Investigating Inequalities:

Transcription

1 Investigating Inequalities: Choose roles: Record each group member s name next to their role: Anuncer: Recorder: Walker A: Walker B: Set-up: use the number cards to construct a number line on the floor. Conduct the investigation: Walkers stand at starting numbers (see table below). Recorder confers with group to determine appropriate inequality symbol comparing Walker positions, and records symbol in the table. Anuncer calls out operation and both walkers calculate their new numbers and walk to their new locations on the number line. Recorder records their new positions and again confers with group to determine appropriate inequality symbol. Be sure to write a true inequality statement. Repeat until table is complete, then answer the questions that follow. Operation Walker A s Position Inequality Symbol Walker B s Position Starting number 2 4 Add 2 Subtract 3 Add 2 Subtract 4 Multiply by 2 Subtract 7 Multiply by 3 Add 5 Divide by 4 Subtract 2 Multiply by 1 Use your completed table to answer the questions on the next page.

2 1. What happens to the walkers relative positions on the number line when the operation adds or subtracts a positive number? A negative number? Does anything happen to the direction of the inequality symbol? 2. What happens to the walkers relative positions on the number line when the operation multiplies or divides by a positive number? Does anything happen to the inequality symbol? 3. What happens to the walkers relative positions on the number line when the operation multiplies or divides by a negative number? Does the inequality symbol change directions? 4. Which operations on an inequality reverse the inequality symbol? Does it make any difference which numbers you use? Consider fractions and decimals as well as integers. 5. Check your findings about the effects of adding, subtracting, multiplying, and dividing by the same number on both sides of an inequality by creating your own table of operations and walkers positions:

3 True or Not? Substitute each value in the table into the inequality at the top. If the resulting inequality is true, shade the box with T. If resulting inequality is false, shade the box with F. 5m 10 a 2 0 m 5 T F a 5 T F m 4 T F a 4 T F m 3 T F a 3 T F m 2 T F a 2 T F m 1 T F a 1 T F m 0 T F a 0 T F m 1 T F a 1 T F m 2 T F a 2 T F m 3 T F a 3 T F m 4 T F a 4 T F m 5 T F a 5 T F On each number line below, place dots on the values that made the inequality true. 5m 10 a 2 0 In the first table, how would values of m between 2 and 3 be shaded? Why? All rights reserved. 211

4 True or False? Substitute each value in the table into the inequality at the top. If the resulting inequality is true, shade the box with T. If resulting inequality is false, shade the box with F. 3x 9 2y 6 x 5 T F y 5 T F x 4 T F y 4 T F x 3 T F y 3 T F x 2 T F y 2 T F x 1 T F y 1 T F x 0 T F y 0 T F x 1 T F y 1 T F x 2 T F y 2 T F x 3 T F y 3 T F x 4 T F y 4 T F x 5 T F y 5 T F Transfer your answer to the number line below by placing dots on the values that made the inequality true. 3x 9 2y 6 Write a sentence describing the values that make each inequality true. All rights reserved. 213

5 Mr. Willett s Purchase Mr. Willett decided to buy a suit and a pair of shoes. He wants to spend less than $350. The price of the suit is 3 times the price of the shoes. Use the table below to find 3 possible purchases Mr. Willett could buy. In addition, find at least 1 purchase that Mr. Willett would t buy. Cost of Shoes Cost of Suit Total Cost Less than $350? How could you determine the purchase he would t make? All rights reserved 209