## Try for Five

In this lesson, students explore the many ways to decompose numbers, and they build on their knowledge of addition and subtraction to find missing addends.

To begin the lesson, you may wish to read a book about food. Several are suggested in the Bibliography of Books About Food.

Bibliography of Books About Food

Review the sections of the food pyramid with students. Ask them to select foods from any two sections of the food pyramid so that seven foods will be selected in all. Record the students' choices on the board or overhead projector. You might copy the colored pictures of the foods to transparency film for use on the overhead projector.

Then ask volunteers to name how many foods came from each section of the food pyramid. Write the corresponding number sentence where all the students can see it. Now ask them to select seven foods in another way. Remind the students that they may use more than two addends if they wish.

Call on several students to tell their choices, and record each in a number sentence on the board. Repeat the activity with other numbers up to 12. To record the ways a number can be decomposed into addends, ask the students to draw a meal on their paper plate so that they will have five items in the meal. Encourage them to record the modeled addition sentence on the back of the paper plate. Then call on volunteers to tell how they created a meal of five items. You may wish to display these drawings or place them in the students' portfolios.

Ask the students to focus on the vegetable section of the pyramid. Ask how many servings are required each day [three to five]. Now ask the students to draw on a 10 strip that has been cut in half.

Draw or paste two to four pictures of vegetables, one in each section of the strip. Model how to write a missing addend statement that describes how many vegetables must be drawn to complete the "5" strip. [For example, if three vegetables have been drawn, the sentence would be 3 + _ = 5.] Place the students in pairs, and have them compare the number of food pictures they drew with the number sentences.

3 | + __________ | = 5 |

Ask the students to exchange papers, complete their partner's strip, and fill in the missing addend. Call on volunteers to describe the strip using words and then using a subtraction sentence. Repeat the procedure, using the other half of the 10 strip and allowing the students to select up to five foods from either the fruit or vegetable sections. When the students are ready, call them together. Display the strips that they drew and the related number sentences with missing addends. If no students choose a number sentence in which the missing addend is zero, model this for the students.

For the second half of the lesson, divide the class into groups, and tell the students that they are going to act out stories about making healthy food choices. Assign one group of students to each section of the food pyramid, and ask them to draw one food from that section on their paper plate. In turn, call on one volunteer from each group to select a day's worth of healthy foods from among the student drawings. For each section, assign a volunteer to record the number sentences that the groups are modeling. [For the group assigned to the fruit section, for example, if two students drew oranges, one student drew an apple, and another drew a pear, the number sentence would be 2 + 1 + 1 = 4.]

Call out the food groups one at a time and ask the students who drew the pictures in that group to stand. Record the group and the number of students on the board [fruits, six; vegetables, eight]. Now ask a student to name any food group, note how many students are in that group, and write a missing addend statement on the board [6 + __ = 8]. Next, have the student call on the number of students to come to the front of the room that are required to represent the given addend [6].

Ask the other students, "How many more students need to join them to make the addition sentence correct?" [Two] Have the volunteer give the answer by calling the correct number of additional students to the front and completing the number sentence. [For example, if the sentence is 5 + _ = 9, five students will be called in the first group and then four more called.] Then, call on other volunteers to provide and model other number sentences with missing addends.

### Reference

- Richardson, Kathy.
*Developing Number Concepts: Addition and Subtraction*. N.J.: Dale Seymour Publications, 1999.

- Scissors
- Paper plates
- Crayons
- Paper
- Pictures of food
- 10 Strips cut in half
- Bibliography of Books About Food

**Assessments**

- The students' answers to the above questions will show the individual achievement of your students.
- You may wish to add to your Class Notes recording sheet for this unit. These notes may be helpful as you plan future lessons.

**Extensions**

- Repeat the activity using "10" strips cut to various lengths.
- Kathy Richardson's book,
*Developing Number Concepts*, presents many ways to lead students to a sound sense of number and number relationships. Richardson suggests that hiding cubes under a container helps students begin to realize that the missing addend is related to the total number of objects.

**Questions for Students**

- If you want two groups with seven food pictures in all, what two addends can you model? Is there another way you can have two groups with seven foods in all? How could you have seven pictures in all three groups?
- Show me three ways you can make food groups that add to eight. (Repeat with other numbers.)
- Suppose I want to draw five fruits in all and I've drawn four of them. How many more will I have to draw? What number sentences will describe that?
- How could you help a friend find the missing addend in 5 + _ = 9? How about 5 +_ = 5?

**Teacher Reflection**

- Which students easily recalled addends for a given number?
- Which students easily recorded with number sentences?
- Which students associated finding missing addends with subtraction? Which did not?
- Which students are still having difficulty with the objectives of this lesson? What additional instructional experiences do they need?
- What will I do differently the next time that I teach this lesson?

### Sorting Foods

### Eating Patterns

### Pyramid Power

### Combining Foods

### Learning Objectives

Students will:

- Decompose numbers.
- Find addend sets for numbers up to 12.
- Find missing addends.
- Model situations that involve the addition and subtractions of whole numbers, using objects, pictures, and symbols.

### NCTM Standards and Expectations

- Count with understanding and recognize "how many" in sets of objects.

- Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

- Understand the effects of adding and subtracting whole numbers.

- Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.

### Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.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).

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.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.

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.5

Fluently add and subtract within 5.

-Kindergarten, Number & Operations

- CCSS.Math.Content.K.NBT.A.1

Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.B.4

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

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.C.6

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade 1, Algebraic Thinking

- CCSS.Math.Content.1.OA.D.8

Determine the unknown whole number in an addition or subtraction equation relating to 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 = _.

Grade 1, Number & Operations

- CCSS.Math.Content.1.NBT.C.4

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade 2, Algebraic Thinking

- CCSS.Math.Content.2.OA.B.2

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP6

Attend to precision.