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 11
Challenge Level

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

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?

The Numbers Give the Design

Age 7 to 11
Challenge 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 11
Challenge 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 14
Challenge Level

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

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.

Holes

Age 5 to 11
Challenge 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 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?

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?

Cuisenaire Environment

Age 5 to 16
Challenge Level

An environment which simulates working with Cuisenaire rods.

Carrying Cards

Age 7 to 11
Challenge 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 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?

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?

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?

Farey Sequences

Age 11 to 14
Challenge Level

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

Sept 03

Age 11 to 14
Challenge Level

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

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?

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?

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...

Sticky Triangles

Age 7 to 11
Challenge 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 11
Challenge 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 14
Challenge Level

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

Bundles of Cubes

Age 7 to 11
Challenge 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 14
Challenge Level

Which of these pocket money systems would you rather have?

Swimming Pool Tiles

Age 7 to 11
Challenge Level

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

Diagonal in a Spiral

Age 7 to 11
Challenge Level

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

Centred Squares

Age 7 to 11
Challenge Level

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

Maxagon

Age 11 to 14
Challenge Level

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

Growing Surprises

Age 11 to 14
Challenge Level

Can you find the connections between linear and quadratic patterns?

Fibonacci Surprises

Age 11 to 14
Challenge Level

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

Impossibilities

Age 11 to 14
Challenge Level

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

Quadratic Patterns

Age 11 to 14
Challenge Level

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

Beach Huts

Age 11 to 14
Challenge 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 11
Challenge Level

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

Train Spotters' Paradise

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 14
Challenge Level

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

Magic Letters

Age 11 to 14
Challenge 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 14
Challenge Level

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

Polygonals

Age 7 to 11
Challenge 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 11
Challenge Level

Explore one of these five pictures.

More Pebbles

Age 7 to 11
Challenge Level

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

Sorting the Numbers

Age 5 to 11
Challenge 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 11
Challenge 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 11
Challenge 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 11
Challenge 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 11
Challenge 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 11
Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.