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.

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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?

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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?

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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?

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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?

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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?

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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...

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Consecutive Sums Poster

Age

11 to 14

Challenge level

Consecutive Sums Poster

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Beach Huts

Age

11 to 14

Challenge level

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

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Growing Surprises

Age

11 to 14

Challenge level

Can you find the connections between linear and quadratic patterns?

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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...

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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?

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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?

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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?

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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?

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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?

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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?

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Triangle Numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

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Squares In Rectangles Poster

Age

11 to 14

Challenge level

Squares In Rectangles Poster

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Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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Seven Squares

Age

11 to 14

Challenge level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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What numbers can we make now?

Age

11 to 14

Challenge level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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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?

Patterns and Sequences - Stage 3 STEM footer

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Patterns and Sequences: Age 11-14

Picturing Square Numbers

Elevenses

Shifting Times Tables

Charlie's delightful machine

What numbers can we make?

Odds, Evens and More Evens

Consecutive Sums Poster

Beach Huts

Growing Surprises

Days and Dates

Summing Consecutive Numbers

Frogs

Picturing Triangular Numbers

Seven Squares - Group-worthy Task

Coordinate Patterns

Squares in rectangles

Triangle Numbers

Squares In Rectangles Poster

Tower of Hanoi

Seven Squares

What numbers can we make now?

1 Step 2 Step