### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Tweedle Dum and Tweedle Dee

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

### Matching Fractions, Decimals and Percentages

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

# Bouncing Ball

##### Age 11 to 14 Short Challenge Level:

Working out the height after each time it hits the ground
The first time the ball hits the ground, it has fallen from a height of 125 cm. So it will bounce to a height of $\frac{3}{5}$ of 125 cm, which is 125$\div$5$\times$3 = 25$\times$3 = 75 cm.

The second time the ball hits the ground, it has fallen from a height of 75 cm. So it will bounce to a height of $\frac{3}{5}$ of 75 cm, which is 75$\div$5$\times$3 = 15$\times$3 = 45 cm.

The third time the ball hits the ground, it has fallen from a height of 45 cm. So it will bounce to a height of $\frac{3}{5}$ of 45 cm, which is 45$\div$5$\times$3 = 9$\times$3 = 27 cm.

Working out the height after each time it hits the ground using 3s and 5s
125 = 5$\times$5$\times$5, and so $\frac{3}{5}$ of 125 is 3$\times$5$\times$5 (since $\frac{1}{5}$ of 125 is 5$\times$5). So after hitting the ground once, the ball will bounce 3$\times$5$\times$5 cm.

Similarly, $\frac{3}{5}$ of 3$\times$5$\times$5 is 3$\times$3$\times$5, so after hitting the ground twice it will bounce 3$\times$3$\times$5 cm.

And $\frac{3}{5}$ of 3$\times$3$\times$5 is 3$\times$3$\times$3, so after hitting the ground three times it will bounce 3$\times$3$\times$3 = 27 cm.

Using powers
Each time the ball hits the ground, it bounces to $\frac{3}{5}$ of the height from which it fell. So after each bounce, its height is multiplied by $\frac{3}{5}$.

So after 3 bounces, its height will be multiplied by $\left(\frac{3}{5}\right)^3=\frac{27}{125}$.

So after 3 bounces, its height will be $125\times\frac{27}{125}=27$ cm.

You can find more short problems, arranged by curriculum topic, in our short problems collection.