Rational Numbers: Compare and Operate

Name:

Date:

Page 1: Card Sort

Directions: Cut apart the cards or separate them. Work with your group to sort cards into equivalent-value sets. Then create comparison pairs using cards that show different rational numbers. Record evidence for each match or comparison.

Card A: −3/4

Card B: −0.75

Card C: A point 0.75 unit to the left of 0 on a number line

Card D: The temperature is 0.75°F below 0°F

Card E: 2/3

Card F: A point 2/3 unit to the right of 0 on a number line

Card G: 1 − 1/3

Card H: −3/2

Card I: −1 − 1/2

Card J: An account balance of −$1.50

Card K: 5/8

Card L: 0.625, or a point halfway between 0.5 and 0.75

Challenge: For at least two sets, agree on the most convincing evidence: a calculation, equivalent decimals, a number line, or a real-world meaning.

Page 2: Record, Apply, and Explain

Card Sort Recording

Record four card sets or comparison pairs. Include the comparison symbol when the values are not equal.

Card pair or set: ____________________
Comparison: ______ Evidence: ____________________
Justification: __________________________________________

Scaffold Box

Key vocabulary: rational number, opposite, additive inverse, absolute value, equivalent, greater than, less than.

Sentence starters: “_____ is greater than _____ because _____.” “I represented this by _____.” “Subtracting _____ is equivalent to adding _____.”

Independent Applications

1. At 6:00 a.m., the temperature is −6.5°F. It rises 9.25°F during the day. What is the new temperature? Write an equation and one sentence explaining your answer.

2. A bank account has a balance of $14.75. A purchase of $18.50 is made. What is the new balance? Rewrite the subtraction as adding the opposite, then explain the result.

3. A hiker is at −2.4 miles relative to a trail marker and walks to 3.75 miles. What distance does the hiker travel? Use the absolute value of a difference and explain.