Resources tagged with: Describing patterns and sequences

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

Taking Steps

Age 7 to 11
Challenge Level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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?

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.

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?

Frogs

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?

Paving Paths

Age 11 to 14
Challenge Level

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

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?

Pattern Power

Age 5 to 14

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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?

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?

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?

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?

Lost Books

Age 7 to 11
Challenge Level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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.

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?

Beads

Age 7 to 11
Challenge Level

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Pyramid Numbers

Age 7 to 11
Challenge Level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

Lastly - Well

Age 11 to 14
Challenge Level

What are the last two digits of 2^(2^2003)?

More Pebbles

Age 7 to 11
Challenge Level

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

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?

Fibonacci Surprises

Age 11 to 14
Challenge Level

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

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.

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.

Taking a Die for a Walk

Age 5 to 11
Challenge Level

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

Domino Sets

Age 7 to 11
Challenge Level

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

Even Up

Age 11 to 14 Short
Challenge Level

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?

Counter Ideas

Age 7 to 11
Challenge Level

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

Magazines

Age 7 to 11
Challenge Level

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.

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"?

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.

Triangular Hexagons

Age 7 to 11
Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.

Beach Huts

Age 11 to 14
Challenge Level

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

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?

Magic Crosses

Age 7 to 14
Challenge Level

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

Lawn Border

Age 5 to 11
Challenge Level

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

Growing Surprises

Age 11 to 14
Challenge Level

Can you find the connections between linear and quadratic patterns?

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...

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?

It's All about 64

Age 7 to 11
Challenge Level

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Maxagon

Age 11 to 14
Challenge Level

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

Pocket Money

Age 11 to 14
Challenge Level

Which of these pocket money systems would you rather have?

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...

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?

Impossibilities

Age 11 to 14
Challenge Level

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

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?

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?

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?

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.