Lesson 7-4: Compare and Order Integers and Rational Numbers

Warm-Up 1

Which integer is greater: −3 or −7?

Vocabulary: To compare means to decide which number is greater or less. On a number line, numbers farther to the right are greater.
Hint: Picture −3 and −7 on a number line. Which one is farther right?

✓Correct! −3 is to the right of −7 on the number line, so −3 > −7.

✗Not quite. On a number line, −3 is to the right of −7. Numbers farther right are greater, so the answer is B: −3.

Warm-Up 2

True or false: −2 > −1

Vocabulary: The symbol > means "is greater than." A number is greater if it is farther right on the number line.
Think: Is −2 to the right of −1?

✓Correct! −2 is to the left of −1, so −2 < −1. The statement −2 > −1 is false.

✗−2 is to the left of −1 on the number line, which means −2 is less than −1. The statement is false.

Practice 1

Write the correct symbol: < or > to compare each pair of numbers.

Vocabulary: < means "less than" and > means "greater than." Think about where each number falls on a number line. The number farther right is greater.
Tip: The symbol always points toward the smaller number.

a. −4 −9

b. 2.5 −2.5

c. −1/2 −1/4

Sentence frame: "−4 is to the ___ of −9, so −4 ___ −9."

✓All correct! −4 > −9, 2.5 > −2.5, and −1/2 < −1/4.

✗Some answers need another look. Remember: on a number line, the number farther right is greater. Answers: −4 > −9, 2.5 > −2.5, −1/2 < −1/4.

Practice 2

Drag the numbers into the box to order them from least to greatest.

Vocabulary: To order numbers means to arrange them from smallest to largest (or largest to smallest). Negative numbers are always less than positive numbers. Among negatives, the one with the larger absolute value is less.
Strategy: Picture a number line. Place each number, then read left to right for least to greatest.

3

−5

0

−1

2.5

−3.5

Least to Greatest:

Sentence frame: "The least number is ___ because it is farthest ___ on the number line."

✓Perfect! The correct order is −5, −3.5, −1, 0, 2.5, 3.

✗Not quite right. The correct order from least to greatest is: −5, −3.5, −1, 0, 2.5, 3. Remember to read left to right on the number line.

Practice 3

Which list is in order from least to greatest?

Strategy: Check each list by placing the numbers on a mental number line. The correct list should go from farthest left to farthest right.

Explain how you checked:

✓Correct! −8 < −5 < −3 < 0 < 4. Each number is to the right of the previous one on the number line.

✗Check again. From least to greatest means from the most negative to the most positive: −8, −5, −3, 0, 4. The answer is C.

Practice 4

True or false: Any positive number is greater than any negative number.

Think about it: On the number line, where are all positive numbers? Where are all negative numbers? Is there any overlap?

Explain your reasoning:

✓Correct! All positive numbers are to the right of 0, and all negative numbers are to the left. So every positive number is greater than every negative number.

✗Think again. Positive numbers are always to the right of 0, and negative numbers are always to the left. This means the statement is true.

Practice 5

On a number line, −6 is to the ___ of −2, so −6 ___ −2.

Vocabulary: On a number line, the number to the left is always less than the number to the right.
Think: Where is −6 compared to −2?

Explain your reasoning:

Sentence frame: "−6 is to the ___ of −2 on the number line. The number on the left is always ___, so −6 ___ −2."

✓Correct! −6 is to the left of −2, and left means less than. So −6 < −2.

✗−6 is farther left than −2 on the number line. Left means less than. The answer is B: left, <.

Challenge

Four cities recorded these temperatures on a winter morning:
Springfield: −12°F Lakewood: 5°F Riverside: −3°F Hilltop: 0°F

Order the temperatures from least to greatest, then explain your reasoning using number line position.

Strategy: Place each temperature on a number line. Read them from left to right for least to greatest. −12 is the farthest left, 5 is the farthest right.
Sentence frame: "The coldest temperature is ___ because it is farthest ___ on the number line. The order from least to greatest is ___, ___, ___, ___."

Order from least to greatest:

Explain using number line reasoning:

Sentence frame: "The coldest temperature is ___ because it is farthest ___ on the number line. Next is ___, then ___, and the warmest is ___. The order is ___, ___, ___, ___."

🟠 Level 0 — Extra Support

Warm-Up

Practice

Challenge