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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?
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
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?
Can you find a way to identify times tables after they have been shifted up or down?
Watch the video to see how Charlie works out the sum. Can you adapt his method?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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.
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?
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?
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?
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?
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 find examples of magic crosses? Can you find all the possibilities?
What's the greatest number of sides a polygon on a dotty grid could have?
In a city with a grid system of roads, how do you get from A to B?
It starts quite simple but great opportunities for number discoveries and patterns!
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.
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?
Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.
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?
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?