Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
How good are you at finding the formula for a number pattern ?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
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?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Make some loops out of regular hexagons. What rules can you discover?
Show that all pentagonal numbers are one third of a triangular number.
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Can you find a rule which relates triangular numbers to square numbers?
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Can you use the diagram to prove the AM-GM inequality?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
Balance the bar with the three weight on the inside.
A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
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?
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Can you find a rule which connects consecutive triangular numbers?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Label this plum tree graph to make it totally magic!
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Kyle and his teacher disagree about his test score - who is right?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.
Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
The Number Jumbler can always work out your chosen symbol. Can you work out how?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?