Paramount Unified School District Educational Services

Paramount Unified School District Educational Services Grade K – Unit 2 Stage One – Desired Results Unit 2: Compose and Decompose Numbers to 10 In t...
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Paramount Unified School District Educational Services

Grade K – Unit 2 Stage One – Desired Results

Unit 2: Compose and Decompose Numbers to 10 In this unit, Kindergarten students:  decompose and compose numbers up to 10 to reinforce how a whole can be broken into two parts and how two parts can be joined to make a whole.  use the number bond model for composing and decomposing so students begin to understand the relationship between parts and wholes before moving into formal work with addition and subtraction.  begin to conceptualize addition as putting together, or adding to, and subtraction as taking apart, or taking from.

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Unit 2 Overview: Compose and Decompose Numbers to 10 Transfer Goals 1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution. 2) Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience. 3) Construct viable arguments and critique the reasoning of others using precise mathematical language.

Meaning-Making

Standards OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).

Understandings Students will understand that…

Essential Questions Students will keep considering…

 Decomposing numbers builds an understanding of number grouping and promotes fluency

 How can understanding smaller numbers help you to understand larger numbers?  How can we use our knowledge of decomposing numbers to understand 10?

OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

*Counting and Cardinality standards from Unit 1 are revisited throughout Unit 2 and are included in the end of unit assessment.

Acquisition Knowledge Students will know…

Skills Students will be skilled at and able to do the following…

Vocabulary – make, take apart, equal, quantity, total

 Combine smaller numbers to show a larger number  Break larger numbers apart into smaller numbers  Record the composition and decomposition of numbers using drawings  When provided a number from 1 to 9, find the number that makes 10

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Paramount Unified School District

Grade K – Unit 2 Stage Two – Evidence of Learning

Educational Services

Unit 2: Compose and Decompose Numbers to 10 Transfer is a student’s ability to independently apply understanding in a novel or unfamiliar situation. In mathematics, this requires that students use reasoning and strategy, not merely plug in numbers in a familiar-looking exercise, via a memorized algorithm. Transfer goals highlight the effective uses of understanding, knowledge, and skills we seek in the long run – that is, what we want students to be able to do when they confront new challenges, both in and outside school, beyond the current lessons and unit. These goals were developed so all students can apply their learning to mathematical or real-world problems while simultaneously engaging in the Standards for Mathematical Practices. In the mathematics classroom, assessment opportunities should reflect student progress towards meeting the transfer goals. With this in mind, the revised PUSD transfer goals are: 1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution. 2) Effectively communicate orally, in writing, and by using models (e.g., concrete, representational, abstract) for a given purpose and audience. 3) Construct viable arguments and critique the reasoning of others using precise mathematical language. Multiple measures will be used to evaluate student acquisition, meaning-making and transfer. Formative and summative assessments play an important role in determining the extent to which students achieve the desired results in stage one. Formative Assessment

Summative Assessment Aligning Assessment to Stage One

 What constitutes evidence of understanding for this lesson?  Through what other evidence during the lesson (e.g. response to questions, observations, journals, etc.) will students demonstrate achievement of the desired results?  How will students reflect upon, self-assess, and set goals for their future learning?      

Discussions and student presentations Checking for understanding (using response boards) Ticket out the door, Cornell note summary, and error analysis Learn Zillion end-of-lesson assessments “Check My Progress”, teacher-created assessments/quizzes ST Math (curriculum progress, data reports, etc.)

 What evidence must be collected and assessed, given the desired results defined in stage one?  What is evidence of understanding (as opposed to recall)?  Through what task(s) will students demonstrate the desired understandings?

Opportunities  Unit assessments  Teacher-created chapter tests or mid-unit assessments  Challenge lessons  Illustrative Mathematics tasks (https://www.illustrativemathematics.org/)  Performance tasks

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Paramount Unified School District Educational Services

Grade K – Unit 2 Stage Three –Learning Experiences & Instruction

Unit 2: Compose and Decompose Numbers to 10 Prior to planning for instruction, it is important for teachers to understand the progression of learning and how the current unit of instruction connects to previous and future courses. Teachers should consider: What prior learning do the standards and skills build upon? How does this unit connect to essential understandings of later content? How can assessing prior knowledge help in planning effective instruction? What is the role of activating prior knowledge in inquiry? Looking Ahead In Grade 1, students will: 

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.



Apply properties of operations as strategies to add and subtract.



Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8.



Relate counting to addition



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.



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



Determine the unknown whole number in an addition and subtraction equation relating three whole numbers. For example, 8 + __ = 11, 5 = ___ -3

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Transfer Goals

Unit 2: Compose and Decompose Numbers to 10

1) 2) 3)

Timeframe: Oct. 17 – Nov. 18 (19 days for instruction; 5 days for assessment) Course Textbook: McGraw Hill, My Math

Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution. Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience. Construct viable arguments and critique the reasoning of others using precise mathematical language.

Understandings:  Decomposing numbers builds an understanding of number grouping and promotes fluency Time Skill Learning Goal Break larger numbers apart into smaller numbers Combine smaller numbers to show a larger number

2-3 days

ST Math Objectives:  Making 10 and Number Pairs  Understanding Addition and Subtraction within 5  Understanding Addition and Subtraction within 10

Record the composition and decomposition of numbers using drawings

Use different colored concrete objects to make and take apart 4 in different ways (2 and 2, 3 and 1, 0 and 4) Record these compositions using drawings Use different colored concrete objects to make and take apart 5 in different ways 5 (2 and 3, 4 and 1, 0 and 5) Record these compositions using drawings Use a number bond to show the relationship between the number (whole) and its decomposition (parts) Explain to a partner how understanding smaller numbers help you to understand larger numbers

Essential Questions:  How can understanding smaller numbers help you to understand larger numbers?  How can we use our knowledge of decomposing numbers to understand 10? Lesson/Activity/ Knowledge Focus Questions Teacher Notes Resource Vocabulary What are the different Note: This chapter focuses Investigation on decomposing and Make/Compose ways to make/take Give students objects in Take apart/ apart 4 and 5 (using composing numbers to 10. different colors. Have objects, drawings and Formal lessons in addition them experiment making Decompose Equal numbers)? and subtraction will be 4 using different color Total taught in Unit 3. combinations. Students How can then draw these models. understanding smaller Number Talks Students share work at numbers help you to Explore a variety of document camera and understand larger strategies for teacher facilitates numbers? manipulating numbers discussion asking The textbook teaches composing and to 10. students questions about decomposing as separate skills but it is what they observe about more meaningful to students when making and taking apart these skills are introduced together. 4. Repeat process for 5. Chapter 4 When breaking apart a set, students use the Lesson 1 Make 4 & 5 (see Modeling understanding that a smaller set of objects exists within that larger set. Example: “The the Math pg. 257B) bear has 5 buttons on his jacket. How many Lesson 2 ways can you use blue and red crayons to Take Apart 4 & 5 color his buttons? Draw a picture of all your (see Modeling the Math ideas.” Students could draw pictures of pg. 263B) 4 blue and 1 red button 3 blue and 2 red buttons 2 blue and 3 red buttons 1 blue and 4 red buttons

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Time

Skills

Learning Goals

Lesson/Activity/ Resource

Combine smaller numbers to show a larger number

Use different colored concrete objects to make and take apart 6 in different ways (2 and 5, 3 and 3, 5 and 1 and 0 and 6)

Investigation Give students objects in different colors. Have them experiment making 6 using different color combinations. Students then draw these models. Students share work at document camera and teacher facilitates discussion asking students questions about what they observe about making and taking apart 6. Repeat for process for 7.

Break larger numbers apart into smaller numbers

5-6 days

Record the composition and decomposition of numbers using drawings

Record these compositions using drawings Use different colored concrete objects to make and take apart 7 in different ways (2 and 5, 4 and 3, 6 and 1, 0 and 7) Record these compositions using drawings Use a number bond to show the relationship between the number (whole) and its decomposition (parts)

1 day

Explain to a partner how understanding smaller numbers help you to understand larger numbers

Lesson 3 Make 6 and 7 (see Modeling the Math pg. 269B)

Knowledge Vocabulary Make/Compose Take apart/ Decompose Equal Total

Focus Questions for Lessons What are the different ways to make/take apart 6 and 7 (using objects, drawings and numbers)?

Teacher Notes Lesson 5 can be combined with Lessons 3 and 4.

How can understanding smaller numbers help you to understand larger numbers?

The textbook teaches composing and decomposing as separate skills but it is more meaningful to students when these skills are introduced together.

Lesson 4 Take Apart 6 & 7 (see Modeling the Math pg. 275B) Lesson 5 Problem Solving: Act it Out

Check My Progress Cumulative Review and Error Analysis of Unit 1 Extended Constructed Responses Introduce students to the 4-point Extended-Constructed Response rubric. Use this opportunity to get students familiar with rubric. Possible activities include evaluating their own work, peer feedback, whole-class discussion about displayed exemplars, reflecting on next steps, etc. 6

Time

Skills

Learning Goals

Combine smaller numbers to show a larger number

Use different colored concrete objects to make and take apart 8 in different ways Record these compositions using drawings Use different colored concrete objects to make and take apart 9 in different ways Record these compositions using drawings

Break larger numbers apart into smaller numbers

4-5 days

Record the composition and decomposition of numbers using drawings

Use a number bond to show the relationship between the number (whole) and its decomposition (parts) Explain to a partner how understanding smaller numbers help you to understand larger numbers

Lesson/Activity/ Resource Inquiry Question Diana has 4 red and 4 yellow counters. Teng has 2 red and 6 yellow counters. Diana thinks she has more. Do you agree or disagree with Diana? Prove your thinking. After students share their ideas and the teacher facilitates a discussion, students can go on to find other ways to make 8. Then, repeat process for 9. Lesson 6 Make 8 & 9 (see Modeling the Math pg. 289B)

Knowledge Vocabulary Make/Compose Take apart/ Decompose Equal Total

Focus Questions for Lessons

Teacher Notes

What are the different ways to make/take apart 8 and 9 (using objects, drawings and numbers)? How can understanding smaller numbers help you to understand larger numbers?

The textbook teaches composing and decomposing as separate skills but it is more meaningful to students when these skills are introduced together.

Lesson 7 Take Apart 8 & 9 (see Modeling the Math pg. 295B)

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Time

Skills

Learning Goals

Combine smaller numbers to show a larger number

Use different colored concrete objects to make and take apart 10 in different ways

Break larger numbers apart into smaller numbers

Record these compositions using drawings Use a number bond to show the relationship between the number 10 (whole) and its decomposition (parts) When provided a number from 1 to 9, find the number that makes 10

4-5 days

Record the composition and decomposition of numbers using drawings When provided a number from 1 to 9, find the number that makes 10

Nov. 14-18 5 days

Lesson/Activity/Resource Inquiry Question In a basketball game, there are 10 players on the court separated into 5 players on one team and 5 on the other. What are other possible combinations of players that show how to take apart 10?

Lesson 8 Make 10 (see Modeling the Math pg. 301B)

Knowledge Vocabulary Make/Compose Take apart/ Decompose Equal Total

Focus Questions for Lessons

Teacher Notes

What are the different ways to make/take apart 10 (using objects, drawings and numbers)? How can understanding smaller numbers help you to understand larger numbers?

In lesson 9, students determine how to take apart 10 but the standard states that for any number from 1 to 9, students must find the number that makes 10 when added to the given number, using objects or drawings, and record the answer with a drawing or equation. For example, when working with 2-different colored beans, given 6 beans, a student determines that 4 more beans are needed to make a total of 10.

Lesson 9 Take Apart 10 (see Modeling the Math pg. 307B

Review and Administration of Unit 2 Assessment

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