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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?


Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Division Rules

Age 7 to 11
Challenge Level
Begin by deciding on your divisor. Then create your first dividend and complete the calculation.

Then try another calculation! Remember to record your results. You could use a table like the one below.

Table for recording results for a divisor of 2:

Calculation Whole number answer Remainder of 1
269 ÷ 2 = 134 r1   269
547 ÷ 2 = 273 r1   547
466 ÷ 2 = 233 466  
728 ÷ 2 = 364 728  

Look at the dividends which result in a whole number answer.
Can you spot any similarities?
Can this help you to conjecture a rule about which other dividends will have a whole number answer when divided by 2?
Test your rule for other dividends.

Can you spot a rule for the dividends which give a remainder of 1 when divided by 2?