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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Patterns and Sequences: Age 11-14

### Frogs

### Growing Surprises

### 1 Step 2 Step

### Odds, Evens and More Evens

### Picturing Triangular Numbers

### Elevenses

### Picturing Square Numbers

### Days and Dates

### Shifting Times Tables

### Beach Huts

### Summing Consecutive Numbers

### Squares in Rectangles

### Triangle Numbers

### Tower of Hanoi

### Seven Squares - Group-worthy Task

### Coordinate Patterns

### Train Spotters' Paradise

### Spaces for Exploration

### Charlie's Delightful Machine

### Seven Squares

### What Numbers Can We Make Now?

### Patterns and Sequences - Short Problems

### What Numbers Can We Make?

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

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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?

Age 11 to 14

Challenge Level

Can you find the connections between linear and quadratic patterns?

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?

Age 11 to 14

Challenge Level

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

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?

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?

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?

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...

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

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?

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?

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.

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?

Age 11 to 14

Challenge Level

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Age 11 to 16

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

Age 11 to 14

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

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?

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?

Age 11 to 14

Challenge Level

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

Age 11 to 16

A collection of short problems on patterns and sequences.

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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