There are lots of different methods to find out what the shapes are worth - how many can you find?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Can you find the values at the vertices when you know the values on the edges?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you move the tiles around, can you make squares with different coloured edges?
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Explore the relationships between different paper sizes.
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Where should you start, if you want to finish back where you started?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
There are nasty versions of this dice game but we'll start with the nice ones...
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
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?
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?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Can you find any two-digit numbers that satisfy all of these statements?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
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?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Which set of numbers that add to 10 have the largest product?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
You'll need to know your number properties to win a game of Statement Snap...
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Play around with sets of five numbers and see what you can discover about different types of average...
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
Use your skill and judgement to match the sets of random data.
Can you work out which spinners were used to generate the frequency charts?
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
How well can you estimate 10 seconds? Investigate with our timing tool.
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?