There are lots of different methods to find out what the shapes are worth - how many can you find?
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?
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?
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?
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?
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?
Explore the relationships between different paper sizes.
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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?
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
If you move the tiles around, can you make squares with different coloured edges?
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?
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 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?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Where should you start, if you want to finish back where you started?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Which set of numbers that add to 10 have the largest product?
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?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.
Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
Play around with sets of five numbers and see what you can discover about different types of average...
How well can you estimate 10 seconds? Investigate with our timing tool.
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
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?
There are nasty versions of this dice game but we'll start with the nice ones...
Use your skill and judgement to match the sets of random data.
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.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Can you work out which spinners were used to generate the frequency charts?
Can you find any two-digit numbers that satisfy all of these statements?
Which countries have the most naturally athletic populations?