Arithmetic sequences

problem
Skip counting

Age

5 to 7

Challenge level

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
problem
Buzzy bee

Age

5 to 7

Challenge level

Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
problem
Next domino

Age

5 to 7

Challenge level

Which comes next in each pattern of dominoes?
problem
Alphabet blocks

Age

5 to 11

Challenge level

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
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
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
Matchsticks

Age

7 to 11

Challenge level

Reasoning about the number of matches needed to build squares that share their sides.
interactivity
Proof sorter - sum of an arithmetic sequence

Age

16 to 18

Challenge level

Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence
problem
Pocket money

Age

11 to 14

Challenge level

Which of these pocket money systems would you rather have?