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Number Balance

Number · Year 1–Year 6

Equals means the same as, on a beam that tips until it is.

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About the number balance

Pick a number on the toolbar and tap a pan to drop it in. The beam tips towards the heavier side and goes level when the two sides are the same. Tap a number in a pan to take it out again.

It is here for the biggest misconception in primary maths. A class that has only ever seen sums written as 5 + 3 = ? reads the equals sign as “and the answer comes next”, which is why they write 5 + 3 = 8 + 2 = 10, and why 7 + ? = 12 is so much harder than it looks. Equals means THE SAME AS, and a balance is that sentence as a picture.

So both pans hold sums, and neither side is the answer to the other. 5 + 3 balances 6 + 2, and a class that has seen that has somewhere to stand when the equals sign turns up in the middle of a longer line.

The sentence under the balance is always true. When the sides differ it uses the greater than or less than sign, pointing the way the beam went, so the sign a class has to remember the direction of is written beside a picture of it.

Press New for a fresh question that does not balance and can be made to, and Clear to empty both pans and start from nothing.

How to use it on your whiteboard

  1. 1Tap a number on the toolbar to pick it up.
  2. 2Tap a pan to drop it in. The beam tips towards the heavier side.
  3. 3Tap a number in a pan to take it back out.
  4. 4Ask the class what would make it balance, then let them try it.
  5. 5Press New for another question, or Clear and build both sides from nothing.

Questions

Why do both pans hold sums?
Because a tool where one pan held the question and the other held the answer would be the worksheet again with a picture on top. The whole point is that 5 + 3 can balance 6 + 2: the equals sign says the two sides are the same, not that an answer is coming.
Why only four numbers in a pan?
It is a limit on the picture rather than on the arithmetic. Four tiles are as many as a pan can draw at a readable size, and a fifth would mean shrinking them all, which would make a tile in one pan a different size from a tile in the other.
Can it show greater than and less than?
Yes, and it does it without being asked. Whenever the sides differ the sentence uses the right sign for what the pans actually hold, so the picture and the symbol arrive together.
Does the beam tip all the way over?
No, on purpose. A real balance at its stop looks the same whether it is out by one or by twenty, so a class adding numbers would see nothing happen until it suddenly levelled. The lean grows with the difference and reaches its limit at six.