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Dividing By 2 and 5 (Two And Five)This article is one part of a series of articles on Teaching Division. The first article in the series is: Learning to Use Division (Division Unit Rationale). The remainder of the articles in the series are listed at the end of the article.
Heather Breaux
3rd. Grade
Division Unit
Lesson 5: Dividing by 2 and 5
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
7. Reasoning and Proof
8. Communication
Behavioral Objectives: Upon completion of this lesson, students will be able to….
1. Divide by 2 and 5
2. Know how to use multiplication to check their division facts
Materials/Technology Needs: Crafty Math and What If problem; dry erase boards and markers; word label cards for dividend, divisor, and quotient; “Reteach 13.1” RW67; table problems 2 and 3 from p. 259; “Practice 13.1” PW67 for homework.
Anticipatory Set: Inform the class that today we are going to become masters at dividing by 2 and 5. Tell everyone to put on their thinking caps and to get out their dry erase boards. Do “Quick Review” problems 1-5 and have the class record their answers on their dry erase boards.
Procedure:
1. Put the “Crafty Math” problem found on p. 258 on the board and have a student in the class read it out loud. Have the class determine that the number sentence is 12÷2= ? Using word label cards, ask the students to label each number as the dividend, divisor, and the quotient. Explain to the class that when you have a 2 as the divisor and you are trying to find the quotient, try to solve for the missing factor of a multiplication sentence. They can do this by having 2 as a factor and a product equal to the dividend.
A. Crafty Math Problem: Mrs. Jackson knit 12 hats. She put an equal number of hats on each of 2 shelves in the craft shop. How many hats are on each shelf?
B. Have the class find the related multiplication fact to find the quotient for the division problem. Write 2x ?=12 on the board and explain that we can use 2 as a factor and 12 as the product. We know this because the quotient is the same as the product in a multiplication problem. Since we know that 2x6=12, we now know that 12÷2=6. Ask the students to answer the question to the problem (there are 6 hats on each shelf).
C. Ask the class, “Why can we use a multiplication sentence to solve a division problem again?” (Division and multiplication are inverse operations).
2. Solve the “What If” problem found on p. 258 with the class by having them label each number of the division sentence as the dividend, divisor, and quotient with the word labeling cards. Explain that we can use multiplication sentences in the same way when 5 is our divisor. To find the quotient, we need to solve for the missing factor of a multiplication sentence with 5 as a factor and the product is equal to the dividend. Have the children identify 5 as a factor and 15 as the product. Explain that 15 is the quotient because the product and quotient are equal to each other.
A. What If Problem: Mrs. Jackson knits 15 hats and puts an equal number of hats on each of 5 shelves. How many hats are on each shelf?
B. Ask questions like “What is the 5 in the multiplication sentence? What is the product?”
C. Write the multiplication sentence 5x ?= 15. Ask the class to write the missing factor on their dry erase boards. Rewrite the sentence as 5 x 3= 15, and say, “Because we know this is true due to our knowledge on inverse operations and fact families, 15 ÷ 5=3 and there are 3 hats on each shelf.
3. Pass out “Reteach 13.1” to the class. Have a student read examples A and B at the top of the page to the class to strengthen what we just discussed. Do problems #1-6 as a class, making sure to call on students to identify the dividend, divisor, and quotient to each problem.
4. Have the students complete problems 7-23 with a partner. When they are finished solving the problems, they may ask each other to find a multiplication sentence to check the division problems. They may do this until the rest of the class is finished or until time has run out.
5. Copy tables #2 and #3 from p. 259 on the board for the class to solve. Have the class rewrite each problem from the table and solve it on their dry erase boards before going over them as a class.
6. Pass out “Practice 13.1” for homework.
Accommodations: I will seat Jessica at the front of the room so that she can see all problems on the board, as well as provide her with enlarged worksheets to work with at her desk and for homework.
Closure: Write 20÷5=4 on the board. Ask for someone to explain how you can use multiplication to check your answer. Listen to the answers and then reiterate by saying to check that the divisor multiplied by the quotient equals the dividend, so 5x4=20. This can sound confusing, so be sure to point to the problem when explaining.
Key Questions:
1. “What process can we use to check our division facts?”
2. “Why can we use this process?”
3. “What two divisors did we work with a great deal today?”
Evaluation: I will be using “Reteach 13.1” problems 1-6 and the table problems #2 and 3 from p. 259 as my formative assessment. The students’ homework assignment will be used as their summative assessment for the day.
Assignment: “Practice 13.1” PW67 on p. 258
Resources Used:
1. (2004). Harcourt Math Teacher Edition: Third Grade. Vol. 2.) Harcourt, Inc.
Articles In This Series
Learning to Use Division (Division Unit Rationale)
Division - Meaning, Manipulatives and Relationships
Relating Division And Subtraction Lesson Plan
Connecting Division And Multiplication
Division Unit: Writing A Number Sentence
Dividing By 2 and 5 (Two And Five)
Dividing By 3 and 4 (Three and Four) Lesson Plan
Dividing With 1 and 0 (One and Zero) Lesson Plan
Frank D'Angelo, who submitted these articles, writes: [This] is an excellent unit submitted by a student in my Elementary Mathematics Methods Course.
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