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There are **107** NRICH Mathematical resources connected to **Describing patterns and sequences**, you may find related items under Patterns, sequences and structure.

Problem
Primary curriculum
Secondary curriculum
### Growing Surprises

Can you find the connections between linear and quadratic patterns?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fibonacci Surprises

Play around with the Fibonacci sequence and discover some surprising results!

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Impossibilities

Just because a problem is impossible doesn't mean it's difficult...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quadratic Patterns

Surprising numerical patterns can be explained using algebra and diagrams...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Beach Huts

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

Age 11 to 14

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Train Spotters' Paradise

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

Age 11 to 16

Problem
Primary curriculum
Secondary curriculum
### What Numbers Can We Make Now?

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Seven Squares

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

Problem
Primary curriculum
Secondary curriculum
### Magic Letters

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Odds, Evens and More Evens

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Numbers Can We Make?

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Charlie's Delightful Machine

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Little Light Thinking

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Numbers Give the Design

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Partly Painted Cube

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Times Tables Shifts

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shifting Times Tables

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Slick Summing

Watch the video to see how Charlie works out the sum. Can you adapt his method?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tower of Hanoi

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

Problem
Primary curriculum
Secondary curriculum
### Holes

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Elevenses

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

Problem
Primary curriculum
Secondary curriculum
### Caterpillars

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Numbers

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

Problem
Primary curriculum
Secondary curriculum
### Squares in Rectangles

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

Interactive
Primary curriculum
Secondary curriculum
### Cuisenaire Environment

An environment which simulates working with Cuisenaire rods.

Age 5 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chairs and Tables

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hundred Square

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Painted Cube

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coordinate Patterns

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Seven Squares - Group-worthy Task

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

Problem
Primary curriculum
Secondary curriculum
### Picturing Square Numbers

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

Problem
Primary curriculum
Secondary curriculum
### Picturing Triangular Numbers

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

Problem
Primary curriculum
Secondary curriculum
### Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Frogs

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

Problem
Primary curriculum
Secondary curriculum
### The Tomato and the Bean

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 1 Step 2 Step

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

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summing Consecutive Numbers

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

Problem
Primary curriculum
Secondary curriculum
### Days and Dates

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

Problem
Primary curriculum
Secondary curriculum
### Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sticky Triangles

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magazines

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counter Ideas

Here are some ideas to try in the classroom for using counters to investigate number patterns.

Age 7 to 11

Challenge Level