How a balance scale solves equations
An equation is a balance scale. The equals sign means both sides weigh the same. In this game each brown box is the unknown number x, each bright block is a weight, and each red balloon is a minus number that lifts the pan up. Your job is to find what one box weighs.
Teachers explain the same move in two ways, and the game shows both at once. On the scale, you do the same thing to both sides, so the scale stays level. In the equation, the number moves to the other side and changes its sign: when + 3 jumps over the equals sign it lands as minus 3. Both ways give the same answer, because taking 3 from both sides is exactly what moving + 3 across does.
The game has 40 levels in ten worlds: jumping numbers, minus balloons, times becomes divide, two-step equations, fixing a wonky scale when x is known, fraction boxes like x/2, x on both sides, a guess and check detective round, brackets shown as bags, and a boss mix. Each level has a target number of moves for three stars. A notebook under the equation writes your working line by line, just as it would look in an exercise book. It suits Grade 5 to 8 (Class 5 to 8) and works on a phone with no sign up.
Worked example: 2x + 3 = 11
- Start: 2x + 3 = 11
- Move + 3 across. It jumps over the equals sign and becomes minus 3: 2x = 11 − 3, so 2x = 8. On the scale, 3 came off both sides.
- Move the 2 across. 2x means 2 times x, so times 2 becomes divide by 2: x = 8 ÷ 2, so x = 4.
- Check: put 4 in place of x. 2 × 4 + 3 = 11, and the right side is 11. Both sides match.
Practice questions with answers
Solve each one on paper first, moving one thing at a time. Then open the answer.
1. Solve x + 6 = 15
Show answer
x = 9. Move + 6 across, where it becomes minus 6: x = 15 - 6 = 9.
2. Solve 4x = 28
Show answer
x = 7. Times 4 moves across and becomes divide by 4: x = 28 divided by 4 = 7.
3. Solve 3x + 5 = 20
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x = 5. Move + 5 across to get 3x = 20 - 5 = 15, then x = 15 divided by 3 = 5.
4. Solve x - 4 = 9
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x = 13. Minus 4 moves across and becomes + 4: x = 9 + 4 = 13.
5. Solve x/3 + 2 = 6
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x = 12. Move + 2 across to get x/3 = 4, then divide by 3 moves across as times 3: x = 4 times 3 = 12.
6. Solve 5x + 2 = 3x + 12
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x = 5. Move the smaller x term, 3x, across to get 2x + 2 = 12, move + 2 across to get 2x = 10, then x = 10 divided by 2 = 5.
7. Solve 2(x + 3) = 16
Show answer
x = 5. Times 2 moves across as divide by 2: x + 3 = 8, then x = 8 - 3 = 5. Opening the brackets first, 2x + 6 = 16, gives the same answer.
8. Solve 2x + 15 = 5x + 3
Show answer
x = 4. Move 2x across to get 15 = 3x + 3, move + 3 across to get 12 = 3x, then x = 12 divided by 3 = 4.
Questions about the solving equations game
Why does +3 become -3 when it crosses the equals sign?
Moving + 3 to the other side is a shortcut for taking 3 away from both sides. On the side it leaves, + 3 and minus 3 cancel to nothing. On the side it reaches, minus 3 is what is left. That is why the game shows it flipping from plus to minus in mid air, while the scale stays level.
How does a balance scale help you solve equations?
An equation says two amounts are equal, just as a level scale says two pans weigh the same. Taking the same amount off both pans keeps the scale level, so it keeps the equation true. Keep doing that until one box is alone, and the other pan shows what x is.
Why can I not move some pieces?
The scale stops moves that would leave less than nothing, or that break the order of solving. For example, in 2x + 3 = 11 the times 2 waits until the + 3 has gone, and with x on both sides you move the smaller x term. The scale tells you why, so a blocked move still teaches something.
What do the stars and the target mean?
Every solving level has a target: the fewest moves that solve it. Hit the target for three stars, or one move over for two stars. In the wonky scale and guess and check worlds, fewer tries earn more stars. A hint gives at most two stars.
Who is this game for, and is it free?
It suits Grade 5 to 8 (Class 5 to 8) and anyone starting algebra: one-step and two-step equations, minus numbers, fractions of x, brackets and x on both sides. It is free, needs no sign up and works on a phone, tablet or computer.