Heather Breaux
3rd. Grade
Division Unit
Lesson 2: Relating Subtraction and Division
Date:
Approximate Time: 60 minutes

Berks County Standards:
1. 2.1.3 Numbers, Number Systems and Number Relationships- C. Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols.
2. 2.1.3 Numbers, Number Systems and Number Relationships- L. Demonstrate knowledge of basic facts in four basic operations.
3. 2.2.3 Computation and Estimation- D. Demonstrate concept of division as repeated subtraction and as sharing.

NCTM Standards:
1. Number and Operations
2. Algebra
6. Problem Solving
7. Reasoning and Proof
8. Communication
9. Connections

Behavioral Objectives: Upon completion of this lesson, students will be able to….
1. Relate the process of division to subtracting equal groups

Interdisciplinary Connections: Recently we have been discussing the concept of voting in social studies class, especially multiple reasons where we vote for something. For example, we vote for President, for clubs we want, for what activities we can do in class, etc. Because of this, I will relate this when I have the class vote in my Anticipatory Set.

Materials/Technology Needs: 12 Enlarged green circles (for demonstration and discussion); colored chalk (especially red and blue); word labeling cards for dividend, divisor, and quotient; worksheet “Check” on p. 241; WS PW63“Practice 12.2” for homework” on page. 240.

Anticipatory Set: I will begin today by placing 12 enlarged green circles on the board in one big group. I will say, “Today we are going to think about division in a new way. We are going to use repeated subtraction to find out our answer today when solving division problems. Review what the word repeated means (continuing something over and over). Take a vote with the class: Who thinks that it’s possible to use subtraction to find the answer to a division problem? Who doesn’t think that it’s possible? Relate this type of voting with what we’ve been discussing in social studies class. We’ll just have to wait and see if it is possible to use subtraction to divide!”

Procedure:
1. Write “Get in the Game” problem from p. 240 on the board, followed by writing 12 (# of pieces) divided by 4 (# for each player) = (BLANK) # of players. Explain to the students that because the problem says that each player is getting 4 pieces, we are going to subtract 4 from 12 and continue to subtract 4 until we’ve reached zero. Demonstrate by writing out these subtraction problems on the board, followed by labeling each problem as 1, 2, etc. Explain that since we subtracted 4 from 12 three different times, there are 3 groups of 4 in 12. This means that our answer to the division problem 12 ÷4= 3.
Get in the Game problem: Ana has 12 game pieces for a game. Each player gets 4 pieces. How many people can play?
2. Demonstrate the same problem using a number line. Draw a number line and have the class help you label it properly by making sure the arrows extend in each direction and that the numbers are properly labeled. Show how once again you come up with 3 groups because 4 was subtracted 3 times on the number line. Use a different piece of colored chalk to show the subtraction of 4 each time, so it’s easy for the students to see each group.
3. Ask children what repeated subtraction and division have in common. Explain that both math processes separate objects into equal groups, so both processes can be used. Ask, “What does counting back and subtracting over and over until we reach zero do?” (this process of subtraction allows us to separate all pieces equally, just like we did yesterday when we were dividing counters into different groups that were all equal in value.
4. Write 12 ÷ 4= 3 and explain that this is one way to write a division number sentence. Using labeling cards, label the 12 as the dividend; the 4 as the divisor; and the 3 as the quotient. Explain and write on the board that the dividend is the number that is being divided in a division problem. The divisor is the number that divides from the dividend, and that the quotient is the number that is the result, or answer, after dividing. Write 12÷4=3 using the division bracket. Label problem with labeling cards once again for the dividend, divisor, and the quotient.
5. Hand out “Check” WS on p. 241 to the class. Answer questions 1-3 as a class by calling on volunteers to come up to the board to answer each question using different colored chalk to represent each group. Assign numbers 4-13 to the class: they may work individually if they feel they are able to solve them on their own or they may work in pairs. If the class as a whole is still confused with using repeated subtraction, continue to finish the worksheet as a class. Collect the worksheet and take a vote again to see if it’s possible to use subtraction to solve a division problem.
6. Hand out WS “Practice 12.2” for homework” on page. 240.

Accommodations: I will accommodate Jessica by seating her in the front of the room and by providing enlarged worksheets.

Closure: Complete #18 from “Check WS” on p. 241 as a class. Put problem on overhead for class to see then solve by writing the steps out on the slide. Follow by answering the “Key Questions”.
Problem #18: Scott buys 22 baseball cards. He keeps 10 cards and divides the rest equally between 2 friends. How many cards will each friend get? (6 cards).

Key Questions:
1. “When we use repeated subtraction, why do you count back or continue to subtract until you reach zero?” (separates all pieces into equal groups)
2. “Who can come up and write the division problem 18 divided by 6 in two different ways for me, as well as answer the division problem for me?”

Evaluation: For my formative assessment, I will evaluate my students’ answers to my questions about division and repeated subtraction and see how well they are grasping this concept. Also, I will know how well the class feels about the concept by whether they want to continue on and answer questions 4-13 by themselves, in pair, or as a class. I will use their homework assignment “WS Practice 12.2” as my summative assessment for the students.

Assignment: WS “Practice 12.2” for homework” on page. 240.

Resources Used:
1. (2004). Harcourt Math Teacher Edition: Third Grade. Vol. 2.) Harcourt, Inc.

Frank D'Angelo, who submitted these articles, writes: [This] is an excellent unit submitted by a student in my Elementary Mathematics Methods Course.