List

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.

Days and Dates
problem
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Days and dates

Age
11 to 14
Challenge level
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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Summing Consecutive Numbers
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Summing consecutive numbers

Age
11 to 14
Challenge level
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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?

Frogs
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Frogs

Age
11 to 14
Challenge level
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How many moves does it take to swap over some red and blue frogs? Do you have a method?
Picturing Triangular Numbers
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Picturing triangular numbers

Age
11 to 14
Challenge level
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Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Picturing Square Numbers
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Picturing square numbers

Age
11 to 14
Challenge level
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Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Elevenses
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Elevenses

Age
11 to 14
Challenge level
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How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Shifting Times Tables
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Shifting times tables

Age
11 to 14
Challenge level
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Can you find a way to identify times tables after they have been shifted up or down?

Charlie's delightful machine
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Charlie's delightful machine

Age
11 to 16
Challenge level
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

What numbers can we make?
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What numbers can we make?

Age
11 to 14
Challenge level
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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Odds, Evens and More Evens
problem
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Odds, evens and more evens

Age
11 to 14
Challenge level
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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Beach Huts
problem
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Beach huts

Age
11 to 14
Challenge level
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Can you figure out how sequences of beach huts are generated?
Growing Surprises
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Growing surprises

Age
11 to 14
Challenge level
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Can you find the connections between linear and quadratic patterns?
1 Step 2 Step
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1 step 2 step

Age
11 to 14
Challenge level
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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?
Seven Squares - Group-worthy Task
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Seven squares - group-worthy task

Age
11 to 14
Challenge level
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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?
Coordinate Patterns
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Coordinate patterns

Age
11 to 14
Challenge level
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Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Squares in rectangles
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Squares in rectangles

Age
11 to 14
Challenge level
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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?
Triangle Numbers
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Triangle numbers

Age
11 to 14
Challenge level
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Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
Tower of Hanoi
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Tower of Hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Seven Squares
problem
Favourite

Seven squares

Age
11 to 14
Challenge level
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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
What numbers can we make now?
problem
Favourite

What numbers can we make now?

Age
11 to 14
Challenge level
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?



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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.