## Lost Buttons

In this lesson and the following one, students investigate subtraction more directly, beginning with the easier “take away” mode. They model “take away” subtraction with buttons and write subtraction sentences. They also work with the additive identity (0) as an addend and as a difference and find missing addends.

Call seven students to the front of the room and roll a number cube to decide how many will return to their seats. Have a volunteer record on the board the subtraction equation the students acted out. Repeat with different sets of seven students. Then ask zero students to sit down and call on a volunteer to record the sentence 7 – 0 = 7. Finally, ask all seven students to sit down and ask a volunteer to record the number sentence 7 – 7 = 0 where all can see it. Have the students identify the difference in each number sentence.

Ask the students whether they have ever lost a button. [At this point you may wish to read *Corduroy* by Don Freeman. In this story, a stuffed bear lost a button.] Now group the students in pairs and give each pair
a bag of buttons, two number cubes, and a copy of one of the Shirt Template.
Tell them to put six to 10 buttons on the shirt, and then take some
buttons away as if the buttons had been lost. Ask them to make a record
of how many they started with, how many they “lost” and how many were
left.

Call attention to a chart with columns you have labeled “Number of Buttons,” “Number Lost,” and “Number Left.” Display a shirt with six buttons and roll a number cube to see how many buttons to take away, for example, two buttons. Then demonstrate how to enter this information in the chart. For example, 6 (written in purple), 2 (written in red), and 4 (written in blue).

Next ask the students to create new entries for the chart and to record them under their picture of the shirt using the colors modeled on the chart. When they are ready, help them enter their findings on the class chart. Then ask them what would be recorded if they started with 7 buttons and took 7 away. Repeat with a model for 7 – 0. Prompt them to add entries to the chart. Now call on a volunteer to write each row of the chart as a subtraction sentence.

To help the students become more familiar with the “take away” model for subtraction, ask them to choose a row of the chart and make up stories about lost buttons using the numbers in that row. [Some children may need to use manipulatives to complete this task.] Then demonstrate how to use the Sums to 10 chart to find the answer when they know the sum and one addend. [Find the red addend. Go across the row until you get to the sum. Then go up the column to find the other addend.]

At the end of the lesson, ask children to choose one of the number sentences derived from the chart. They should draw a shirt with buttons on it and cross some out to illustrate one subtraction fact. Remind the students to write the number sentence under the picture. The drawings would make an appropriate entry for their mathematics portfolio.

- Number cubes
- Buttons
- Sums to 10 Chart
- Shirt Template
- Crayons

**Assessment Option**

At this stage of the unit, it is important for students to know how to:

- model “take away” subtraction using the set model
- identify differences and addends
- recognize the effect of subtracting all and subtracting zero
- find a missing addend

**Extension**

Move on to the next lesson, *Shirts Full of Buttons*.

**Questions for Students**

- What happens when we take away four buttons from seven buttons? Can you show that with these buttons?
- Which difference on our chart was the greatest? If we use only 10 buttons, do you think we could get a larger difference? How?
- What would be the smallest difference we could get with eight buttons? How would you get it?
- Suppose you had five buttons. What would the difference be if you lost two buttons? If you lost zero buttons? How about if you lost five buttons?
- Look at the chart we made. How did someone get a difference of five? Did anyone get a difference of five another way?
- Can you draw a picture to show that you had seven buttons and lost three of them?
- If you know there are seven buttons on a shirt and you can only see three of them, how many can’t you see?
- Show me how to use the Sums to 10 Chart to find the addend that’s missing when the sum is six and one addend is two.

**Teacher Reflection**

- Which pairs of students worked effectively together? Which pairs should be reconfigured?
- Which students did not meet the objectives of this lesson? What caused them particular difficulty?
- Can most of the students justify the difference when one addend is zero? Can they justify a difference of zero?
- Can most of the children use the addition chart efficiently?
- Which children met all the objectives of this lesson? What are appropriate next steps for them?
- What parts of the lesson went smoothly? Which parts should I change the next time that I teach this lesson?

### Button Trains

*before*,

*after*, and

*between*. They also review and use both cardinal and ordinal numbers.

### Many Sets of Buttons

### How Many Buttons?

### More and More Buttons

### Numbers Many Ways

*fact families*. (A fact family is a set of three [or two] numbers that can be related by addition and subtraction, for example: 7 = 4 + 3, 7 = 3 + 4, 7 - 4 = 3, and 7 - 3 = 4. When the number is a double, there are only two members of the fact family. An example would be 10 - 5 = 5, and 5 + 5 = 10.)

### Shirts Full of Buttons

### Looking Back and Moving Forward

### Learning Objectives

Students will:

- Determine the results of removing sets.
- Review the term “difference.”
- Investigate subtracting zero and subtracting all.
- Find a missing addend.

### 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.

- Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.

- Use multiple models to develop initial understandings of place value and the base-ten number system

- 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.

- Develop and use strategies for whole-number computations, with a focus on addition and subtraction.

- Develop fluency with basic number combinations for addition and subtraction.

- Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

### Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

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

Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

-Kindergarten, Algebraic Thinking

- CCSS.Math.Content.K.OA.A.2

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

-Kindergarten, Algebraic Thinking

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

Fluently add and subtract within 5.

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 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.

Grade 2, Number & Operations

- CCSS.Math.Content.2.NBT.B.7

Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP6

Attend to precision.