Integers Game: Hot and Cold Maze

Make your number match the goal. Starts easy at age 8, ends with multiplying negative numbers at 14.

World 1 · Level 1Make 5
Now0
Goal0

0 → 5

Tap a square with a yellow ring.

How to play the integers game

  1. Tap a square next to you. Its number changes yours: +3 adds 3, −2 takes away 2.
  2. Make your number the same as the goal, then walk into the goal.
  3. Stuck? Press Show me and watch. Then try it yourself.

About this integers game

Negative numbers are easier when you can see them. Every level in this free integers game tells a small story. In the first worlds you hop along a number line: plus is forward, minus is back. Then the number line becomes a thermometer. You switch on the AC to cool a room, walk from a cold December to a warm June, and fly a plane across a world map, from Moscow to Dubai or London to Toronto, to find the difference in temperature.

The last world is for older students: multiplying and dividing negative numbers with the sign rules. Each level needs only 2 or 3 steps, so younger children can finish it, but every step is a real sum. The game shows the working each time, for example 30 − 4 = 26. The first level of every world is guided, and Show me plays any level step by step.

The season and city temperatures are real, rounded averages: Karachi from the Pakistan Meteorological Department, Lahore from its 1991 to 2020 climate averages, Murree from NOAA records for 1961 to 1990, Moscow from 2009 to 2018 records, Dubai from WeatherSpark, Skardu from weather2travel, London from 2001 to 2009 city records and Toronto from 1991 to 2020 averages. The map outline is from Natural Earth, which is free to use.

The integer ideas inside the game

Plus means forward2 + 3 = 5Hop forward 3 on the number line, or 3 degrees warmer.
Minus means back5 − 4 = 1Hop back 4, or 4 degrees colder.
Below zero2 − 5 = −3Hop back past zero and you reach the negative numbers.
Difference35 − 28 = 7A June afternoon in Karachi is about 35°, a December afternoon about 28°. June is 7 degrees warmer.
Compare−8 < −3−8 is colder, lower down the thermometer, so it is the smaller number.
Multiply and divide−3 × (−2) = 6Same signs give plus. Different signs give minus: −12 ÷ 3 = −4.
Take out the ice−3 − (−2) = −1Taking away a negative is the same as adding: −3 + 2 = −1.

Integer questions with answers

Try these in your head, then open each one to check.

Start at 2 and hop back 5. Where do you land?

−3. 2 − 5 = −3, past zero.

−4 + 6 = ?

2. Start at −4 and hop forward 6.

The room is 31°. The AC cools it by 6 degrees. What is it now?

25°. 31 − 6 = 25.

It is 3° in the morning and −5° at night. How much colder is the night?

8 degrees. From 3 down to 0 is 3, then down to −5 is 5 more: 3 + 5 = 8.

On a January night Lahore is about 8° and Murree is about −3°. What is the difference?

11 degrees. Murree is 11 degrees colder than Lahore.

Which is less, −8 or −3?

−8. It is further below zero, so it is the smaller number.

−4 × 3 = ?

−12. Different signs give minus.

−5 − (−2) = ?

−3. Taking away a negative is adding: −5 + 2 = −3.

Questions about the integers game

What does this integers game teach?

It teaches adding and subtracting on a number line, negative numbers below zero, temperature going up and down, the difference between two temperatures, comparing integers, taking away a negative number, and multiplying and dividing negative numbers. Every step shows the sum.

Which class is it for?

It starts at age 8 and goes up to age 14, about Class 3 to Class 8 (Grade 3 to 8). Each world in the level list shows the age it suits. Worlds 1 to 3 are for ages 8 to 9. World 8, multiplying and dividing negative numbers, is for ages 13 to 14. Every level needs only 2 or 3 steps.

Are the temperatures real?

Yes. The season and city levels use rounded average temperatures from weather records for Karachi, Lahore, Murree, Skardu, Dubai, Moscow, London and Toronto. The room and ice levels are made-up stories.

Why is taking away a negative the same as adding?

Think of a negative number as ice. Take ice out of a box and the box gets warmer, so the number goes up. That is why −3 − (−2) is the same as −3 + 2, which is −1.

How do I get three stars?

Reach the goal with its exact number, walk through the gem on the way, and do not use a hint. Every level is open, so you can go back and try again for more stars.

Do I need to sign up or pay?

No. The game is free with no sign up. Your stars and best score are kept in this browser on this device.

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