What it shows
A hanger with a cup on each side stays level only when both sides weigh the same. A sealed bag of marbles stands for x; with 3 loose marbles beside it balancing 7 on the other side, removing 3 from each side keeps the balance and reveals that the bag holds 4.
The science
An equation says two quantities are equal, like two pans that balance. Whatever you do to one side you must do to the other, or the balance tips. Taking 3 marbles off both sides of x + 3 = 7 leaves x = 4. For 2x = 10, sharing both sides into two equal halves gives x = 5. The model makes the rule "do the same to both sides" something you can feel, and shows why you cannot subtract from only one side.
Materials
Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A plastic clothes hanger
- Two identical paper cups hung on thread from the hanger ends
- About 30 identical marbles or large steel washers
- Three small opaque bags or film canisters as unknowns
- A hook or a string to hang the hanger from
Safety
For this project: Keep marbles away from small children and hang the hanger where it cannot swing into anyone.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Hang the hanger from a hook and check the empty cups balance. If not, add a bit of clay to the lighter cup.
Secretly put 4 marbles in a bag and seal it. Place the bag plus 3 loose marbles in the left cup and 7 marbles in the right cup. It balances: x + 3 = 7.
Remove 3 loose marbles from each cup. It still balances, and now the bag alone matches 4 marbles, so x = 4. Open the bag to check.
Set up 2x = 10 with two bags of 5 on the left and 10 marbles on the right. Take away one bag and 5 marbles from the sides and show one bag matches 5.
Set up x + 5 = 8 and let a visitor solve it on the hanger before opening the bag.
Write each step as an equation on a card beside the hanger so the algebra and the balance match line by line.
Show what happens if you remove marbles from one side only: the hanger tips, so the equation is no longer true.
What you should see
Each puzzle balances at every step and the bag always holds the predicted number: 4 for x + 3 = 7, 5 for 2x = 10 and 3 for x + 5 = 8.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1What does the bag represent?
The unknown number x.
2Why must you remove marbles from both cups?
To keep the balance, which is the equation, true. Changing one side only breaks the equality.
3How would you solve 3x = 12 on the hanger?
Put three bags on one side and 12 marbles on the other, then split both sides into three equal groups: one bag matches 4.
4Can the hanger show x take away 2 = 5?
Not directly with weights, since you cannot have negative marbles, but you can add 2 to both sides first to get x = 7.
Take it further
Solve 2x + 1 = x + 6 by placing bags on both sides and removing a bag and a marble from each side.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
Free ebooks for this project
Science projects
Maths Working Models and Activities
Make maths visible: models for number, geometry, algebra and data
Science projects
Science Projects for Class 6 to 8
Working models matched to middle-school science topics