Lesson 6

At the Circus: Join and Take Away

Est. Class Sessions: 2

Developing the Lesson

Part 1: Connecting Addition and Subtraction Problems

Direct students to look at the display of the At the Circus page from Lesson 3 or in the Adventure Book as you read the addition story below. See Materials Preparation.

Ask:

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  • There are 2 clowns on the high wire and 3 clowns on the platform. How many clowns are there in all?

Select a student to model the situation using cubes on the display of the Part-Whole Diagram and Number Sentences Master.

Ask:

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  • Who can model the problem using cubes on the part-whole diagram? (The 2 clowns on the high wire and the 3 clowns on the platform are the parts and the 5 clowns make the whole. See Figure 1. After a student models the problem with cubes, write the numbers on the part-whole diagram.)
  • What is a number sentence for this story? (Possible responses: 2 + 3 = 5; 3 + 2 = 5)
  • What is another addition number sentence for this story? (Response will depend on the number sentence students gave for the first question.)
  • For addition problems, can you reverse the order of the numbers and get the same sum? (Yes, it doesn't matter if you add 2 + 3 or 3 + 2, you'll still get 5.)
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When using cubes to model problems in part-whole diagrams or box diagrams, remember to use no more than the total number of cubes (the whole) at any one time, as shown in Figure 1.

Ask students to help you change the addition story to a subtraction story. Direct students to use the part-whole diagram and the number sentences for the addition story to help you write a subtraction story related to the addition story. Use the display of the Taking Away at the Circus page Question 2 to model how to write the subtraction story. See the Sample Dialog for a guide for this discussion.

The following subtraction story is an example:

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There are 5 clowns. Three clowns got off the high wire. How many are still on the high wire?

Ask students to think of a number sentence and to determine what numbers go in the part-whole diagram.

Ask:

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  • What do you notice about the addition and subtraction number sentences? (Possible response: They use the same numbers: 2, 3, 5.)
  • If you change the order of the numbers in the addition problem, will you get the same sum? (yes)
  • Show an example of what you mean. (Possible response: 2 + 3 = 5 and 3 + 2 = 5. The order of the parts does not matter. The answer is still 5.)
  • When we write a subtraction number sentence, does it matter which number you write first? (Possible response: Yes, in subtraction, you have to write the biggest number first.)
  • Why is it important to write the largest number first? (Possible response: If you write 3 - 5 = 2, you can't start with 3, take away 5, and get 2. That doesn't make sense.)
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This lesson will help students begin to develop a conceptual understanding of the relationship between addition and subtraction. Students learn that they can change the order of the addends in an addition problem and use the same numbers to write the inverse operation by starting with the largest number. Students will be introduced to fact families and the properties of subtraction later in this unit.

Discuss other examples of take away or separate situations depicted in the At the Circus page. As students describe what they see in the picture, write them on a chart or display. The following is a list of some examples:

  • the elephants with one going away
  • the balloon man selling three balloons
  • the juggling bear losing two balls
  • the monkey eating four bananas
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Make an imaginary high wire in your classroom with string, metersticks, or measuring tape so that students can act out the subtraction situation for the clowns on the high wire. Select other students to act out the various take away or separate situations shown on the At the Circus page.

Explain to students that they will work in pairs on the Taking Away at the Circus pages in the Student Activity Book. For Question 1, they read and draw a picture for the subtraction story, fill in the part-whole diagram and write a number sentence. For Question 2, they write and draw a picture of their own subtraction story, fill in the part-whole diagram and write a number sentence. Before they start, ask students to look at the At the Circus page and generate a list of words they may need in writing their subtraction stories. On a chart or other display, write this list as well as a list of common take-away or separate words. See Figure 2 for a sample list.

To guide student pairs as they write their own number stories, ask:

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  • How many did you start with (the whole)?
  • How many did you take away or separate (the part)?
  • What does the reader have to solve?
  • What is your question?

Have copies of the Part-Whole Diagram and Number Sentences Master, connecting cubes, number lines, and ten frames readily available to help students solve their subtraction problems.

After students write their subtraction stories, have some of the student pairs read their number stories and ask other students to solve the problems. Ask students to fill in the display of the Part-Whole Diagram and Number Sentences Master and describe how they solved the story problem.

Adventure Book: At the Circus
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Student Activity Book: 145 146
Answers
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Master:
Using a part-whole diagram to represent the clown situation with cubes and numbers
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Common take-away or separate words
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