Arithmetic sequences

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
Squares in rectangles

Age

11 to 14

Challenge level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
problem
Coordinate patterns

Age

11 to 14

Challenge level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
problem
Seven squares - group-worthy task

Age

11 to 14

Challenge level

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
problem
More number pyramids

Age

11 to 14

Challenge level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
problem
Squares, squares and more squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
problem
Polite numbers

Age

16 to 18

Challenge level

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
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
Six in a circle

Age

5 to 7

Challenge level

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?