Integers and Negatives
The number line runs both ways, and two minuses really do make a plus
Free trail · Math · ages 11–12 · 6 stations
The Line Goes Both Ways
An integer is any whole number — positive, negative or zero — with no fraction part. Negatives are not a piece of maths trickery; they measure real things that live below a natural zero.
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A road with zero in the middle. Numbers grow as you walk right and shrink as you walk left, so −6 sits further left, and is lower, than −2.
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Winter temperature in Leh, a bank balance after a loan, a basement floor in a lift, a diver below sea level. Each has a genuine zero with a genuine "below".
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−7 and +7 stand the same distance from zero but in opposite directions. That distance, always positive, is the number's magnitude.
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Almost everyone says −7 is bigger than −3, because 7 beats 3. On the line −7 is further left, so it is smaller. A debt of ₹7 is worse than a debt of ₹3.
This is one station of 6 in the trail, and finishing the trail earns an Explorer badge. Create a free account to play the rest →
Inside the app
The station above is the real thing — and it is one of 6. Inside the app your child plays the whole trail — every station is something they touch, drag and try, each one earns a checkmark, finishing the trail awards an Explorer badge, and the Practice Zone builds a fresh set of questions every visit. Progress is saved to their player, so they can stop and pick it up later.
What your child does, station by station
Learning mode has no timers, no scores and no wrong answers — every station is something the child touches and moves. This trail is one of the free ones, so it opens on any account.
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The Line Goes Both Ways
Flip cards
An integer is any whole number — positive, negative or zero — with no fraction part. Negatives are not a piece of maths trickery; they measure real things that live below a natural zero.
Negative numbers are not a trick — they describe the world on the far side of zero.
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Crossing Zero
Slider explorer
Drag the marker across zero. Notice that nothing special happens at the crossing — the numbers keep spacing themselves evenly, exactly as they did on the positive side.
Slide the marker through zero and watch how the language changes but the maths does not.
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The Two Minuses, Explained
Try it
"Two minuses make a plus" is true, but stated like that it is a spell rather than a reason. Each round below shows why the sign behaves the way it does.
Everybody is told the rule. Here is the reason behind it, so you never mix it up.
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Predict the Sign
Sorting baskets
Skilled calculators decide the sign before they touch the digits, because a wrong sign ruins a right answer. Sort each calculation by the sign of its result.
Work out only whether the answer is positive, negative or zero — the digits can wait.
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Coldest to Warmest
These are plausible winter readings from around India and beyond. Tap them from coldest to warmest, and watch how the negatives reverse the order you expect.
Order six real temperatures. Remember: further left on the line means smaller.
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Practice Zone
Practice Zone
Ten questions on this topic — a proper practice set, fresh every time.
Ten questions on this topic. New ones every time you come back.
Free printable worksheet
Ten questions from this topic on one page, with an answer key at the bottom — a PDF you can print for homework, a car journey or a classroom. No account needed and nothing to sign up for. The Practice Zone in the app builds a fresh set every visit; this is a fixed set you can hold.
More Math for ages 11–12
🧬 Factors, HCF and LCM · 🍕 Fractions, All Four Ways · 🔟 Decimals and Rounding · ⚖️ Ratio and Proportion · 💯 Percentages in Real Life · ⏫ Powers and Roots · 🔣 Order of Operations · 🔤 Introduction to Algebra
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