A balanced scale shows two sides with the same mass, just like an equation. You can take the same amount off both sides and it stays balanced. Take off everything beside the boxes until the boxes are on their own. If there are several boxes, share what is left equally between them. If there are boxes on both sides, take the same number of boxes off each side first.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- balance
- both sides have the same mass
- unknown
- a value we don't know yet, shown as a box or a letter
Worked examples
A box and 4 cubes (1 kg each) balance 11 cubes. What is the mass of the box?
- 1.Take 4 cubes off each side.
- 2.The box balances 11 − 4 = 7 cubes.
= 7
3 boxes and a 5 kg weight balance a 26 kg weight. What is the mass of one box?
- 1.Take 5 kg off each side: 3 boxes balance 21 kg.
- 2.21 ÷ 3 = 7.
= 7
4 boxes and 3 kg balance 1 box and 18 kg. What is the mass of one box?
- 1.Take 1 box off each side: 3 boxes and 3 kg balance 18 kg.
- 2.Take 3 kg off each side: 3 boxes balance 15 kg, so 15 ÷ 3 = 5.
= 5
For parents
Method: Do the same to both sides
What to say: What can you take off both sides? How many boxes are left?
Common mistakes:
- Says a box weighs the same as everything on the other side, forgetting what is beside the box.
- Adds the mass beside the box to the other side instead of taking it away from both sides.
- Counts the box as if it were one more cube.
- Finds what all the boxes weigh together and forgets to share it between them.
- Shares the other side between the boxes without first taking off the mass beside the boxes.
- With boxes on both sides, ignores the boxes on the right.
- Adds the boxes on both sides together instead of taking them away from each other.