Describing patterns and sequences

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
Changing places

Age

14 to 16

Challenge level

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?
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
Number tracks

Age

7 to 11

Challenge level

Ben's class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
problem
Break it up!

Age

5 to 11

Challenge level

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
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
Picturing triangular numbers

Age

11 to 14

Challenge level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
problem
All seated

Age

7 to 11

Challenge level

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
problem
Light blue - dark blue

Age

7 to 11

Challenge level

Investigate the successive areas of light blue in these diagrams.
problem
Taking steps

Age

7 to 11

Challenge level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.