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Can you find the connections between linear and quadratic patterns?
Play around with the Fibonacci sequence and discover some surprising results!
Just because a problem is impossible doesn't mean it's difficult...
Surprising numerical patterns can be explained using algebra and diagrams...
Can you figure out how sequences of beach huts are generated?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
How many possible symmetrical necklaces can you find? How do you know you've found them all?
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find a way to identify times tables after they have been shifted up or down?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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?
What can you see? What do you notice? What questions can you ask?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
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?
An environment which simulates working with Cuisenaire rods.
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?
A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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?
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
There are lots of ideas to explore in these sequences of ordered fractions.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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?
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?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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?
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.
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.
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
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.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Here are some ideas to try in the classroom for using counters to investigate number patterns.