# Resources tagged with: Describing patterns and sequences

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There are 82 NRICH Mathematical resources connected to Describing patterns and sequences, you may find related items under Patterns, Sequences and Structure.

Broad Topics > Patterns, Sequences and Structure > Describing patterns and sequences

### Domino Sets

##### Age 7 to 11Challenge Level

How do you know if your set of dominoes is complete?

### Seven Squares

##### Age 11 to 14Challenge Level

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

### The Numbers Give the Design

##### Age 7 to 11Challenge Level

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

### Times Tables Shifts

##### Age 7 to 11Challenge Level

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

### Shifting Times Tables

##### Age 11 to 14Challenge Level

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

### Tower of Hanoi

##### Age 11 to 14Challenge Level

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

### Holes

##### Age 5 to 11Challenge Level

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?

### Elevenses

##### Age 11 to 14Challenge 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?

### Triangle Numbers

##### Age 11 to 14Challenge 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?

### Cuisenaire Environment

##### Age 5 to 16Challenge Level

An environment which simulates working with Cuisenaire rods.

### Carrying Cards

##### Age 7 to 11Challenge Level

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?

### Seven Squares - Group-worthy Task

##### Age 11 to 14Challenge 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?

### Picturing Square Numbers

##### Age 11 to 14Challenge Level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

### Picturing Triangular Numbers

##### Age 11 to 14Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

### Farey Sequences

##### Age 11 to 14Challenge Level

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

### Sept 03

##### Age 11 to 14Challenge Level

What is the last digit of the number 1 / 5^903 ?

### 1 Step 2 Step

##### Age 11 to 14Challenge 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?

### Summing Consecutive Numbers

##### Age 11 to 14Challenge 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?

### Days and Dates

##### Age 11 to 14Challenge Level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Sticky Triangles

##### Age 7 to 11Challenge Level

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

### Pebbles

##### Age 7 to 11Challenge Level

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?

### Magic Crosses

##### Age 7 to 14Challenge Level

Can you find examples of magic crosses? Can you find all the possibilities?

### Bundles of Cubes

##### Age 7 to 11Challenge Level

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

### Pocket Money

##### Age 11 to 14Challenge Level

Which of these pocket money systems would you rather have?

### Swimming Pool Tiles

##### Age 7 to 11Challenge Level

This activity creates an opportunity to explore all kinds of number-related patterns.

### Diagonal in a Spiral

##### Age 7 to 11Challenge Level

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

### Centred Squares

##### Age 7 to 11Challenge Level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

### Maxagon

##### Age 11 to 14Challenge Level

What's the greatest number of sides a polygon on a dotty grid could have?

### Growing Surprises

##### Age 11 to 14Challenge Level

Can you find the connections between linear and quadratic patterns?

### Fibonacci Surprises

##### Age 11 to 14Challenge Level

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

### Impossibilities

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

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

### Beach Huts

##### Age 11 to 14Challenge Level

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

### More Number Patterns Upper Primary

##### Age 7 to 11

These upper primary activities offer opportunities for children to recognise, extend and explain number patterns.

### Pattern Sniffing

##### Age 5 to 11

This article for primary teachers outlines how we can encourage children to create, identify, extend and explain number patterns and why being able to do so is useful.

### Rods and Rods

##### Age 7 to 11Challenge Level

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

##### Age 11 to 16

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

### Steps to the Podium

##### Age 7 to 14Challenge Level

It starts quite simple but great opportunities for number discoveries and patterns!

### Magic Letters

##### Age 11 to 14Challenge Level

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

### Odds, Evens and More Evens

##### Age 11 to 14Challenge Level

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

### Polygonals

##### Age 7 to 11Challenge Level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

### Extending Great Squares

##### Age 7 to 11Challenge Level

Explore one of these five pictures.

### More Pebbles

##### Age 7 to 11Challenge Level

Have a go at this 3D extension to the Pebbles problem.

### Sorting the Numbers

##### Age 5 to 11Challenge Level

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

### Birds in the Garden

##### Age 5 to 11Challenge Level

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

### Mobile Numbers

##### Age 5 to 11Challenge Level

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

### Investigating Pascal's Triangle

##### Age 7 to 11Challenge Level

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

### Street Sequences

##### Age 5 to 11Challenge Level

Investigate what happens when you add house numbers along a street in different ways.

### Digital Roots

##### Age 7 to 14

In this article for teachers, Bernard Bagnall describes how to find digital roots and suggests that they can be worth exploring when confronted by a sequence of numbers.

### Triangular Hexagons

##### Age 7 to 11Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.