Negative numbers: how to help your child practice

What are negative numbers?

Negative numbers are the numbers to the left of zero on a number line: −1, −2, −3 and so on. Kids already know them from real life: a temperature below zero, a floor below ground level, or a depth below sea level.

The key idea is direction. The farther left a number is, the smaller it is, so −7 is less than −2 even though 7 is more than 2. The distance from zero, ignoring the sign, is called absolute value: both −5 and 5 are 5 steps from zero.

In most US schools, 6th graders learn to read, order and compare negative numbers, find absolute value, and plot points with negative coordinates. 7th graders add, subtract, multiply and divide them. The 7th grade guide covers what else comes up that year, and the math topic guide shows how integers lead into algebra.

How do you add and subtract negative numbers, step by step?

Use a number line until the rules feel natural:

1. Start at the first number. For −3 + 5, put your finger on −3.
2. Adding a positive: move right. Move 5 steps right and land on 2. So −3 + 5 = 2.
3. Adding a negative: move left. For −8 + 5, start at −8 and move 5 right to land on −3. For 2 + (−7), start at 2 and move 7 left to land on −5.
4. Subtracting: add the opposite. Change the subtraction to addition and flip the sign of the second number. −2 − (−6) becomes −2 + 6 = 4. And 2 − 7 becomes 2 + (−7) = −5.

For multiplying and dividing in 7th grade, the sign rule is short: same signs give a positive answer, different signs give a negative one. −3 × −4 = 12, and −3 × 4 = −12.

A quick sense check helps: when adding a positive and a negative, the answer takes the sign of the number farther from zero.

What negative numbers mistakes do kids make most?

Thinking −7 is bigger than −2

A child says −7 > −2 because 7 is bigger than 2. On a number line, −7 is farther left, so it's smaller: −7 < −2. Ask, "Which is colder, −7 degrees or −2 degrees?"

Treating minus a negative as plain subtraction

A child solves 4 − (−3) as 4 − 3 = 1. Subtracting a negative is the same as adding a positive, so it's 4 + 3 = 7. Have your child rewrite every subtraction as "add the opposite" before solving.

Adding the sizes and keeping the minus

For −8 + 5, a child adds 8 and 5 and writes −13. Moving 5 to the right from −8 lands on −3. When the signs are different, find the difference (8 − 5 = 3) and keep the sign of the number farther from zero.

How can you practice negative numbers at home in 10 minutes?

A drawn number line or a thermometer makes negative numbers concrete.

• Minutes 1–3: temperature talk. "It's −4 degrees and it warms up 11 degrees. What's the temperature now?" (7 degrees.) Have your child show the move on a number line from −10 to 10.
• Minutes 4–8: five mixed problems. One comparison (which is greater, −6 or −3?), one positive plus negative (−5 + 8), one subtraction that crosses zero (3 − 9), one subtraction of a negative (−1 − (−5)), and, for 7th graders, one multiplication (−2 × 6).
• Minutes 9–10: explain one move. Ask your child to explain on the number line why 4 − (−3) lands on 7. Taking away a debt of 3 leaves you 3 better off is one way to say it.

Use new numbers each night.

How can Easy Twin help with negative numbers?

Scan your child's integers worksheet and Easy Twin makes a twin with the same kinds of questions and new numbers. Every question comes with two hints and worked steps, number lines are redrawn with new data, and your child can play the twin as a quest or you can print it with an answer key.

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