Main Curriculum Tie:
Background For Teachers:
Ways to Gain/Maintain Attention (Primacy):
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
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
Lesson segment 4: Application Multiplication Games
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
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