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. . . .
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
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
Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .
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?”
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .
Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .
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?
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
How good are you at finding the formula for a number pattern ?
The answer is $5x+8y$... What was the question?
Make some loops out of regular hexagons. What rules can you discover?
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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?
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?
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?
First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...
Is there a temperature at which Celsius and Fahrenheit readings are the same?
Show that all pentagonal numbers are one third of a triangular number.
Can you find a rule which relates triangular numbers to square numbers?
Can you find a rule which connects consecutive triangular numbers?
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.
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?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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 ?
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.
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
The Number Jumbler can always work out your chosen symbol. Can you work out how?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Kyle and his teacher disagree about his test score - who is right?
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Where should you start, if you want to finish back where you started?
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Can you find the lap times of the two cyclists travelling at constant speeds?
Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .
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?