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I'm thinking of a rectangle with an area of 24. What could its perimeter be?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Take three consecutive numbers and add them together. What do you notice?
This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Which countries have the most naturally athletic populations?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
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 way to identify times tables after they have been shifted up or down?
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?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
What's the largest volume of box you can make from a square of paper?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Imagine you were given the chance to win some money... and imagine you had nothing to lose...
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
These clocks have only one hand, but can you work out what time they are showing from the information?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you find the values at the vertices when you know the values on the edges?
Can you work out what step size to take to ensure you visit all the dots on the circle?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
If you move the tiles around, can you make squares with different coloured edges?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
Which set of numbers that add to 100 have the largest product?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.