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Overview

In this activity, students will practice generating a variety of ways to decompose a number and record their decomposition using pictures, numbers, or equations to build their understanding.

This activity results from the ALEX Resource Development Summit.

UP:MA19.K.10

• Decompose
• Equation

Knowledge

Students know:
• "equal to" and the concept of equality meaning "the same as."
• Addition is putting together numbers and subtraction is taking apart numbers.

Skills

Students are able to:
• Represent quantities physically, pictorially, and symbolically.

Understanding

Students understand that:
• quantities may be named in a variety of ways.

Phase

During/Explore/Explain
Learning Objectives

Learning Objectives

Students will generate a variety of ways to decompose a number and record their decomposition using pictures, numbers, or equations to build their understanding.

Activity Details

1. The teacher will gather students to carpet or another area of the room where they can all easily view the demonstration. The teacher will have the following materials for the demonstration: 1 small cup or container, 5 two-color counters, 2 "Make 5" recording sheets, 1 red crayon, and 1 yellow crayon. The teacher should select a student partner to work with during the demonstration of the game.

2. The teacher will show students the 5 two-color counters, showing both sides of the counters and counting them before placing them in the cup.

3. The teacher will demonstrate how to cover the top of the cup and gently shake twice, then spill the counters gently out of the cup (you can chant "shake, shake, spill" to reinforce the routine).

4. Once the counters have been spilled on the work surface, the teacher will ask students, "How many yellow counters do I have?" and demonstrate how to count the number of counters that landed on yellow.  The teacher will then ask the student partner, "Do you agree?" If the student partner agrees with the count, the teacher and student partner will demonstrate coloring that number of circles in the first area of the recording sheet and writing the corresponding numeral. If the teacher and student partner do not agree on the count, they should demonstrate discussing why and show one another their strategies until a correct count has been agreed on.

5. The teacher will then repeat the process for the red counters that were spilled on the work surface.

6. Finally, the teacher will ask, "How many counters do I have altogether?" and demonstrate counting the entire set. The teacher will then ask the student partner, "Do you agree?" If the student partner agrees with the count, the teacher and student partner will demonstrate writing the total number counted in the first area of the recording sheet. If the teacher and student partner do not agree on the count, they should demonstrate discussing why and show one another their strategies until a correct count has been agreed on before recording the total.

7. The teacher will demonstrate working with a partner by handing a partner student the cup of counters. The teacher and student partner will repeat the above steps. Continue the demonstration until all students have an understanding of the activity.

8. The teacher will then partner all students and provide each set of students with a cup, 5 two-color counters, and a "Make 5" recording sheet for each student.

9.  Students will play Make 5 with their partner to generate various ways of decomposing the number 5.

10. After students have played several rounds of Make 5, have students come to the carpet with their recording sheets to discuss their findings. If available in your classroom, use a number balance or an online number balance as you discuss findings. Challenge students with questions such as: "Is 3 and 2 the same as 2 and 3?" "Why or why not?" Have them use the number balance to figure out or prove their answer. "Is 1 and 4 the same as 3 and 2?" "Why or why not?" Have them use the number balance to figure out or prove their answer.

Assessment Strategies

Assessment Strategies

Informal Assessment/Observation: As students work, the teacher will ask students to describe the different ways they decomposed 5. The teacher will look for the students' ability to explain more than one way that they decomposed 5 using language similar to 4 and 1 make 5, 3 and 2 make 5, etc.

Assessment of Recording Sheet: The teacher will note whether students were able to successfully generate multiple ways of decomposing 5.

Variation Tips

This activity can be done with any number 2-10 depending on student needs.

If available in your classroom, allow students to use a number balance or an online number balance to demonstrate the equality of each pair of numbers to 5 (ex: 5 on one side of the number balance, 4 and 1 on the other side to demonstrate the equality of the two sets of numbers).

Challenge students with questions such as:

"Is 3 and 2 the same as 2 and 3?" "Why or why not?" Have them use the number balance to figure out or prove their answer.

"Is 1 and 4 the same as 3 and 2?" "Why or why not?" Have them use the number balance to figure out or prove their answer.

Background / Preparation

Prior to the activity, the teacher should:

create student pairings/partners.

gather 1 cup per pair of students.

gather 5 two-color counters for each pair of students.

print "Make 5" Recording Sheet for each student.