.OA.7

1 day

Subtract a 2-digit number from a 2-digit number without regrouping.

13.4 Subtraction With Regrouping

Subtract a 1-digit number from a 2-digit number with regrouping;

1.NBT.2.a1.OA.41.OA.71.OA.8

2 days Day 1:ST: p. 111-114

Subtract a 2-digit number from a 2-digit number with regrouping.

Day 2:ST: p. 115-118SW: p. 73-76

13.5 Adding Three Numbers

Add three 1-digit numbers. 1.OA.3, 6-8 1 day

13.6 Real World Problems

1.OA.2, 7-8 1 day

Ch. 13 Quiz ½ day45 min.

Put On Your Thinking Cap

Thinking Skill & Problem Solving Strategies

1.OA.7 ½ day 45 min.

Ch. 13 Test Prep ½ day45 min.

Math Workstations

Review Day: Ch. 1- 4, 7-8, 12-13

2 days Math Workstations

15

Ch. 13 Test Prep:Extended Responses

½ day45 min.

Authentic Assessment Score with rubricMath Workstations

Activity Description CCSS Time Lesson NotesPre-Test Ch. 14

Addition and subtraction facts

The part-whole concept in number bonds

Place values of numbers to 20

½ day45 min.

Differentiate: Assign instructional groups based on results.

Chapter Opener: Mental Math Strategies

Big Idea: Number bonds help you to add and subtract mentally.

1.OA.31.OA.41.OA.8

½ day45 min.

14.1 Mental Addition

Mentally add 1-digit numbers.

Mentally add a 1-digit number to a 2-digit number.

Mentally add a 20-digit number to tens.

1.NBT.51.OA.31.OA.6

2 days Day 1:ST: p. 138-140

Day 2:ST: p. 141-142SW: p. 99-102

14.2 Mental Subtraction

Mentally subtract 1-digit numbers.

Mentally subtract a 1-digit number from a 2-digit number.

Mentally subtract tens from a 2-digit number.

1.NBT.51.OA.31.OA.61.OA.8

2 days Day 1:ST: p. 143-146

Day 2:ST: p. 147-149SW: p. 103-104

Ch. 14 Quiz Mid chapter assessment ½ day45 min.

Put On Your Thinking Cap

Thinking Skills Identifying patterns and

relationshipsProblem Solving Strategies Make a systematic list Work backward

1.OA.3 ½ day45 min.

Ch. 14 Test Prep 1 day Math WorkstationsReview Day: Ch. 1- 4, 7-8, 12-14

2 days Math Workstations

Ch. 14 Test Prep: Extended

½ day45 min.

Authentic Assessment Score with rubric

16

Responses Math Workstations

Pacing CalendarNOVEMBER

Monday Tuesday Wednesday Thursday Friday2 3 4 5

NJEA ConventionDistrict Closed

6NJEA ConventionDistrict Closed

9 10 11 12 13

16Chapter 7 Pre-TestChapter Opener

177.1

187.2

197.3

207.4

23Ch. 7 Quiz

Put On Your Thinking Cap

24Review Day: Ch. 1- 4, 7Math Workstations

25Ch. 7 Test Prep

Math Workstations

26Thanksgiving RecessDistrict Closed

27 Thanksgiving RecessDistrict Closed

17

30Ch. 7 Test Prep Extended ResponsesMath Workstations

DECEMBER Monday Tuesday Wednesday Thursday Friday

1Review Day: Ch. 1- 4, 7Math Workstations

2Chapter 8 Pre-TestChapter Opener

38.1

48.1

78.1

88.2

98.2

108.3

11Ch. 8 Quiz

Math Workstations

14Review Day: Ch. 1- 4, 7-8Math Workstations

15Ch. 8 Test Prep

Math Workstations

16Ch. 8 Test Prep Extended Responses

Math Workstations

17Review Day: Ch. 1- 4, 7-8

Math Workstations

18Chapter 12Pre-TestChapter Opener

2112.1

2212.2

23Review Day: Ch. 1- 4, 7-8, 12Math Workstations

24Holiday RecessDistrict Closed

25Holiday RecessDistrict Closed

18

28Holiday RecessDistrict Closed

29Holiday RecessDistrict Closed

30Holiday RecessDistrict Closed

31Holiday RecessDistrict Closed

JANUARY Monday Tuesday Wednesday Thursday Friday

1Holiday RecessDistrict Closed

412.3

5Ch. 12 Quiz

Math Workstations

6Review Day: Ch. 1- 4, 7-8, 12Math Workstations

7Ch. 12 Test Prep

Math Workstations

8Ch. 12 Test PrepExtended Response

Math Workstations

11Chapter 13Pre-TestChapter Opener

1213.1

1313.2

1413.2

1513.3

18MLK BirthdayDistrict Closed

1913.4

2013.4

2113.5

2213.6

19

25Ch. 13 Quiz

Math Workstations

26Review Day: Ch. 1- 4, 7-8, 12-13

Math Workstations

27Ch. 13 Test Prep

Math Workstations

28Ch. 13 Test PrepExtended Response

Math Workstations

29Review Day: Ch. 1- 4, 7-8, 12-13

Math Workstations

FEBRUARYMonday Tuesday Wednesday Thursday Friday

1

Chapter 14Pre-TestChapter Opener

2

4.1

3

4.1

4

4.2

5

4.2

8 9 10 11 12

15 16 17 18 19

22 23 24 25 26

20

Assessment Est. Time Format Graded ?Pre Test 7 45 min Individual Scored for data analysisChapter 7 Quiz 45 min Individual Out of 10

Chapter 7 Test Prep 45 min Individual

Possible 23 pointsQuestion # Points1-8, 12-14 111, 15 210 39 5

Authentic Assessment: Ch. 7 Test Prep: Extended Responses 45 min Individual See attached rubric below

Pre Test 8 45 min Individual Scored for data analysis

Chapter 8 Quiz 45 min Individual Out of 10

Chapter 8 Test Prep 45 min Individual

Possible 18 pointsQuestion # Points1-5, 10-14 16-9 25, 7-8 1

Authentic Assessment: Ch. 8 Test Prep: Extended Responses 45 min Individual See attached rubric below

Pre Test 12 45 min Individual Scored for data analysisChapter 12 Quiz 45 min Individual Out of 10

Chapter 12 Test Prep 45 min Individual

Possible 22 pointsQuestion # Points1 52-12, 14-17 113 2

Authentic Assessment: Ch.12 Test Prep: Extended Responses 45 min Individual See attached rubric below

Pre Test 13 45 min Individual Scored for data analysisChapter 13 Quiz 45 min Individual Out of 10

Chapter 13 Test Prep 45 min IndividualPossible pointsQuestion # Points1-13 1

Authentic Assessment: Ch.13 Test Prep: Extended Responses 45 min Individual See attached rubric below

Pre Test 14 45 min Individual Scored for data analysis21

Chapter 14 Quiz 45 min Individual Out of 10

Chapter 14 Test/Review 45 min IndividualPossible 20 pointsQuestion # Points1-20 1

Authentic Assessment: Ch.14 Test Prep: Extended Responses 45 min Individual See attached rubric below

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Authentic Assessment Rubric

Got ItEvidence shows that the student essentially has the target concept or big math idea.

Not There YetStudent shows evidence of a major misunderstanding, incorrect concepts or procedure, or a failure to engage in the task.

PLD Level 5: 100%Distinguished command

PLD Level 4: 89%Strong Command

PLD Level 3: 79%Moderate Command

PLD Level 2: 69%Partial Command

PLD Level 1: 59%Little Command

Clearly constructs and communicates as a complete response based on explanations/reasoning using the: Properties of operations Relationship between

addition and subtraction Understanding of base ten

system grade appropriate strategies precise use of math

vocabularyResponse includes an efficient and logical progression of mathematical reasoning and understanding.

Clearly constructs and communicates a complete response based on explanations/reasoning using the: Properties of operations relationship between addition

and subtraction grade appropriate strategies use of math vocabularyResponse includes a logical progression of mathematical reasoning and understanding.

Constructs and communicates a complete response based on explanations/reasoning using the: properties of operations relationship between addition

and subtraction understanding of base ten

system grade appropriate strategiesResponse includes a logical but incomplete progression of mathematical reasoning and understanding. Contains minor errors.

Constructs and communicates an incomplete response based on student’s attempts of explanations/reasoning using the: properties of operations relationship between addition

and subtraction understanding of base ten

system grade appropriate strategiesResponse includes an incomplete or illogical progression of mathematical reasoning and understanding.

The student work shows little understanding of the mathematics. Student attempts to construct and communicates a response using the: properties of operations relationship between addition

and subtraction understanding of base ten

system grade appropriate strategiesResponse includes limited evidence of the progression of mathematical reasoning and understanding.

5 points 4 points 3 points 2 points 1 point

PLD Genesis ConversionRubric Scoring

PLD 5 100PLD 4 89PLD 3 79PLD 2 69PLD 1 59

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Unit 2: Transition Guide References:

Chapter 7 Objective Additional Reteach Support

Additional Extra Practice

Support

Kindergarten Progression

Lesson 1 Counting to 20 1A, pp. 109-114 1A, pp. 107-112 Count and write numbers 0 to 20 (Chaps. 1, 2, 4 and 6).

Lesson 2 Place Value 1A, pp. 115-118 1A, pp. 113-114Lesson 3 Comparing

Numbers1A, pp. 119-126 1A, pp. 115-116

Chapter 8 Objective Additional Reteach Support

Additional Extra Practice

Support

Kindergarten Progression

Lesson 1 Ways to add 1A, pp. 133-142 1A, pp. 123-130 Represent addition stories with small whole numbers. (Chap. 17)

Lesson 2 Ways to subtract 1A, pp. 143-148 1A, pp.131-136Lesson 3 Real-world

problems1A, pp.149-152 1A, pp.137-138

Chapter 12 Objective Additional Reteach Support

Additional Extra Practice

Support

Kindergarten Progression

Lesson 1 Counting to 40 1B, pp.31-36 1B, pp. 33-34 Count and write numbers 0-20. (Chaps. 1,2,4, and 6)

Lesson 2 Place Value 1B, pp. 37-40 1B, pp.35-36Lesson 3 Comparing,

Ordering and Patterns

1B, pp. 41-50 1B, pp. 37-42

Chapter 13 Objective Additional Reteach Support

Additional Extra Practice

Support

Kindergarten Progression

Lesson 1 Addition without Regrouping

1B, pp.51-60 1B, pp.45-48 Represent addition stories with small whole numbers. (Chap. 17)

Lesson 2 Addition With Regrouping

1B, pp.61-68 1B, pp.49-52

Lesson 3 Subtraction Without Regrouping

1B, pp.69-76 1B, pp.53-56

Lesson 4 Subtraction With Regrouping

1B, pp.77-84 1B, pp.57-60

Chapter 14 Objective Additional Reteach Support

Additional Extra Practice

Support

Kindergarten Progression

Lesson 1 Mental Addition 1B, pp.93-100 1B, pp.69-70 Find parts and wholes in addition and subtraction stories. (Chaps. 17 and 18)

Lesson 2 Mental Subtraction

1B, pp.101-104 1B, pp.71-72

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PARCC Assessment Evidence/Clarification StatementsCCSS Evidence Statement Clarification Math

Practices

1.OA.A.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 unknown in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

i) Tasks should include all problem situations and all of their subtypes and language variants. Mastery is expected in “Add To” and “Take From” – Result and Change Unknown Problems, “Put Together/Take Apart” Problems, “Compare” – Difference Unknown, Bigger Unknown (more version) and Smaller Unknown (fewer version) Problems (for more information see CCSS Table 1, p. 88 and OA Progression, p. 9.)

ii) Interviews (individual or small group) are used to assess mastery of different problem types.

MP.1, MP.4

1.OA.B.3

Apply properties of operations as strategies to add and subtract. 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.

i) Tasks should not expect students to know the names of the properties.

ii) Interviews (individual or small group) should target students’ application of properties of operations to add and subtract.

MP.7, MP.8

1.OA.D.7

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6=6, 7=8-1, 5+2=2+5, 4+1=5+2.

i) Interviews (individual or small group) should target students’ understanding of the equal sign.

MP.7, MP.8

1.OA.D.8

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8+?=11, 5=?-3, 6+6=?

i) Interviews (individual or small group) should target students’ thinking strategies for dete3rmining the unknown in an addition or subtraction equation relating 3 whole numbers. Thinking strategies expect3ed in Grade 1 (Level 2 and 3) are defined in 1.OA.6 and in OA Progression (p. 14-17)

MP.7, MP.8

1.NBT.B.2

Understand that 10 can be thought of as a bundle of ten ones – called a “ten”

i) Tasks should focus on the understanding of ten “ones” as a unit of one “ten.”

ii) Interviews (individual or small group) should target this

MP.7, MP.8

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understanding.

1.NBT.2-3

Understand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

i) Tasks should focus on the understanding of numbers from 11 to 19 as composed of one “ten” and some number of “ones.”

ii) Interview (individual or small group)_ should target this understanding.

MP.7, MP.8

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 >, = and <.

i) Tasks should focus on the understanding that the digit in the “tens” place is more important for determining the size of a two-digit number.

ii) Interviews (individual or small group) should target this understanding.

MP.1, MP.2

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.

i) Tasks should focus on the connections among the students’ concrete models/drawings, written numerical work, and explanations in terms of strategies/reasoning.

ii) Interviews (individual or small group) should target these connections.

MP.3, MP.7

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.

i) Tasks should target not only the mental calculation

MP.3, MP.7

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.

i) Tasks should focus on the connections among the computation, strategies used and the explanation of the reasoning. For example, students may explain their reasoning by representing 70-30 with base ten blocks. They may demonstrate and say that 7 tens minus 3 tens is equal to 4 tens using the blocks. Students may also use the relationship between addition and subtraction when they view 70-30 as an unknown addend addition problem and say that 30+ ? = 70 They reason that 4 tens must be added to 30 to make 70 so 70 – 30 = 40.

ii) Interviews should target the connections among the

MP.3, MP.7

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computations, strategies, and reasoning.

Connections to the Mathematical Practices

1

Make sense of problems and persevere in solving themThe problems we encounter in the “real world”—our work life, family life, and personal health—don’t ask us what chapter we’ve just studied and don’t tell us which parts of our prior knowledge to recall and use. To survive and succeed, we must figure out the right question to be asking, what relevant experience we have, what additional information we might need, and where to start. And we must have enough stamina to continue even when progress is hard, but enough flexibility to try alternative approaches when progress seems too hard. What makes a problem “real” is not the context. A good puzzle is not only more part of a child’s “real world” than, say, figuring out how much paint is needed for a wall, but a better model of the nature of the thinking that goes with “real” problems: the first task in a crossword puzzle or Sudoku is to figure out where to start. A satisfying puzzle is one that you don’t know how to solve at first, but can figure out.

Mathematical Practice #1 asks students to develop that “puzzler’s disposition” in the context of mathematics. Teaching can certainly include focused instruction, but students must also get a chance to tackle problems that they have not been taught explicitly how to solve, as long as they have adequate background to figure out how to make progress. Young children need to build their own toolkit for solving problems, and need opportunities and encouragement to get a handle on hard problems by thinking about similar but simpler problems, perhaps using simpler numbers or a simpler situation.

2

Reason abstractly and quantitativelyStudents are asked to be able to translate a problem situation into a number sentence (with or without blanks) and, after they solve the arithmetic part (any way), to be able to recognize the connection between all the elements of the sentence and the original problem. It involves making sure that the units in problems make sense.

3

Construct viable arguments and critique the reasoning of othersTo “construct a viable argument,” let alone understand another’s argument well enough to formulate and articulate a logical and constructive “critique,” depends heavily on a shared context, especially in the early grades. Given an interesting task, they can show their method and “narrate” their demonstration. Rarely does it make sense to have them try to describe, from their desks, an articulate train of thought, and even more rarely can one expect the other students in class to “follow” that lecture any better than—or even as well as—they’d follow the train of thought of a teacher who is just talking without illustrating. The standard recognizes this fact when it says “students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.” The key is not the concreteness, but the ability to situate their words in context—to show as well as tell.

To develop the reasoning that this standard asks children to communicate, the mathematical tasks we give need depth. Problem that can be solved with only one fairly routine step give students no chance to assemble a mental sequence or argument, even non-verbally. The inclination to “justify their conclusions” also depends on the nature of the task: certain tasks naturally pull children to explain; ones that are too simple or routine feel unexplainable. The way children learn language, including mathematical and academic language, is by producing it as well as by hearing it used. When students are given a suitably challenging task and allowed to work on it together, their natural drive to communicate helps develop the academic language they will need in order to “construct viable arguments and critique the reasoning of others.”.

4

Model with mathematicsThe intent of this standard is not to pretend that “problems arising in [the] everyday life” of an adult would be of educational value, let alone interest, to a child. Children, themselves, pay closest attention to learning how the world around them works. What we call “play” is their work: they experiment, tinker, push buttons, say and ask whatever comes to mind, all in an attempt to see what happens. And their curiosity naturally includes ideas we call mathematics: thinking about size, shape and fit, quantity, number.

One intent of this standard is to ensure that children see, even at the earliest ages, that mathematics is not just a collection of skills whose only use is to demonstrate that one has them. Even puzzles suffice for that goal. Another intent is to ensure that the mathematics students engage in helps them see and interpret the world—the physical world, the mathematical world, and the world of their imagination—through a mathematical lens. One way, mentioned in the standard, is through the use of simplifying assumptions and approximations. Children typically find “estimation” pointless, and even confusing, when they can get exact answers, but many mathematical situations do not provide the information needed for an exact calculation.

25

5

Use appropriate tools strategicallyCounters, base-10 blocks, Cuisenaire® Rods, Pattern Blocks, measuring tapes or spoons or cups, and other physical devices are all, if used strategically, of great potential value in the elementary school classroom. They are the “obvious” tools. But this standard also includes “pencil and paper” as a tool, and Mathematical Practice Standard #4 augments “pencil and paper” to distinguish within it “such tools as diagrams, two-way tables, graphs.” The number line and area model of multiplication are two more tools—both diagrammatic representations of mathematical structure—that the CCSS Content Standards explicitly require. So, in the context of elementary mathematics, “use appropriate tools strategically” must be interpreted broadly and sensibly to include many choice options for students.Essential, and easily overlooked, is the call for students to develop the ability “to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.” This certainly requires that students gain sufficient competence with the tools to recognize the differential power they offer; it also requires that their learning include opportunities to decide for themselves which tool serves them best. It also requires curricula and teaching to include the kinds of problems that genuinely favor different tools. It may also require that, from time to time, a particular tool is prescribed—or proscribed—until students develop a competency that would allow them to make “sound decisions” about which tool to use.

6

Attend to precisionThe title is potentially misleading. While this standard does include “calculate accurately and efficiently,” its primary focus is precision of communication, in speech, in written symbols, and in specifying the nature and units of quantities in numerical answers and in graphs and diagrams.

The mention of definitions can also be misleading. Elementary school children (and, to a lesser extent, even adults) almost never learn new words effectively from definitions. Virtually all of their vocabulary is acquired from use in context. Children build their own “working definitions” based on their initial experiences. Over time, as they hear and use these words in other contexts, they refine their working definitions and make them more precise. In mathematics, too, children can work with ideas without having started with a precise definition. With experience, the concepts will become more precise, and the vocabulary with which we name the concepts will, accordingly, carry more precise meanings. Formal definitions generally come last.

Curriculum and teaching must be meticulous in the use of mathematical vocabulary and symbols. With elementary school children, it is generally less reasonable to expect them to “state the meaning of the symbols they choose” in any formal way than to expect them to demonstrate their understanding of appropriate terms through unambiguous and correct use. If the teacher and curriculum serve as the “native speakers” of Clear Mathematics, young students, who are the best language learners around, can learn the language from them.

7

Look for and make use of structureChildren naturally seek and make use of structure. It is one of the reasons why young children may say “foots” or “policemans,” which they have never heard from adults, instead of feet or policemen, which they do hear. They induce a structure for plurals from the vast quantity of words they learn and make use of that structure even where it does not apply. Mathematics has far more consistent structure than our language, but too often it is taught in ways that don’t make that structure easily apparent. Kindergarteners who have no real idea how big “hundred” or “thousand” are (though they’ve heard the words) are completely comfortable, amused, and proud to add such big numbers as “two thousand plus two thousand” when the numbers are spoken, even though children a year older might have had no idea how to do “2000 + 3000” presented on paper. “Standard arithmetic” can be taught with or without attention to pattern. The CCSS acknowledges that students do need to know arithmetic facts, but random-order fact drills rely on memory alone, where patterned practice can develop a sense for structure as well.

8

Look for and express regularity in repeated reasoningA central idea here is that mathematics is open to drawing general results (or at least good conjectures) from trying examples, looking for regularity, and describing the pattern both in what you have done and in the results.The recognition that adding 9 can be simplified by treating it as adding 10 and subtracting 1 can be a discovery rather than a taught strategy. Describing the discovery then becomes a case of “expressing regularity” that was found through “repeated reasoning.”

26

Potential Student Misconceptions

- 1.OA.A.1The vocabulary of comparison situations can cause confusion for students. While the words more than implies addition and fewer than implies subtraction, in comparison situations, that is not always the case. For example: Patty has 16 tickets for the raffle. She has 8 fewer than Marcos. How many tickets does Marcos have? Although the problem includes the word fewer, a student would actually add 16+8 to find the solution. Modeling with concrete objects to use the information by showing Patty’s tickets and 8 more will help students realize that this is actually an addition problem.

- 1.OA.A.2Some students think it is not possible to add more than two numbers. Although they may be familiar with seeing addition equations with three or more addends, they do not write equations with three or more addends.

Students consider composing and decomposing numbers to learn facts, develop computation strategies, and do mental mathematics. The understanding that addition equations can contain more than two addends is important. Once students have had experience working with three addends, using concrete materials and drawings, they should have opportunities to write and solve equations with three or more addends.

- 1.OA.B.3Although subtraction is not commutative, it is important not to contribute to a potential student misconception by saying that you cannot take a larger number from a smaller number. It is appropriate to say that 8 – 5 ≠ 5 – 8. It is possible to take a larger number from a smaller number. The result will be a negative number.

- 1.OA.B.4Students may confuse the order of parts of addition and subtraction equations. Write the terms addend, missing addend, and total on large cards. Write an addition equation on the board and have students identify each part of the equation. Write a related equation with a missing addend and have students repeat identifying each part of the equation with the vocabulary cards. Write the related subtraction facts having students identify each part of the subtraction equation. Discuss what is similar in each equation.

- 1.OA.C.5Watch for students who may double count a number when adding or subtracting. This may occur with physical objects, pictures, or using a hundreds chart. For example, if a student is adding 6+4, she may begin with the 6 (6,7,8,9) with a result of 9 rather than counting on from the 6 (7,8,9,10). The same may happen in subtraction. If a student is counting to subtract 8-5, he may count the 8 as part of the count (8,7.6.5.4) with a result of 4 rather than subtracting from the 8 (7,6,5,4,3) to get the accurate amount. Not only should this be pointed out to students, but it is essential also to provide more explicit experiences with concrete materials in which students are adding on to the given addend or subtracting from the total.

27

- 1.OA.C.6Continue to watch for students who are double counting a number when adding or subtracting.

- 1.OA.D.7Some students may develop the misconception that the equal sign indicates the answer comes next or calls for the action of doing the mathematical operation. Students should have experiences early on that reinforce that the equal sign indicates both sides of the equation represent the same amount. Using a balance scale or picture of a balance scale with the equal sign on the center helps students to understand that the equal sign means both sides are balanced. As teachers model writing equations or give students examples to solve, it is important to repeat that the equal sign means “the same as.” It is appropriate in early experiences using the equal sign to have students read it as “is the same as.” For example, students would read 10 – 7 = 3 as “10 minus 7 is the same as 3.”

- 1.OA.D.8Although students may be able to model problem situations with materials and pictures, the transition to writing equations using symbols may be more difficult for them, particularly when their reasoning requires finding a missing addend. Asking students to explain their reasoning as they solve the problem with materials will help them to connect what they have done with the materials to the symbolic equation. Be sure that students have multiple experiences solving equations in which the unknown is in different positions.

- 1.NBT.A.1It is not expected that students develop an understanding of place value with this standard. However, watch for students who reverse digits in writing the numeral or do not demonstrate an understanding that 21 does not have the same value as 12. When reversals occur, have students model each number, using straws or linking cubes to reinforce the place value of digits and to help students differentiate between numbers.

- 1.NBT.B.2Continue to watch for students who reverse digits. These students need more opportunities to decompose numbers into groups of ten and ones using concrete materials and then to put the items in the correct places on a place value chart. They describe the numbers in terms of tens and ones and then write the numeral below concrete representations.

- 1.NBT.B.3Students who recognize two-digit numbers but do not understand that the position of the digit determines its value need additional work with concrete representations. Give each student a number and ask them to represent that number on their place value chart. They work with a partner to determine which number is greater. They use cards with <, >, or = and put the correct sign between their charts. Only when students show understanding with materials and pictorial representations should they begin to connect those representations to using numerals.

It is important for students to associate the symbols < and > with their real meaning. Rather than use aids such as alligators or Pac-Man, it may help students who confuse the symbols to think that the open end of the symbol is always closest to the greater number and the closed end is always pointed to the lesser number. It is also important to give students opportunities to change the order of the numbers to see how it impacts the symbols and their meaning.

28

- 1.NBT.C.4Students who do not know basic facts may be inaccurate computing with two-digit numbers. As those students continue to work on facts, physical models will help in adding accurately. Be sure that all students have ample experience with adding physical models on place value charts, counting on by benchmark numbers (tens and ones), using a hundreds chart, and using ten frames as appropriate. Make explicit connections among written physical models, strategies, and written formats.

- 1.NBT.C.5Since understanding the concept of 10 more or 10 less leads to understanding additional place value concepts, students who depend on counting or using their fingers have not met this standard. Students who cannot determine 10 more or 10 less than a number from 1 to 100 need more experience with concrete materials, such as linking cubes or bundles of straws. Finding patterns on the hundreds chart is also helpful, but the language can be confusing for some students.

- 1.NBT.C.6Some students may subtract the digits in the tens place but ignore the digits in the ones place. Ask them to describe what they are subtracting in terms of place value. For example, in subtracting 70-40, students should say they are taking 4 tens from 7 tens (or 7 tens minus 4 tens). Have them put concrete models on the place value chart and then subtract or physically remove the 4 tens from the 7 tens. They describe the difference as 3 tens. Ask them how to write 3 tens (30) and how many ones are in that number. They should explain why there are 0 ones and why it is necessary to put the digit 0 in the ones place.

29

Chapter 7 Quiz _____/10

Name ______________________________ Date ________________________

1. There are _______ bananas. 2. There are _______________ pigs.

3. There are _______ cars. 4. There are _______ dvds.

5. There are ____________ leaves.

6. Write 14 in words.

______________________________________

7. Write the number 17 in words.

____________________________________ 8. 15 = 1 ten and __________ ones

9. 19 is ________ tens and 9 ones

10. Write the numbers from least to greatest.

16, 17, 13, 10

30

________, ________, ________, ________

31

Chapter 8 Quiz _____/10Name ______________________________ Date ________________________

1. 6 + 7 = 6 + 6 + 1 6 + 7 = _____

2. Make a 10 to add. Write the numbers that belong in the bond.

3. 8 + 7 = 10 + 5 8 + 7 = __________

4. Make a 10 to add. Write the numbers that belong in the bond.

5. 4 + 5 = ? 4 + 5 = 4 + __________ + 1

6. 6 + 8 = ? 6 + 8 = 6 + _____ + 2

7. 17 – 7 = __________ 8. Make a 10 to subtract. Write the numbers that belong in the bond.

9. 20 – 5 = __________ 10. Write the numbers that belong in the bond.

32

Chapter 12 Quiz _____/10Name ______________________________ Date ________________________

1. ________ is between 29 and 31.

2. _________ comes just before 30.

3. _________ comes just after 37.

4. _________ is between 38 and 40.

5. Write the number twenty-six.

_______________________

6. Write the number thirty-eight.

_________________________

7. 28 in words is _____________________________

8. 39 in words is _______________________________

9. The number is __________ 10. Write the missing number in the place value chart to make fifteen.

33

34

Chapter 13 Quiz _____/10Name ______________________________ Date ________________________1.

2.

3.

4 + 36 = __________4.

5.

6.

7.

8.

9.

____________________

10.

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Chapter 14 Quiz _____/10Name ______________________________ Date ________________________1. Add mentally

7 + 6 = __________

2. Add mentally.

5 + 8 = __________

3. Add mentally.

7 + 8 = __________ + __________ + 1

4. Add mentally.

5 + 6 = 5 + __________ + 1

5. Add mentally.

6 + 9 = __________

6. Add mentally.

27 + 6 = __________7. Add mentally.

5 + 33 = __________

8. Add mentally.

26 + 9 = __________ 9. Add mentally.

22 + 10 = __________

10. Add mentally.

20 + 18 = __________

Extensions and SourcesOnline Resources

36

Think Centralhttps://www-k6.thinkcentral.com/ePC/start.do

Common Core Toolshttp://commoncoretools.me/http://www.ccsstoolbox.com/http://www.achievethecore.org/steal-these-tools

Achieve the Corehttp://achievethecore.org/dashboard/300/search/6/1/0/1/2/3/4/5/6/7/8/9/10/11/12

Manipulatives

http://nlvm.usu.edu/en/nav/vlibrary.htmlhttp://www.explorelearning.com/index.cfm?method=cResource.dspBrowseCorrelations&v=s&id=USA-000http://www.thinkingblocks.com/

Problem Solving Resources

Illustrative Math Project http://illustrativemathematics.org/standards/k8

The site contains sets of tasks that illustrate the expectations of various CCSS in grades K–8 grade and high school. More tasks will be appearing over the coming weeks. Eventually the sets of tasks will include elaborated teaching tasks with detailed information about using them for instructional purposes, rubrics, and student work.

Inside Mathematicshttp://www.insidemathematics.org/index.php/tools-for-teachersInside Mathematics showcases multiple ways for educators to begin to transform their teaching practices. On this site, educators can find materials and tasks developed by grade level and content area.

Engage NY

http://www.engageny.org/video-library?f[0]=im_field_subject%3A19

Sample Balance Math Taskshttp://www.nottingham.ac.uk/~ttzedweb/MARS/tasks/

Georgia Department of Educationhttps://www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspxGeorgia State Educator have created common core aligned units of study to support schools as they implement the Common Core State Standards.

Kindergarten: http://ccgpsmathematicsk-5.wikispaces.com/Kindergarten

1st Grade: http://ccgpsmathematicsk-5.wikispaces.com/1st+Grade

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Formative Assessment : http://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+%28FALs%29

Number Talks and Multi-grade Resources: http://ccgpsmathematicsk-5.wikispaces.com/Number+Talks+and+other+Multi+Grade+Resources

OHIO

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Kindergarten_Math_Model_Curriculum_March2015.pdf.aspx

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Grade_1_Math_Model_Curriculum_March2015.pdf.aspx

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Grade_2_Math_Model_Curriculum_March2015.pdf.aspx

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Grade_3_Math_Model_Curriculum_March2015.pdf.aspx

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Grade_4_Math_Model_Curriculum_March2015.pdf.aspx

http://education.ohio.gov/getattachment/Topics/Ohio-s-New-Learning-Standards/Mathematics/Grade_5_Math_Model_Curriculum_March2015.pdf.aspx

Gates Foundations Tasks

http://www.gatesfoundation.org/college-ready-education/Documents/supporting-instruction-cards-math.pdf

Minnesota STEM Teachers’ Centerhttp://www.scimathmn.org/stemtc/frameworks/721-proportional-relationships

Singapore Math Tests K-12http://www.misskoh.com

Math Score: Math practices and assessments online developed by MIT graduates.http://www.mathscore.com/

Massachusetts Comprehensive Assessment Systemwww.doe.mass.edu/mcas/search

Performance Assessment Links in Math (PALM)

PALM is currently being developed as an on-line, standards-based, resource bank of mathematics performance assessment tasks indexed via the National Council of Teachers of Mathematics (NCTM).http://palm.sri.com/

Mathematics Vision Projecthttp://www.mathematicsvisionproject.org/

38

NCTMhttp://illuminations.nctm.org/

Assessment Resources

o *Illustrative Math: http://illustrativemathematics.org/ o *PARCC: http://www.parcconline.org/samples/item-task-prototypes o NJDOE: http://www.state.nj.us/education/modelcurriculum/math/ (username: model; password:

curriculum)o DANA: http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html o New York: http://www.p12.nysed.gov/assessment/common-core-sample-questions/o *Delaware: http://www.doe.k12.de.us/assessment/CCSS-comparison-docs.shtml

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