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Integer Island: find your way across zero

Play Integer Island

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Temperatures rise and fall, lifts move above and below ground, and number lines cross zero. Use those pictures to make signed-number rules stick.

Ages 11+
5–10 min
integers
negative numbers
integer operations
Free · no sign-up

How to play Integer Island

Choose a grade that matches the learner's current school work.
Pick one topic from the skill cards and try a question.
Read the immediate feedback, then continue at a level that adjusts to answers.
Reach the mastery target or switch to another skill whenever you are ready.

Tips and strategy

Sketch a number line for addition and subtraction; use sign pairs for multiplication and division.
Ask the learner to explain one answer in their own words; the reasoning matters as much as speed.

What you'll learn

Integers include positive numbers, negative numbers and zero. A number line makes addition and subtraction visible: adding a negative moves left, while subtracting a negative reverses direction. For multiplication and division, equal signs give a positive result and different signs give a negative result.

Worked example

A morning temperature is −2°C and rises by 5 degrees: start at −2 and move five steps right to reach 3°C. For 4 − (−3), subtracting a negative means move in the opposite direction to subtracting a positive, so the result is 7. In multiplication, (−4) × 3 = −12 because three groups of negative four make −12; (−4) × (−3) = 12 under the sign rule for products.

A common sticking point

The phrase “two negatives make a positive” is only useful when the operation is clear. In −4 + (−3), both numbers are negative and the answer is −7, not positive. In 4 − (−3), the second negative is being subtracted, so the value increases. Use a number line for addition and subtraction, then practise multiplication and division sign pairs separately.

Try it away from the screen

Draw a number line on paper and mark zero, then use a token to model a change in temperature or a lift moving between floors. Say the starting value and direction before moving. For signed multiplication, make a two-column chart of positive and negative factor pairs and predict the sign before calculating the size of the product.

Mini challenge with answers

Calculate −3 + 8, then 5 − (−2), then (−3) × 4. Answers: 5, 7 and −12. Draw the first two on a number line and write the multiplication as four groups of negative three. These examples use three different operations; naming the operation before applying a sign rule helps prevent treating every pair of negative symbols alike.

How to use this practice path

Separate the practice into two stages. First, use a number line for addition and subtraction, describing the start point and direction for each move across zero. Then use sign-pair patterns for multiplication and division, keeping the size of the answer separate from its sign. Mix operations only after each model feels clear. This gives the learner a way to reason through a new example rather than relying on a memorised chant.

Where the idea goes next

Integers also appear in coordinate grids. A point such as (−2, 3) starts two spaces left of zero and moves three spaces up. Plotting several points helps a learner connect signed numbers to direction and position. Read the horizontal coordinate first and the vertical coordinate second; switching their order moves the point somewhere else. A grid game is a useful visual follow-up after number-line practice.

This free browser practice has grades 6 to 7 and is intended for learners aged about 11 to 13. Each topic has short questions, a mastery meter and progress saved in this browser on this device. It is independent practice, not a school-board test or a substitute for a teacher's advice about a particular learner.

Want paper practice too? Browse the printable maths worksheets, then explore all Grade 1 to 8 maths skills or ask a parent or guardian to enquire about a class.

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FAQ

Integer Island: questions

Is Integer Island free to play?

Yes. It is free, runs in a modern browser and does not need an account or download.

What does Integer Island teach?

Can I choose a grade?

Grades 6 to 7 are available. School grade systems differ, so choose the level that best matches what the learner is studying now.

Does the game save progress?

The game saves mastery scores in local browser storage on this device. It does not create an online student account.

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