Arithmetic sequences

problem
Doplication

Age

7 to 11

Challenge level

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
problem
The great tiling count

Age

7 to 11

Challenge level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
problem
Red balloons, blue balloons

Age

7 to 11

Challenge level

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
problem
Tables without tens

Age

7 to 11

Challenge level

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
problem
Multiplication square jigsaw

Age

7 to 11

Challenge level

Can you complete this jigsaw of the multiplication square?
problem
Unravelling sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?
problem
Cherries come in twos

Age

7 to 11

Challenge level

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
problem
Pocket money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?
problem
Days and dates

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?