Patterns and sequences: Age 11-14

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

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

Summing consecutive numbers

Age

11 to 14

Challenge level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

problem

Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

problem

Picturing triangular numbers

Age

11 to 14

Challenge level

What do you notice about the sum of two identical triangular numbers?

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

Elevenses

Age

11 to 14

Challenge level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

problem

Shifting times tables

Age

11 to 14

Challenge level

Can you find a way to identify times tables after they have been shifted up or down?

problem

Charlie's delightful machine

Age

11 to 16

Challenge level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

problem

What numbers can we make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

problem

Odds, evens and more evens

Age

11 to 14

Challenge level

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

problem

Beach huts

Age

11 to 14

Challenge level

Can you figure out how sequences of beach huts are generated?

problem

Growing surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

problem

1 step 2 step

Age

11 to 14

Challenge level

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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

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

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?