Module on Division for Grade 3

By

Jillian Sebastiao

Table of Contents Math Module Template Overview of Daily Lessons Lesson 1: Concept of Division Lesson 2: Dividing into Equal Parts Lesson 3: Grouping and Division Using Repeated Subtraction Lesson 4: The Quotient Lesson 5: Writing Division Horizontally Lesson 6: Relationship between Multiplication and Division Lesson 7: Solve by Finding a Mathematical Expression Lesson 8: Multiplication and Division Using Larger Numbers Pretest Form A Adapted from: Korean Mathematics, Grades 2-3. (2001). Edited by Janice Grow-Maienza, translated

by Sue Chung Nugent. Kirksville, MO: Truman State University. From Ministry of Education. Arithmetic, Grades 1-6. Seoul, Korea: National Textbooks Inc, l993.

Exploring Mathematics, Grade 3. (1994). Glenview, IL: Scott, Foresman, and Company.

Module development was partially funded by the Missouri Coordinating Board for Higher Education through the Eisenhower Professional Development Program.

Translations were partially funded by NSF ESIE SGER Project 0086580.

Math Module Template

Strand: Division

Grade Level: 3

Concepts Included in Module:

• Dividing into equal parts by sharing

• Dividing into equal parts by grouping

• Using a picture in division

• Using repeated subtraction to find the quotient

• Using multiplication to find the quotient

• Fact families

• Writing division in two different ways

• Solving word problems by finding the mathematical expression

• Dividing with larger numbers when dividends are multiples of 10

Author: Jillian Sebastiao

District: Wentzville R-IV, Green Tree Elementary

Statement of Basis for Selection of Strand/Concepts:

I chose to supplement the current curriculum with the Korean Mathematics

textbook. Therefore, the content chosen for this module is an integration of the Korean

Mathematics translation into the Scott Foresman curriculum that is currently in place in

the Wentzville R-IV school district. Interestingly, the concepts covered in the third grade

Exploring Mathematics textbook were covered in the second grade Korean Mathematics

textbook.

Overview of Daily Lessons:

Approximately fifty minutes each day were spent on mathematics instruction. We

began each lesson with a real-application word problem. I would give the students some

time to figure out the problem independently. Then, I would let individual students show

their answers on an overhead transparency or on the chalkboard. This allowed students

to see that there are different approaches to mathematics and that division is commonly

used in real life.

After the application word problem, I taught from the Korean Mathematics

curriculum. During these lessons, the students would write in their own modified version

of the Korean translation. First, I would teach a concept. Then, I would lead the class in

dependent practice. Next, the class would practice a few problems independently. This

method is very similar to the method used to teach mathematics in Korea (Grow, 2002).

The last fifteen minutes of class were spent on the Exploring Mathematics lesson.

Often the class found that the material presented in this book was very elementary in

comparison to the work they had completed throughout the first part of class. I continued

to assign homework from this textbook. The students were given about five minutes in

class to work on their homework. During this time, I checked for the students' conceptual

understanding by asking them questions about their work.

The students were assessed with a pretest and a posttest. Also, throughout the

unit, I administered two mid-chapter check-ups. I learned a lot from these check-ups

about what concepts the students needed more work on.

Lesson 1: Picnic Sharing Activity Introduction to the Concept of Division

Objectives: Students will share items equally in groups of three or four. Plan: Students are seated in groups of three or four. Each group is given a picnic basket with various amounts of food. Their task is to divide the food equally among the three or four students. They also draw the division of the food on their worksheet. Materials: one picnic basket per group of 3-4 students; various fruits or candy (pretzels work really well for the larger numbers)- each group will need four different types of food; Picnic Sharing worksheet 1. You can also use paper plates to add more of a "picnic atmosphere." Informal Assessment: 1. Walk around to see the different methods that groups are using to share the food. You will talk about the different methods tomorrow when division as sharing is more formally introduced. 2. Collect the Picnic Sharing Activity sheets to make sure that all students understood the activity.

Worksheet 1 Name: _____________________________ Date: _____________

Picnic Sharing Activity Write the name of the food item, the total amount in the picnic basket (draw a picture), the number of people in your group, and the number that each person in your group gets (draw a picture). Follow the example. Food Item: Total amount: Given to Each person

____ people gets _____

Example: Watermelon 4 4 1

Lesson 2: Dividing into Equal Parts Objectives: Students will divide objects equally with no remainders. Plan: 1. Real-life application problem: Give twelve mints (or other candies) to groups of three or four. Have them divide the food equally. Ask for volunteers to show the class the method they used to divide their candy. 2. Go through the problems in Korean modification pages 1 and 2. Students should write in the books. They should circle the pictures to find their answers in this lesson. 3. Read through pages 296-297 in the Scott Foresman textbook. 4. Assign homework:

page 298 #5-18; worksheets P83 from Practice/Exploring Mathematics in Scott Foresman; E83 from Enrichmemtn/Exploring Mathematics in Scott Foresman.

Materials: three to four pieces of candy per student Informal Assessment: Walk around the room to make sure that each student is circling the correct amounts on each problem. Go over the first three problems in Scott Foresman book as a class.

Page One of Korean modification

1. There are 6 strawberries. 2 strawberries are put in a dish. How many dishes does it take to hold all 6 strawberries?

______ dishes are needed.

2. There are 15 bananas. 5 bananas are put in a basket. How many baskets are needed?

______ baskets.

3. There are 12 apples which will be put in 3 dishes with equal numbers for each. How many apples can be put in a dish?

______ can be put in a dish.

Page Two of Korean Modification 4. There are 10 presents which will be distributed to 5 people with equal numbers for each. How many presents are given to each person?

______ presents 5. There are 20 flowers. They are divided among 4 vases with equal numbers in each. How many tulips are in each vase?

______ flowers.

Lesson 3: Grouping and Division Using Repeated Subtraction

Objectives: Students will define the terms "quotient" and "division." They will understand how to write a division sentence. Students will solve problems using repeated subtraction. Plan: 1. hands-on application problem: Each student is given 16 miniature blocks in a cup. Individually, they must show (one at a time): how to divide the blocks into 2 groups, into 8 groups, and into four groups. After each problem is introduced, students have a couple minutes to work on it at their desks. Then, I take volunteers to show the class on the overhead how they solved the problem. After making sure each student has the correct representation at his/her desk, I show them what the division sentence looks like: either 16 ÷ 2; 16 ÷8; or 16 ÷ 4. After all three problems are completed, introduce the terms "division" and "quotient." 2. Go through the problems in Korean modification pages 3 and 4. This is where repeated subtraction is introduced. Go through the example with the balloons thoroughly with the class. Students should continue to write in the books. Read through pages 300-301 in Scott Foresman textbook. 4. Assign homework:

pages 302-303, #5-25 in Scott Foresman worksheets: Practice/Exploring Mathematics P 84 Enrichment/Exploring Mathematics P 84

Materials: miniature blocks (The ones from the base ten blocks work great!) Informal Assessment: Walk around the room to make sure that each student is following the repeated subtraction. Go over the first three problems in Scott Foresman book as a class.

Page Three of Korean Modification

There are 15 balloons which are tied together in groups of 5. How many groups are there?

Here are 15 balloons.

1. Take away one group of 5. 15 - 5 = 10 balloons left

2. Take away another group of 5.

10 - 5 = 5 balloons left

3. Take away another group of 5. 5 - 5 = 0 There are 3 groups of balloons because 15-5-5-5=0 That is, 15 ÷ 5 = 3 That is read 15 divided by 5 is 3. The expression as 15 ÷ 5 = 3 is called division and 3 is called the quotient.

Page Four of Korean Modification

How many times should be subtracted? Find the quotient. 6 - 2 - 2 - 2 = 0 → 6 ÷ 2 = 3 30 - 5 - 5 - 5 - 5 - 5 - 5 = 0 → 30 ÷ 5 = ___ 24 16 8 -8 ⇒ -8 ⇒ -8 → 24 ÷ 8 = 3 16 8 0 36 27 18 9 -9 ⇒ -9 ⇒ -9 ⇒ -9 → 36 ÷ 9 = ____ 27 18 9 0 Find the quotient of the division.

∆ ∆ ∆ ∆ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ∆ ∆ ∆ ∆ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ♣ ∆ ∆ ∆ ∆ 12 ÷3 = 4 16 ÷ 2 = ____ A tape with the length 8 cm. is cut into sections that are 2 cm. long. How many pieces are there?

8 ÷ 2 = ____ _______ pieces.

Page Five of Korean Modification

10 slices of watermelon are put into 5 dishes with equal numbers in each. How many watermelon slices are there in each dish?

If 10 watermelon slices are put in 5 dishes with equal numbers for each, then 2 watermelon slices are in each dish. Expressing this as division: 10 ÷ 5 = 2 12 apples are divided between 2 people. How many apples are given to each person?

12 ÷ 2 = _____ _____ apples

Page Six of Korean Modification

There are 18 pieces of bubble gum which are divided among three people. How many pieces of gum are given to each person? 18 ÷ 3 = _____ _________________

There are 20 pretzels which are distributed among 4 people. How many pretzels are given to each person?

20 ÷ 4 = _____ _________________

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24 ÷ 6 = _____ 21 ÷ 7 = _____

Lesson 4: Let's Study the Quotient (Division as the Opposite of Multiplication)

If 15 flowers are distributed to people with each person getting 3 flowers, how many people can have flowers?

15 ÷ 3 =

3 flowers which are given to 1 person, 3 x 1 = 3 are given to 2 people, 3 x 2 = 6 are given to 3 people, 3 x 3 = 9 are given to 4 people, 3 x 4 = 12 are given to 5 people, 3 x 5 = 15 3 x 5 = 15 ⇔ 15 ÷ 3 = 5 _________ people

Fill in the box ( ) with the correct number.

4 x = 28 5 x = 40

28 ÷ 4 = 40 ÷ 5 =

7 x = 42 9 x = 36

42 ÷ 7 = 36 ÷ 9 = 12 pieces of pizza are divided among 3 people with equal numbers for each person. How many pieces of pizza are given to each person?

12 ÷ 3 = pieces

3 people

have 1, 1 x 3 = 3

have 2, 2 x 3 = 3

have 3, 3 x 3 = 9

have 4, 4 x 3 = 12

4 x 3 = 12 12 ÷ 3 = 4

Fill in the box with the correct number.

x 2 = 8 x 3 = 18

8 ÷ 2 = 18 ÷ 3 =

x 4 = 20 x 8 = 32

20 ÷ 4 = 32 ÷ 8 = Use the multiplication facts to find the quotient. 4 x 1 = 4 4 x 2 = 8 4 x 3 = 12 4 x 4 = 16 4 x 5 = 20 4 x 6 = 24 4 x 7 = 28 4 x 8 = 32 4 x 9 = 36

24 ÷ 4 =

16 ÷ 4 =

Lesson 5: Writing Division Horizontally

Lesson 6: The Relationship between Multiplication and Division

How many are there? 5 x 3 = 15

If 15 are in bundles of 5, how many bundles are there?

15 ÷ 5 = ____ bundles

If 15 is divided by 3 bundles, how many are there in a bundle?

15 ÷ 3 = There are ____ in a bundle. 15 ÷ 5 = 3 5 x 3 = 15 15 ÷ 3 = 5 10 ÷ 2 = 5 2 x 5 = 10 10 ÷ 5 = 2

12 ÷ = 4 3 x 4 = 12

12 ÷ 4 = 6 x 8 = 48 9 x 5 = 45

48 ÷ = 8 45 ÷ = 5

48 ÷ = 6 45 ÷ = 9

From the multiplication, write two division expressions. 7 x 6 = 42 9 x 6 = 54 _______________ _______________ _______________ _______________ 4 x 8 = 32 3 x 8 = 24 _______________ _______________ _______________ _______________ Fill in the box with the correct number using the multiplication expression.

5 x 4 = 20 → 20 ÷ = 4

3 x 7 = 21 → 21 ÷ 3 =

7 x 9 = 63 → ÷ 7 = 9 Fill in the box with the correct number.

28 ÷ 4 = 36 ÷ 9 =

64 ÷ = 8 56 ÷ = 7

30 ÷ = 6 72 ÷ = 9

Lesson 7: Solve by Finding a Mathematical Expression

1. There are 40 ornaments, which are given to people with 5 ornaments for each person. How many people get ornaments?

expression: _______________________ answer: ____________ people 2. There are 32 pieces of colored paper that are bundled by 8 sheets. How many bundles are there? expression: _______________________ answer: ____________ bundles 3. There are 42 pieces of candy that are put in dishes with 7 for each person. How many dishes are needed? expression: _______________________ answer: ____________ dishes 4. 24 rocks are collected and distributed to 6 people with equal numbers for each person. How many rocks are given to each person? expression: _______________________ answer: ____________ rocks 5.

There are 28 pencils, which are given to 4 people with equal numbers for each. How many pencils are given to a person? expression: _____________________________ answer: ______________ pencils

6. There are 27 stamps which are distributed to 9 people with equal numbers for each. How many stamps are given to a person? expression: _______________________ answer: ____________ stamps 7. There are 72 apples which are put in 8 baskets with equal numbers in each basket. How many apples are put in a basket? expression: _______________________ answer: ____________ apples 8. There is a ribbon with the length of 56 cm which is cut into lengths that are each 8 cm long. How many pieces of ribbon are there? expression: _______________________ answer: ___________ pieces of ribbon 9. There are 24 apples. They are put in dishes with equal numbers in each. How many apples are put in a dish? Give 3 possible answers.

Dishes Apples in each dish2 12

10. Use the picture to write a multiplication expression and a division expression.

multiplication: _______________________ division: ____________________________

11. Use the picture to write a multiplication expression and a division expression.

multiplication: _________________ division: _________________

Lesson 8: Multiplication and Division Using Larger Numbers

Let's study the quotient. There are 6 small bundles of 10 colored papers. These colored papers are divided between Jack and Jill with equal numbers of paper given to each person. How many bundles are distributed to one person? How many papers are given to one person? There are two questions. Let's find a method of solving 60 ÷ 2.

as a bundle 6 ÷ 2 = 3 also 236

as paper 60 ÷ 2 = 30 also 23060

1. 5 ÷ 5 = _____ → 5 5

2. 50 ÷ 5 = _____ → 5 50

3. 8 ÷ 4 = _____ → 4 8

4. 80 ÷ 4 = _____ → 4 80

5. 40 ÷ 4 = 6. 90 ÷ 3 =

7. 70 ÷ 7 = 8. 80 ÷ 2 =

PRETEST FORM A

Number (Do not put your name!): _______ Date: __________________ Answer the questions as best as you can. Your scores will not affect your quarterly grade. Fill in the boxes with the quotient.

1. 8 ÷ 2 = 5. 16 ÷ 4 =

2. 10 ÷ 5 = 6. 60 ÷ 2 =

3. 15 ÷ 3 = 7. 30 ÷ 3 =

4. 12 ÷ 4 = 8. 40 ÷ 4 =

9. 10.

2 6 3 9 11. There are 15 apples which are divided equally among 3 people. How many apples did each person get? _______________________________ 12. There are 4 students in each art group. Each group has 20 crayons to share equally. How many crayons will each student receive? _______________________________ 13. A ribbon that is 10 centimeters long is cut into 5 equal pieces. How long is each piece of ribbon? _______________________________

14. There are 20 pictures. 4 pictures can fit on one page. How many pages are needed? _______________________________ 15. Write a division expression from the following picture of ladybugs.

expression: ___________________________ answer: __________________ 16. Answer the following question in complete sentences. In what ways is division like multiplication? ________________________________________________________________

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17. Explain a situation (not in school) when a person might need to use division.

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18. Explain two different ways to find the answer to the following problem:

8 ÷ 2 = ____

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2._______________________________________________________________

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