## Taking Away Sets

This lesson encourages students to explore another model for subtraction, the familiar set model. Reading one of the many books that feature subtraction set the stage for this lesson in which the students write story problems, find differences using sets, and present results in a table. In the discussion of the table, they focus on the effects of subtracting all and subtracting 0.

To set the stage for this lesson, you may wish to read another of the counting books.

Appropriate books include
*Ten, Nine, Eight*, *How Many Snails?*, and *Mean Machine*.
Now ask students to create subtraction story problems that use sets
bigger than 1. For example, for 6 – 2, a student could ask, "Jose had
6 marbles and lost 2 of them. How many does he have now?"

Encourage a few volunteers to share their problems with the class. Discuss whether these problems can be solved. If they provide too little or too much information, solicit student help to revise the story problems.

Find the Difference Activity Sheet

Then post a large piece of chart paper displaying a Find the Difference chart where all the students can see it. Repeat one of the student’s story problems. Demonstrate how to fill in the columns labeled "Number of Objects" and "Number Taken Away" with the information from the story. Then explain to the students that the column labeled "Number Left" is the difference and that you will find the difference together using real objects. Display a chain that matches the story problem. For the example above, you will make a chain of 6 links and take away 2 links. Place the two links where they are separate from the chain but still visible to students. Ask students to tell you the difference. Enter this information in the chart. Repeat this process with the other student-generated story problems.

Give students the opportunity to practice writing and solving their own subtraction story problems individually or in pairs. After each student or pair of students writes a problem, have them record the information from their problem in a Find the Difference chart. Provide links for the students to solve their story problems.

When they are ready, call students together to share their
story problems and enter their findings on the class chart. Afterward,
review the terms *take away* and *difference*. Then ask the
students what would be recorded if you started with 7 links and took
7 away. Repeat with a model for 7 – 0. Prompt them to add entries to
the chart. At this point, you may choose to encourage children to also
notice rows in which the first column ("Number of Objects") shows the
same number.

At the end of the lesson, ask students to choose one of the rows from the chart and draw a picture illustrating that number fact. You may allow students to display these in the classroom or in a more public place.

- Work mats
- Find the Difference Activity Sheet
- A Counting Book
- Plastic Colored Links or Connecting Cubes

**Assessment Options**

- Use the Questions for Students above to assist you in determining your students’ level of understanding. Other questions may suggest themselves as you talk with your children as well. Record your observations on the Class Notes teacher resource sheet you began earlier in this unit.
- Have students re-use their subtraction problem (or create a new subtraction problem) using a theme such as "At The Pond." Provide students with appropriate stamps to illustrate their problems. Assess whether students are able to model subtraction in written and pictorial form.

**Extension**

Move on to the next lesson,Hopping Backward on the Number Line.

**Questions for Students**

1. What happens when we subtract?

[We take something away, and the group usually gets smaller. (The group will not get smaller if the number we take away is 0.)]

2. Which difference on our chart was the greatest?

[Answers will vary.]

3. If we start with 10 links, what is the greatest difference we can get? How do you know?

[The biggest difference is 10. We get the biggest difference when we subtract 0.]

4. What would be the smallest difference we could get with 10 links? How would you get it?

[The smallest difference would be 0. We get 0 if we take all 10 links away.]

**Teacher Reflection**

- Can students explain the terms
*difference*and*take away*? - Were students able to create story problems for subtraction? If not, what activities can you use to give them additional experience?
- Which students need assistance to record what they know and need to find out from story problems?
- Can most of the children justify the difference when 0 is taken away? Can they justify a difference of 0?
- What other books would you use in this lesson?

### Counting Back and Counting On

### Hopping Backward on the Number Line

### Finding the Balance

### Finding Fact Families

### Practice Makes Perfect

### Looking Back and Moving Forward

### Learning Objectives

Students will be able to:

- Create subtraction story problems.
- Explore the results of subtracting sets.
- Define the term
*difference*. - Explore the effects of subtracting 0 and subtracting all.
- Construct a table showing differences.

### NCTM Standards and Expectations

- Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

### Common Core State Standards – Mathematics

-Kindergarten, Counting & Cardinality

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

Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

-Kindergarten, Counting & Cardinality

- CCSS.Math.Content.K.CC.A.3

Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

-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.5

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

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.