Share Share
Multiplying and Dividing Integers

Curriculum Tie:


  

Summary:
Perform multiplication and division with integers. Use patterns, models, and tools to check for reasonableness.

Main Curriculum Tie:
Mathematics - Pre-Algebra
Standard 1 Objective 3
Solve problems involving rational numbers using addition, subtraction, multiplication, and division.

Materials:


Attachments

Background For Teachers:
Enduring Understanding (Big Ideas):
Operations with integers

Essential Questions:

  • How can algorithms, manipulatives, pictures, and other tools be used to model integer operations and check for reasonableness?
  • How can I predict the outcome of operating with integers?

Skill Focus:
multiply and divide integers

Vocabulary Focus:
integer

Ways to Gain/Maintain Attention (Primacy):
technology, manipulatives, predicting and making inferences from patterns, group discussion, games

Instructional Procedures:
Starter: Review

  1. What fraction of the box contains the x’s?
  2. What is the percent and decimal form for that fraction?
  3. -3 – (-5) = n
  4. Arrange these from least to greatest: 3.4, 350%, 3⅞

Lesson Segment 1: How can algorithms, manipulatives, pictures, and other tools be used to model integer operations and check for reasonableness when multiplying and Dividing Integers?

TI-73 visualization, sketches and notes - Demonstrate the connection between addition/subtraction and multiplication or division Using the Numline Application on the TI-73 by going through a-d as follows. (You can push the trace key to check each step.) The following examples, questions and responses should be sketched and written on a notes paper for their journal

a) Demonstrate 2 x 4 by starting at 0. Then, +2 + 2 + 2 + 2. Ask students what are 4 two’s or 2 x 4? This is starting at 0 and moving forward two places four times or moving in a positive direction. Multiplication is like repeating addition beginning at 0. When you start at 0 and repeat moves in a positive direction, you will end up at a positive number on the number line. To demonstrate 8/2 begin at 8 and subtract 2 four times to get back to 0. There are four two’s in 8. Division can be likened to repeating subtraction beginning at the dividend and ending at 0.

b) Demonstrate -2 x 4 by starting at 0. Then, -2 + -2 + -2 + -2. Ask students what are 4 negative two’s or -2 x 4? This is starting at 0 and moving backwards two spaces four times or moving in a negative direction four times. When you begin at 0 and repeatedly move backwards, you will end up at a negative number on the number line. To demonstrate -8/-2 begin at -8 and subtract -2 four times to get back to 0. Again, division is like repeated subtraction beginning at the dividend ending at 0.

c) We have been looking at what happens when you multiply by a +4. What do you think will happen when we multiply by a -4 Think-team-share question: What direction would you think I would be moving on the number line if I wanted to add 2 negative four times or multiply 2 x -4? Where will I end up? Have them write their prediction on the journal page and sketch and explain their reasoning. Demonstrate by explaining that when we multiplied 2 by 4, we moved forward two places repeated four times. Multiplying by -4 requires us to TURN AROUND before moving forward repeatedly. That can be modeled by using the subtract key to show turning around. Demonstrate 0 – 2 – 2 – 2 – 2 .

d) Think-team-share question: What direction would you think I would be moving on the number line if I wanted to add -2 negative four times or multiply -2 x -4? Where will I end up? Have them write their prediction on the journal page and sketch and explain their reasoning. Demonstrate by explaining that when we multiplied -2 by 4, we moved backward two places repeated four times. Multiplying by -4 requires us to TURN AROUND before moving backwards repeatedly. That can be modeled by using the subtract key to show turning around. Demonstrate 0 – (-2) – (-2) – (-2) – (-2).

Lesson segment 2: How can I predict the outcome when multiplying or dividing integers?
Use the attached journal page to have students see the pattern to justify positive or negative products and quotients when using integers. They should use a calculator to make sure the tables are filled in correctly in order to see the pattern.

Algeblocks and the Quadrant mat are an excellent visualization for helping students remember the rules for multiplying and dividing integers. A student quadrant mat worksheet has been attached to have students sketch the units using an area model. See the Algeblocks manual for helps in teaching this.

Lesson Segment 3: Summary
Have students get out the foldable they began in the addition and subtraction lesson and complete it writing rules and examples in the appropriate place under the flaps for multiplication and division.

Lesson segment 4: Application Multiplication Games
Play Integers Snap where two students are give a card deck to play. Black suits are positive numbers and red suits negative numbers. Aces are 1. Face cards can be removed or assigned a value such as 0, 11, and 12. Students shuffle cards. Each player draws a card and looks at it to determine its value. Both players lay the card face up on the desk simultaneously. The person who snaps out the correct product first keeps both cards. Player with most cards when deck is gone wins the game.

Integer War could also be played so speed is not a factor. Both players draw two cards. The player whose cards have the greatest product get both cards.

Rolling Products Game: Give each group of four two red and a black die (or 2 white and another color). The two like color dice represent negative integers. The one different color die represents a positive integer. If dice are not available, use the TI 73 to generate three dice numbers. The first two numbers in the parentheses represent negative numbers. The third represents a positive number. Players are paired so there are two against two. For their turn, pairs roll the dice and choose any two of their three dice numbers to multiply. They state which two integers they will be using, write them and their product on a recording paper. Pairs take turns rolling the dice. After six turns for each pair, the players add their products. The pair with a sum of products closest to 0 wins.

Assessment: Give the attached quiz

Attachments

Assessment Plan:
writing, performance task, quiz

Bibliography:
This lesson plan was created by Linda Bolin.

Author:
Utah LessonPlans

Created Date :
May 06 2009 10:41 AM
 12806