Explain absolute value as distance from zero on the number line
Read and write |x| notation for positive and negative integers
Find |−n| and |n| using a number line
Tell absolute value apart from opposites
Use absolute value in real-life situations like temperature and floors
The absolute value of a number is its distance from 0 on the number line. We write it with two vertical bars, like |−7|. Distance is never negative, so |−7| = 7 and |5| = 5. The absolute value of 0 is 0, because 0 sits exactly on 0.
I still remember the first time a student asked me, "Miss, how can minus seven become seven?" She wasn't wrong to ask. The minus sign feels like it should stick. But absolute value doesn't care about direction. It asks only one question: how far are you from zero?
Think of a thermometer. −5°C and +5°C sit on opposite sides of freezing, yet both are 5 degrees away from 0°C. That's the whole idea: |−5| = 5 and |5| = 5.
Find the number first. Then count the jumps back to 0. That count is your answer.
For |−4|, start at −4 on the number line and hop to 0: one, two, three, four jumps. So |−4| = 4. For |3|, start at 3 and hop left three times: |3| = 3. Notice the answer is never negative. A distance can't be −4 jumps long.
Here's the trap I watch for every year: students write |−9| = −9. They keep the minus out of habit. I tell my class: the bars eat the sign. Whatever goes in, a plain positive number comes out.
Opposite integers are a pair: −6 and 6. They share the same distance from zero but point in different directions. Absolute value is that distance itself: |−6| = 6.
So opposites answer "which two numbers mirror each other?" while absolute value answers "how far is this number from zero?" The two ideas shake hands here: opposite numbers always have the same absolute value. That's why |−6| and |6| both equal 6.
If your child mixes them up, you're not alone. I see it in class every single term. The fix is one sentence: opposites are two numbers, absolute value is one distance.
The lift. A lift is parked at floor −3, three floors below the ground. How many floors must it climb to reach the ground floor? Count the distance from −3 to 0: |−3| = 3 floors. The minus tells you the direction (down). The absolute value tells you the size of the trip.
The sea. A scuba diver swims at −12 metres (12 metres below sea level) while a seagull flies at +12 metres above it. Who is farther from the surface? Neither. |−12| = 12 and |+12| = 12. Same distance, opposite directions. Divers, pilots and bankers use this thinking daily: a debt of $20 (−$20) and a saving of $20 (+$20) both involve a magnitude of $20.
Lifts and divers are just the start. I put together 10 real-life integer examples every Grade 6 student should know.
This 4-page printable PDF builds the skill the way I teach it in class. Section A opens with 5 multiple choice questions on |x| notation and meaning. Section B has 5 fill in the blanks where students write absolute values and key facts about distance from zero. Section C brings 5 true or false statements that target the classic traps, like |−8| = −8. Section D is match the columns, pairing values like |−10| and |−3| with their answers. Section E asks 5 short written answers, so students explain the difference between absolute value and opposite in their own words. Section F closes with 2 real-life problems: Sana and Bilal on the stairs above and below ground level, and a diver 12 metres below sea level. A riddle and 2 challenge questions wait at the end for fast finishers.
Students start by counting jumps on the number line, because fingers on a line beat rules in a book. Then they meet the |x| notation and practise until the bars feel natural. Only after that do they face the traps: negatives that look scary, and opposites dressed up as absolute values. By the end, they explain in their own words why |−9| = 9. That's when I know it stuck.
Try these with your child:
Use this worksheet for the first absolute value lesson, as homework, for homeschool or one-to-one tutoring, or as a quick check before you move on to ordering and comparing integers. Because it mixes question formats on one idea, it quickly shows which students truly get that |−7| = 7 and which ones are still letting the minus sign boss them around.
What is the absolute value of −7?
7. The number −7 sits 7 jumps away from 0 on the number line, so |−7| = 7. Direction doesn't matter here. Only distance does.
Can absolute value be negative?
No, never. Absolute value measures distance, and distance can't be negative. |−15| = 15, |15| = 15, and |0| = 0.
What's the difference between opposite and absolute value?
An opposite is a number; absolute value is a distance. The opposite of −6 is 6. The absolute value |−6| is 6. Opposites always share the same absolute value.
What is |0|?
0. Zero sits exactly on zero, so its distance from zero is nothing. It is the only integer whose absolute value is 0.
Which Common Core standard does this worksheet cover?
6.NS.C.7: understanding ordering and absolute value of rational numbers, including absolute value as distance from 0 on the number line.
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