Signed Numbers on a Number Line

Understand the idea

Integers include negative whole numbers, zero and positive whole numbers. On a horizontal number line, values increase to the right. Adding a positive number moves right; adding a negative number moves left. Subtracting a number is equivalent to adding its opposite. The absolute value is distance from zero, so it cannot be negative.

Worked example

Start at −3 and add 5: move five units right to reach 2. For 2 − (−4), add the opposite of −4, so 2 + 4 = 6. Compare −7 and −2: −7 is farther left, so −7 < −2, even though its absolute value is greater.

Try it yourself

1. Compute −4 + 7 and explain the direction of movement.
2. Compute 3 − 8 and then −5 − (−2).
3. Which is greater: −9 or −4? Which has the larger absolute value?

Check your reasoning

1. 3; start at −4 and move seven units right.
2. 3 − 8 = −5; −5 − (−2) = −5 + 2 = −3.
3. −4 is greater because it is farther right. −9 has the larger absolute value: 9.

Make it work for your learner

For support, model the example one step at a time and ask the learner to explain each choice in their own words. Use a sketch, organizer or physical model where helpful. For a challenge, create a new example, test an alternative explanation or describe when the model would not apply.

Exit check

Use direction and distance to explain integer addition and subtraction. Explain your reasoning with a specific example before moving on.