Balance scale equations

Solve equations on a balance scale: take the same off both sides until one bag is left on its own.

🧒 Kids: each blue bag hides the same number of blocks. Take blocks or bags off both sides until you find out what is in one bag!

Balance scale

For parents and teachers ↓

What the balance shows

Each puzzle is an equation drawn as a balance. A blue bag is x, the unknown, and an orange block is 1. The scale is level because both sides weigh the same.

There are three moves. Take a block off both sides, take a bag off both sides, or share the blocks equally among the bags. The tool won’t allow a move on one side only, because that would tip the scale.

Ready-made puzzles to try

Each link opens the balance with that puzzle set up. Start at the top: the puzzles get harder as you go down.

Why the balance works so well

Children often learn rules like “move the 7 to the other side and change its sign” without knowing why. The balance shows the reason. Nothing moves across; the same amount is taken from both sides, so the scale stays level.

Once the balance makes sense, written steps are just a record of the moves. 3x + 2 = 14 becomes 3x = 12 (two blocks off each side), then x = 4 (share into 3 groups).

From the balance to written equations

  1. Say it: “three bags and two blocks balance fourteen blocks.”
  2. Write it: 3x + 2 = 14.
  3. Record each move: “take 2 off both sides” becomes 3x = 12.
  4. Finish: “share into 3 groups” becomes x = 4.

After a few puzzles, try the same equations in the equation solver and compare the steps.

What the balance can’t show

A balance works for positive whole numbers. Negative numbers, fractions and subtraction like 2x − 3 = 7 don’t fit well, because you can’t have a negative block. That is the point to move to written steps and the two-step equation practice.

Where the balance fits, grade by grade

Grade 5 and 6 children use the balance to understand what an equation is and to solve one-step equations (6.EE.B.5 and 6.EE.B.7). Grade 7 uses it for two-step equations (7.EE.B.4a). In India, the balance appears in the class 7 chapter “Finding the Unknown”.

Try it at home

Use a real kitchen scale or a coat-hanger balance with paper cups. Hide the same number of coins in each cup, and let your child work out the number by taking coins off both sides.

For teachers

Project the balance and let the class vote on each move. Ask “will this keep it level?” before every tap. To share a puzzle, add ?eq=3x%2B2%3D14 to the address, with small whole numbers only.

More equation help

Back to solving equations for kids · integers · order of operations · 6th grade math · 7th grade math · 8th grade math

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Questions parents ask

How does a balance scale help with equations?

An equation is like a level balance: both sides weigh the same. Taking the same thing off both sides keeps it level, which is exactly how you solve an equation.

What do the bags and blocks mean?

Each blue bag holds the same unknown number of blocks: that is x. Each orange block is 1. So 2 bags and 3 blocks is 2x + 3.

How do you solve a balance puzzle?

Take blocks off both sides until one side has only bags. Take bags off both sides if both have them. Then share the blocks equally among the bags to find how many are in one bag.

Why can’t I take a block off just one side?

That would tip the scale, and the two sides would no longer be equal. In an equation, whatever you do to one side you must do to the other.

What grade is the balance scale for?

Grades 5 to 7. It is the best first picture for one-step and two-step equations (6.EE.B.7 and 7.EE.B.4a).

Can I make my own puzzle?

Yes. Add ?eq= and an equation with small whole numbers to the address, for example ?eq=3x%2B2%3Dx%2B8.