Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Calendar Capers

Choose any three by three square of dates on a calendar page...

Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Bouncing Ball

Age 11 to 14 ShortChallenge Level

Working out the height after each time it hits the ground
First time: $\frac{3}{5}$ of 125 cm = 125$\div$5$\times$3 = 25$\times$3 = 75 cm.

Second time: $\frac{3}{5}$ of 75 cm= 75$\div$5$\times$3 = 15$\times$3 = 45 cm.

Third time: $\frac{3}{5}$ of 45 cm= 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
First time: $\frac{3}{5}$ of 125 is 3$\times$5$\times$5

Second time: $\frac{3}{5}$ of 3$\times$5$\times$5 is 3$\times$3$\times$5

Third time: $\frac{3}{5}$ of 3$\times$3$\times$5 is 3$\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.