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# Division - Meaning, Manipulatives and Relationships

Lesson Plans > Mathematics > Division

## Division - Meaning, Manipulatives and Relationships

Unit Plan #2
Learning to Use Division

General Objective: Upon completion of this unit, students will be able to comprehend the meaning of division through the use of manipulatives, as well as understanding the relationship between the process of subtraction to division and the process of multiplication to division. They will also learn the concept of fact families and inverse operations, which will guide them in solving division problems where the divisors are 2, 3, 4, 5, and 1. Students will learn and be able to defend why 0 cannot be a divisor.

Unit Rationale:
This unit on division will play a profound role in my students' mathematical development because it is an extremely beneficial topic for all to comprehend and put into use. Everyone uses the process of division on a day-to-day basis, but may not even know it! From splitting items proportionately to making sure to have enough transportation available for special trips, division is a common, but very important process that all must be familiar with to survive in today’s society. Division can be very challenging for students to grasp, but I have made a valiant effort to relate the process to many day-to-day experiences in hopes of making the process a little easier to grasp. I felt this was an excellent topic to expand on for third graders.

Overview:
Lesson 1: What Does Division Really Mean?
Lesson 2: Relating Subtraction and Division
Lesson 3: Connecting Multiplication and Division
Lesson 4: Writing a Number Sentence
Lesson 5: Dividing by 2 and 5
Lesson 6: Dividing by 3 and 4
Lesson 7: Dividing with 1 and 0

Heather Breaux
Division Unit
Lesson 1: What Does Division Really Mean?
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.

NCTM Standards:
1. Number and Operations
6. Problem Solving
7. Reasoning and Proof
9. Connections
10. Representation

Behavioral Objectives: Upon completion of this lesson, students will be able to….
1. Model the meaning of division by using counters
2. Verbally state the meaning of division one hundred percent of the time

Interdisciplinary Connections: Because we have been discussing the concept of slavery and the Civil War in Social Studies, I will connect the term “equal” from a math standpoint (meaning the groups are equal because they contain the same amount) to a social studies viewpoint, where all people are equal and are entitled to the same rights.

Materials/Technology Needs: Enlarged animal crackers (for demonstration and discussion); counter chips for entire class; colored chalk (especially red and blue); worksheet “Connect” from p. 239; “Reteach 12.1” RW62 from p. 238.

Anticipatory Set: To start today’s lesson, I will hold up a jar of animal crackers and say, “I have a bunch of animal crackers here and I want to share them with Miss Sweigart and Miss Perritt because I know that they LOVE animal crackers! In order to share them, I need to separate the crackers and make equal groups. I’m going to do this by using a process called division.” Write the word division on the board. Say, “We use division all the time because we are constantly sharing with others by making sure that we have the same amount of stickers, crackers, and other fun things in the classroom. By dividing, we can find out how many items can go into equal groups. What does equal mean? (all having the same amount- connect to Social Studies lesson on slavery and the Civil War) I’m going to need your help to figure out how many crackers Miss Sweigart, Miss Perritt, and I can each have!”

Procedure:
1. Put 12 enlarged animal crackers on the board and tell the children that we’re going to pretend that there are only 12 crackers in the jar right now. Ask students how many people are going to get crackers. (3 people). Draw 3 large boxes on the board with each teacher’s name on a box. Place one cracker in each group at a time, and continue until all of the crackers are gone. Ask what process we used (division). Ask, “How many crackers did each get?” (4). “How many groups were used to divide the crackers equally?” (3) Give students animal crackers to reward them for their help.
2. Divide students into partners and pass out counter chips to each group. Explain that division can be easily modeled by using counter chips. Write “Activity 1 Problem” located on p. 238 on the board for the class. Demonstrate problem on board while groups follow along with the counters at their seats. Remind them that the key to dividing is to always separate the counters into equal groups. Complete “Activity 2” on p. 238 the same way, and ask “What would you do differently if you were to divide 14 counters into 7 equal groups?” (begin by putting 1 counter into each of the 7 groups until there are no more left). “What’s different with this problem compared to the last problem that we did?” (there were 7 groups this time instead of 2).
3. Write the “Try It’s problems “a and b” on the board for partners to complete together. Only have them complete one letter at a time, followed by going over that problem as a class. Have the students then go on to complete letter “b” together, followed by going over that problem as a class.
a. Divide 15 counters into 5 equal groups. How many are in each group?
b. Divide 15 counters into groups of 5. How many groups of 5 counters can you make?
4. Explain to the class that the problem’s we have done as a class have shown us that we can divide in order to find 2 things:
1. To find out how many items are in each group
2. How many equal groups there are
5. Pass out worksheet “Connect” from p. 239. Do first 2 marble problems as a class. Draw groups on the board using red colored chalk. Call on students to draw in the marbles in each group using blue colored chalk. Have children complete questions 1-5 with their partners.
6. Pass out “Reteach 12.1” RW62 from p. 238

Accommodations: I have a student in class named Jessica, who because of a visual impairment needs to sit at the front of the class and be provided special enlarged worksheets. I will accommodate and provide these worksheets for her.

Closure: Congratulate students on their fabulous job of learning division. Ask for volunteers to explain what it means to divide something equally. (separate things into equal groups that are all the same). Write “Lesson Quiz” problem number 1 on the board. Use chalk in a similar fashion from Procedure #5.
1. 10 books are divided into 2 equal groups. How many books are in each group?” (5 books)

Key Questions:
1. “What can the process of division help you find?” (how many items are in each group and how many equal groups there are)
2. “What can we use to easily model division?” (counters)

Evaluation: I will be conducting a formative assessment by roaming around the room as the students work together to solve the division problems with their partners, as well as by listening in on their discussion and the answers to my questions in class. For my summative assessment on today’s lesson, I will be using the homework assignments to determine whether the students are grasping the concept of division, which can be a tricky one for students to grasp.

Assignment: “Reteach 12.1” RW62 from p. 238

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.

Lesson by Frank D'Angelo

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