Overview

Module 4: Number Pairs, Addition and Subtraction to 10

Students begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers to reason about and solve addition and subtraction expressions and equations.

Topic A: Compositions and Decompositions of 2, 3, 4, and 5

Topic B: Decompositions of 6, 7, and 8 into Number Pairs

Topic C: Addition with Totals of 6, 7, and 8

Topic D: Subtraction from Numbers to 8

Topic E: Decompositions of 9 and 10 into Number Pairs

Topic F: Addition with Totals of 9 and 10

Topic G: Subtraction from 9 and 10

Topic H: Patterns with Adding 0 and 1 and Making 10

Advanced Preparation:

- 5-group dot cards
- Hula hoops
- Linking cubes
- Number bonds
- Number path
- Number towers
- Sets of objects

Module Tip Sheet for Parents

These documents provide parents an opportunity to see what their children are learning in the current module including:

- Standards
- Key vocabulary
- Example Problems
- Pictorial Models
- Ideas for how to can help children at home
- Coherence of learning with past and future modules

For guides in Spanish, go here.

Week 1: February 6

Notes:

Lesson 1

Students are introduced to the number bond in this lesson. Using hula-hoops to represent the number bond adds excitement and enthusiasm around a concept that will be crucial to their progress. As you introduce number bonds to your students, create a visual of a number bond and display on the math word wall. Label the parts. As an extension activity, you could have pictures and/or simple story problems around the classroom with numbers bonds below them. Have students work in partners to add the parts and whole. This will be a visual reminder for students and encourage them to use it during partner talks.

Lesson 2

Number bond practice will be embedded in Fluency Activities. Decomposition and composition are taught simultaneously using the number bond model so students begin to understand the relationship

between parts and wholes before adding and subtracting. Teaching these fluency activities with fidelity will help students when they begin adding and subtracting. When reviewing these activities, refer to your word wall and expose students to advanced mathematical terms such as parts and whole, decomposition and composition.

Lesson 3

Model and encourage students to write their squares or pictures within the number bond in an organized way. Some students will still struggle with their one-to-one correspondence and might require a strategy to accurately count story problem drawings. For example, students might need to label their squares with numbers. Students above grade level might be able to try bigger numbers with a variety of ways to decompose.

Lesson 4

During the Concept Development, make time for students to turn and talk and share their story ideas before one person shares with the class. It is important students start making the connection from story problem to the part-part-whole of the number bond. Allow struggling students to use the linking cubes for the Problem Set if necessary. Have them represent the numbers with the linking cubes and then write them in the circle.

Week 2: February 13

Assessment:

Assessment #1

Mid-Module Topic A addresses lessons 1-6.

Administer Mid-Module Topic A only (1 day) on the day of the week that you choose. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Notes:

Lesson 5

The end goal of this topic is for students to be flexible with the number bond model oriented in various ways and to be able to understand the part–part–whole components. By the end of the module,

students understand the number bond’s relationship to the accompanying expression or equation. The final lesson of the topic gives students opportunities to move from the abstract to the concrete by acting out and creating stories based on a given number bond. Throughout Topic A, a fluid movement between composition and decomposition provides a firm foundation for understanding the relationship between addition and subtraction.

Lesson 6

The Concept Development activity serves as a concrete review of the composition and decomposition of the numbers to 5, as well as a chance to practice creating number bonds. This activity could be continued and differentiated for students when working independently or during small group time. For example, at or above grade level students have access to the math word wall vocabulary and keep track of how many times they are able to use words like decompose, compose, part, and whole. Struggling students might just focus on one important vocabulary word.

Lesson 7

It is important for students to have time to discuss what they did in the Concept Development and hear their peers share as well. Struggling students need to be exposed to students using the mathematical terms and explaining their thinking. Make sure that you have time for the Student Debrief. If time is an issue, choose 2 questions from the Student Debrief. One question should focus on the work of the Problem Set and one question should focus on analyzing or reflecting on the overall objective of the lesson. Make sure students have an opportunity to turn and talk and share out whole group for each question.

Lesson 8

Much of this lesson depends on students understanding that circles and triangles are examples of shapes. In order to familiarize students with these shapes, have a Morning Meeting activity that incorporates them. Display shapes for students and have them share with partners and whole group what they remember about them. You might even have partners use their math terms and describe the shape for the class to try and guess.

Standards Addressed in Week's Lessons

Topic A

K.OA.1

K.OA.3

K.OA.5

Topic B

K.OA.3

K.OA.1

K.OA.4

Standards Assessed

Topic A

K.OA.1

K.OA.3

K.OA.5

Week 3: February 20

Notes:

Lesson 9

In order to continue to challenge students working above grade level during the Problem Set, have them show multiple ways to fill in the number bonds and include equations. Give students a recording sheet to keep track of the pairs they identify. As they work in partners or independently you can spend time reviewing with your struggling students.

Lesson 10 Omit

This lesson uses linking cubes sticks to model decomposition. Since students have already had practice with this, consider omitting this lesson for pacing purposes and using it as a support lesson for struggling students in small groups.

Lesson 11

This lesson uses the number bonds to help students identify numbers embedded in 8. Make sure that you represent the number bond in a different orientation. This will help prepare and ensure success on the Problem Set.

Lesson 12

The Fluency Activities continue to play a crucial role in preparing students for the Concept Development. The activities help to solidify students’ understanding of numbers to 10 in relationship to the five, an important understanding as students deepen their work with 6–10. Use these activities in independent workstations for students that are still struggling with this concept.

Week 4: February 27

Assessment:

Assessment #2

Mid-Module Topic C addresses lessons 13-18.

Administer Mid-Module Topic C only (1 day) on the day of the week that you choose. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Notes:

Lesson 13

When conducting the Application Problem, begin to challenge above grade level students by asking them to write their own word problems and showing their work through pictures, numbers, and equations. If there is more than one early finisher, have them trade problems with each other to solve.

Lesson 14

This lesson asks students to focus on MP.2: Reason abstractly and quantitatively (Students reason about the relationships between numbers in composition and decomposition situations). Make sure that ample time is provided for students to discuss and share out. This will also help prepare them for success in the Students Debrief.

Lesson 15 Omit

Students represent decomposition and composition addition stories to numbers 6-8 with drawings and equations with no unknown. For pacing purposes, consider eliminating lesson 15. You can use this lesson to provide additional support to struggling students. Use the Concept Development in lesson 15 as a partner activity when working with your small groups.

Lesson 16 & 17 Combine

Use the fluency practice in lesson 17 for partner work while teacher is conducting small-guided groups. For those partners requiring more rigor, have them write additional number sentences to match their bonds. The worksheets for lesson 17 can be used as materials for your students during independent work time. Consider providing manipulatives and counters for additional support. When you are teaching whole group, refer to lesson 16 for the Sprint, Application Problem, Concept Development and Student Debrief. If time allows, take one of the story problem examples from lesson 17 and review during the Concept Development.

Lesson 18

Lesson 18 deals with the last type of addition situation in kindergarten—both addends unknown (C = ___ + ___). Note that this take apart situation is modeled with an addition equation. Throughout the Concept Development, students working below grade level might benefit from a small group lesson where numbers to 5 replace numbers to 8. Watch students as they are asked to solve a put together with both addends unknown problem, and guide them through it step by step: “5 red and green crayons are on the desk. Draw and color crayons using green and red markers. Now, let’s fill in the number sentence."

Standards Addressed in Week's Lessons

Topic C

K.OA.1

K.OA.2

K.OA.3

K.OA.4

Standards Assessed

Topic C

K.OA.1

K.OA.2

Week 5: March 6

Notes:

Lesson 19

During the Concept Development portion of the lesson, students might benefit from using manipulatives while they are singing “Five Little Monkeys Jumping on the Bed." Have them use linking cubes to represent what is happening in the song. This will help visual learners conceptualize "taking away" and "how many are left." It guides them from the concrete level with students acting out take away stories and working at the pictorial level crossing off to see what remains. It can also help students feel confident contributing during the Student Debrief.

Lesson 20

Display sentence starters for students to help them with new concepts. When they create their own story problems, have them use, "I started with ______?" "I took away ______?" " ______ this many were left?" In addition, make sure the phrase "take away" is on the math word wall for students to use as a reference. This will help prepare them for the upcoming lessons.

Lesson 21

This lesson calls for students to practice MP.4: Model with mathematics. Students use number bonds and addition and subtraction equations to model composition and decomposition. Students tell story problems using drawings, numbers, and symbols. This time will encourage discussion to ensure that students understand the correct placements of the minuend, subtrahend, and difference. In addition, make sure that these key vocabulary words are on your math word wall.

Lesson 22 & 23 Combine

Lesson 22 and 23 require students to Decompose the number 6 and 7 using 5-group drawings by breaking off, hiding, or removing a part, and record each decomposition with a drawing and subtraction equation. Due to pacing concerns, combine these lessons. Follow the structure of lesson 23 with one adjustment. Use the first example and practice in the Concept Development in lesson 22 and the first example and practice in lesson 23. If time permits, continue with more examples from lesson 23 exposing students to the higher number. For students that will struggle with both these numbers, rely on small group time to help scaffold them to 6 and 7.

Week 6: March 13

Module

Notes:

Lesson 24

The objective for this lesson is to decompose the number 8 using 5-group drawings, crossing off a part, and record each decomposition with a drawing and subtraction equation. Since this is a continuation of combined lessons 22 and 23, make sure to add a couple of examples using 6 and 7 while you assess to determine what numbers students might be struggling with. Review this whole group if you see a pattern with your students or small group if it is just a few that need more guidance.

Lesson 25 & 26 Combine

Lesson 25 and 26 follow the same lesson structure for the number 9. Therefore, for pacing purposes combine these lessons. Follow the sequence of Lesson 26 and use lesson 25's Concept Development for small groups for your struggling students. This will address the same skills taught in lesson 26 with more scaffloding.

Lesson 27 & 28 Combine

Lessons 27 and 28 follow the same lesson structure for the number 10. The decompositions are discussed or recorded using number bonds, drawings, and number sentences. Therefore, for pacing purposes combine these lessons. Follow the sequence of Lesson 28 and use lesson 27's Concept Development for small group for your struggling students. This will address the same skills taught in lesson 28 with more scaffloding.

Assessment:

IMPORTANT NOTE: There will be two days of assessments this week. Read the notes on when to administer the topic assessments.

Assessment #3

Mid-Module Topic D addresses lessons 19-24.

Administer Mid-Module Topic D only (1 day) after lesson 24. Consider using small group time.

Assessment #4

End-of-Module Topic E addresses lessons 25-28.

Administer End-of-Module Topic E only (i day) after lesson 28. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Standards Addressed in Week's Lessons

Topic D

K.OA.1

K.OA.2

K.OA.3

Topic E

K.OA.3

Standards Assessed

Topic D

K.OA.1

K.OA.2

K.OA.3

Topic E

K.OA.3

Week 7: March 20

Module

Notes:

Lesson 29 & 30 Combine

In Lessons 29 and 30, students pictorially represent composition and decomposition addition stories using 5-group drawings and equations with no unknown. Use the Grade K Core Fluency Differentiated Practice Sets from lesson 29s Fluency Activity. You can use the rest of the fluency activities in these two lessons as brain breaks or during morning meeting. Use both examples from the Concept Development in lesson 29 and 30. The extra time needed can be taken from the fluency activities. Use only one question from lesson 30's Student Debrief. If timing becomes an issue, teach lesson 29 during small group time for struggling students and teach lesson 30 whole group.

Lesson 31

In the Concept Development students will work with a partner for problems 3 and 4. Provide struggling students with a template to place in their personal white board that provides an area to draw a picture and a blank number sentence like ___ + ___ = ___. In addition, consider pulling struggling students during partner time and giving them step-by-step directions. Be sure to ask students questions as they work to make sure they understand what they are doing while you model your thinking aloud.

Lesson 32

In the Fluency Activities, think about small ways to differentiate for your students varying abilities. It is important to keep meeting the students at their learning level in order for them to grow and to address skill gaps. Students working below grade level might benefit from a 100s chart during Counting to 30 by Ones with the Rekenrek in order to visualize and point to the numbers while practicing extending patterns. During the 5-Group Puzzles, challenge students working above grade level by having them cut 10-frames themselves to show the decompositions of 10.

Lesson 33:

The Problem Set does not specify whether students should cross off or hide to solve. At this point, students may select the strategy that works best for them. Provide suggestions about strategies for students who are struggling to represent subtraction using concrete or pictorial methods. If the majority of your students struggle with this consider modeling this during the Concept Development. Below the model of manipulatives, draw a quick picture and use the cross out strategy to show take away.

Assessment:

Assessment #5

End-of-Module Topic F addresses lessons 30-33.

Administer End-of-Module Topic F only (1 day) on the day of the week that you choose. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Standards Addressed in Week's Lessons

Topic F

K.OA.2

Topic G

K.OA.1

K.OA.2

K.OA.3

Standards Assessed

Topic F

K.OA.2

Week 8: March 27

Module

Notes:

Lesson 34

During the Concept Development, have students at and above grade level working independently to complete number bonds and then turning and talking to discuss answers. Have struggling students sit together and close to you so you can guide them through the work. Make sure to model your thinking and have students share what they are doing. Develop signs and gestures for reoccurring strategies so that you can use these to continue to scaffold your visual learners.

Lesson 35 & 36 Combine

Lesson 35 and 36 have students decomposing the numbers 9 and 10 using 5-group drawings, and record each decomposition with a subtraction equation. Follow the lesson plan for 35 being sure to conduct the Core Fluency Differentiated Practice Sets in the Fluency Activities. This activity assesses students’ progress toward mastery of the required fluency goal for kindergarten:

Add and subtract within 5. This will be important data needed for small groups. During the Concept Development, model the first problem for students and then use the first problem in lesson 36 so students have exposure to the number 10. Take notes on strugglers so that more explicit instruction can be given during small group time.

Lesson 37

Be prepared to spend more than just the 5 minutes allotted for the Application Problem. All students will benefit from acting out the problem and solution while describing what they are doing. Students should do this for the inverse subtraction and addition situations in the story that partners created. This will help prepare them for the Concept Development portion of the lesson.

Assessment:

Assessment #6

End-of-Module Topic G addresses lessons 33-36.

Administer End-of-Module Topic G only (1 day) on the day of the week that you choose. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Standards Addressed in Week's Lessons

Topic G

K.OA.1

K.OA.2

K.OA.3

Standards Assessed

Topic G

K.OA.1

K.OA.2

K.OA.3

Week 9: April 3

Assessment:

Assessment #7

End-of-Module Topic H addresses lessons 37-41.

Administer End-of-Module Topic H only (1 day) on the day of the week that you choose. Consider using small group time.

All assessments are broken up by topic to insure manageable assessments for teachers and students.

Standards Addressed in Week's Lessons

Topic H

K.OA.1

K.OA.2

K.OA.4

Standards Assessed

Topic H

K.OA.1

K.OA.2

K.OA.4

Notes:

Lesson 38

Some students might require manipulatives to ensure success on the Problem Set. Consider providing them with counters to place on the number path so they can count and mark the spaces. They also might benefit from having extra copies (or white boards with a number path template) so they can cross out or add numbers as they count. Have them share out why these strategies helped them during the Student Debrief.

Lesson 39

The Fluency Activity, Growing Apples to 10, prepares students for today’s lesson by providing the opportunity for partners to practice 10 at the concrete level, before moving onto the pictorial and abstract. Put time into preparing sentence strips for students. For example, “I have ____. I need _____ more to make 10.” This will serve as a strong independent workstation for students especially those working at or above grade level. Continue to expose students to sentence strips to encourage student discussion. Use phrases like, "Are there enough?" and "How many more do I need?" for the Application Problem. Refer to these throughout all components of the lesson.

Lesson 40 Omit

Lesson 40 addresses the same objective as lesson 39: Find the number that makes 10 for numbers 1–9 and record each. If you notice students require more practice after lesson 39 then conduct this lesson whole group. However, if only a few students are struggling use the Concept Development for a small group. For additional practice, students can work in independent stations using the game in the second half of the Concept Development. This will provide practice to reinforce lesson 39's skills.

Lesson 41

The culminating task of this module asks students to demonstrate their understanding of addition as putting together, or adding to, and subtraction as taking apart, or taking from. Students use mathematical models and equations to teach a small group of students, administrators, or family members about a decomposition of 10. Build enthusiasm for this final activity and for all the work that students have done by inviting parents and/or another class to observe student presentations.