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Represent Rational Numbers and Their Opposites on the Number Line

Plot rational numbers and identify their opposites on horizontal number lines.

6.NOS.C.6 · Rational Numbers & Opposites
Level
Guided practice with vocabulary support

🟠 Level 0 — Extra Support

Sentence starters: “First, I…” · “The answer is… because…” · “I know this because…”
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Warm-Up

2 questions
Warm-Up 1
Where is -1.5 located on the number line?
Vocabulary: A rational number is any number that can be written as a fraction. Negative numbers are to the left of zero on a horizontal number line.
-3 -2 -1 0 1 2 3 ?
✓Correct! -1.5 is halfway between -2 and -1 on the number line. It is 1.5 units to the left of zero.
✗Not quite. Since -1.5 is negative, it is to the left of zero. It sits exactly halfway between -2 and -1. The answer is B.
Warm-Up 2
True or False: The opposite of 3/4 is -3/4.
Vocabulary: The opposite of a number is the same distance from zero but on the other side of the number line. For example, the opposite of 5 is -5.
✓Correct! The opposite of 3/4 is -3/4. Both are the same distance (3/4 of a unit) from zero, but on opposite sides.
✗Actually, this is true. The opposite of any number has the same absolute value but the opposite sign. The opposite of 3/4 is -3/4.
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Practice

5 questions
Practice 1
Write the opposite of each rational number.
Remember: To find the opposite, change the sign. Positive becomes negative, and negative becomes positive. The opposite of a number is the same distance from zero on the other side of the number line.
a. The opposite of 2.5 is
b. The opposite of -3/4 is
c. The opposite of -1.8 is

Sentence frame: "The opposite of ___ is ___ because they are the same distance from zero but on opposite sides of the number line."

✓All correct! The opposite of 2.5 is -2.5, the opposite of -3/4 is 3/4, and the opposite of -1.8 is 1.8.
✗Some answers need another look. Remember: flip the sign to find the opposite. Positive becomes negative, negative becomes positive.
Practice 2
Which number line correctly shows 1/2 and -1/2?
Hint: Both 1/2 and -1/2 should be the same distance from zero. 1/2 is to the right of zero and -1/2 is to the left.
Explain your reasoning:

Sentence frame: "I chose ___ because 1/2 and -1/2 are opposites. They should be the same distance from ___ but on ___ sides."

✓Correct! 1/2 and -1/2 are opposites. They are each 1/2 unit from zero, with 1/2 to the right and -1/2 to the left.
✗Not quite. Opposites must be the same distance from zero on opposite sides. 1/2 is to the right of zero, and -1/2 is to the left. The answer is A.
Practice 3
Drag each rational number to its correct position on the number line. Place them in order from least to greatest.
Strategy: First, convert fractions to decimals to compare: -1/4 = -0.25, 3/2 = 1.5. Then order from most negative (left) to most positive (right) on the number line.
-3 -2 -1 0 1 2 3
-2.5
0.75
-1/4
3/2
-1
2
Least
 
 
 
 
Greatest
✓All correct! The order from least to greatest is: -2.5, -1, -1/4, 0.75, 3/2, 2.
✗Some numbers are not in the right position. Convert fractions to decimals to help compare: -1/4 = -0.25, 3/2 = 1.5. The correct order is -2.5, -1, -1/4, 0.75, 3/2, 2.
Practice 4
True or False: -0.5 is to the left of -1 on a number line.
Hint: On a number line, numbers get smaller as you move left. Which is smaller: -0.5 or -1? Think about which is closer to zero.
-2 -1 0 1 -1 -0.5
Explain your reasoning:

Sentence frame: "-0.5 is ___ (closer to / farther from) zero than -1, so -0.5 is to the ___ of -1 on the number line."

✓Correct! This is false. -0.5 is closer to zero than -1, so -0.5 is to the right of -1 on the number line.
✗Not quite. -0.5 is greater than -1 (closer to zero), so it is to the right of -1, not the left. The statement is false.
Practice 5
What rational number is at point P on the number line below?
Strategy: Count the tick marks between whole numbers. Each space between -1 and 0 is divided into fourths. Point P is at the third tick mark to the left of zero, which is -3/4 (or -0.75).
-2 -1 0 1 P
How did you determine the value at point P?

Sentence frame: "Point P is at ___ because it is ___ tick marks to the ___ of zero, and each tick mark represents ___."

✓Correct! Point P is at -3/4. It is 3 quarter-marks to the left of zero. Each mark represents 1/4.
✗Look at the tick marks between -1 and 0. There are 4 equal spaces (fourths). Point P is at the 3rd tick from 0, which is -3/4. The answer is B.
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Challenge

1 question
Challenge
Plot 4/3 and its opposite on the number line below. Then explain the distance each is from zero.
Think about it: 4/3 as a decimal is about 1.33. Its opposite is -4/3. Both should be the same distance from zero but on opposite sides. Use the fraction/decimal equivalence to help you place them accurately.
-2 -1 0 1 2
Where would you plot 4/3? Where would you plot -4/3?
Explain the distance each number is from zero:

Sentence frame: "4/3 is located at ___ on the number line, which is ___ units to the right of zero. Its opposite, -4/3, is at ___, which is ___ units to the left of zero. Both are ___ units from zero."