Heather Breaux
3rd. Grade
Division Unit
Lesson 3: Connecting Multiplication 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:
4. Number and Operations
5. Algebra
6. Problem Solving
7. Reasoning and Proof
8. Communication
9. Connections
10. Representation

Behavioral Objectives: Upon completion of this lesson, students will be able to….
1. Understand the relation between division and multiplication
2. Verbally state what an makes up an inverse operation and a fact family
3. Identify an example of a fact family

Materials/Technology Needs: 18 enlarged stamps (for demonstration and discussion); “Reteach 12.3” RW64; “Multiplication and Division” worksheet.

Anticipatory Set: Place 18 enlarged stamps on the board in one group and explain to the class that Miss Breaux is starting to collect stamps for a hobby and needs the classes’ help to organize them nicely into a book. Write “Stick with Stamps” problem from p. 242 on the board. Write the division problem 18÷3= BLANK, where 18 is the number of stamps, 3 is the number of rows, and we are trying to figure out how many stamps will go in each row. Solve by using repeated subtraction with the class to find out there are 6 in each row.

Procedure:
1. Review dividend, divisor, and quotient by relating them to the stamps. Say that the dividend stands for the total number of stamps (18). Ask what does the divisor stand for? Quotient?
2. Place 6 in each row, and write 3x6=18 besides it. Say, “Because 3x6=18, then 18÷3=6. Today we’re going to learn that this is because multiplication and division are inverse operations. (Write inverse operations on board.) This means that these two processes are opposites. They are opposites because multiplication is used to put equal groups together and division separates equal groups.”
A. Place 12 stamps on board in 4 rows with 3 in each row. Ask, “How many stamps do I have?” (12) With the classes help, write the multiplication sentence 4x3=12 and label the 4 and 3 as the factors and the 12 as the product.
B. Then say, “But what if I knew I had 12 stamps and 4 rows, but I wanted to know how many stamps were in each row?” Write division sentence 12÷4=3. Say that we need to use our thinking caps- What was the product? (12) What was the quotient? (12) So we just learned that the product in the multiplication sentence is the exact same number as the quotient in the division sentence!!
C. Write 5x8=40 on the board. Ask, “What division sentence relates to the multiplication sentence 5x8=40?” Remind them that because multiplication and division are inverse operations of each other, that the same numbers are going to be used. Ask students for the product and ask what the product is in the division sentence again. Write the 2 possible division sentences on the board: 40÷8=5 and 40÷5=8.
D. Explain that these are all examples of fact families. Fact families are a set of related multiplication and division number sentences.
3. Pass out “Reteach 12.3” to review the concept of fact families with the class. Ask for volunteers to read the top of the page. Do problems 1-4 as a class. Problems 5-12 can be done in partners or individually if there are students that feel that they have mastered this concept and feel good enough to do the worksheet on their own. Problems 5-12 can be done as a class if the lesson is still very challenging for them to grasp.
4. Pass out “Multiplication and Division” worksheet for homework. Tell the children to remember to use their knowledge of fact families to help them solve the problems.

Accommodations: I will seat Jessica at the front of the room so that she can see all problems on the board.

Closure: As a class, work together to write down all of the fact families for the following problem: 5,6,30. Fact families include: 5x6=30, 6x5=30, 30÷5=6, 30÷6=5.

Key Questions:
1. “Why can we call multiplication and division opposites? What’s the special term for opposites called?” (multiplication puts things together into equal groups and division separates them into equal groups; inverse operations)
2. “What is a fact family?” (a set of related multiplication and division number sentences)
3. “Who can show us an example of a fact family?”

Evaluation: I will use worksheet “Reteach 12.3” as my formative assessment, where I will judge my students knowledge about how multiplication and division are related by how well they can answer my questions and the ones on the worksheet. If the students are able to complete the worksheet on their own or in pairs, I will know that their confidence level is pretty high about the concept. For their summative assessment, I will grade their “Multiplication and Division” homework worksheet to judge their knowledge on this lesson.

Assignment: “Multiplication and Division” worksheet.
Resources Used:
1. (2004). Harcourt Math Teacher Edition: Third Grade. Vol. 2.) Harcourt, Inc.
2. edHelper.com at url http://www.edhelper.com/math/division_tg310.htm

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