Creating and manipulating expressions and formulae

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Favourite

Cubes Within Cubes Revisited

Age

11 to 14

Challenge level

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?
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Favourite

Price Match

Age

7 to 11

Challenge level

Can you find pairs of differently sized windows that cost the same?
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Favourite

Finding 3D Stacks

Age

7 to 11

Challenge level

Can you find a way of counting the spheres in these arrangements?
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Favourite

Your Number Is...

Age

7 to 14

Challenge level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
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Favourite

The Number Jumbler

Age

7 to 14

Challenge level

The Number Jumbler can always work out your chosen symbol. Can you work out how?
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Favourite

Diagonal Sums

Age

7 to 14

Challenge level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
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Favourite

Special Numbers

Age

11 to 14

Challenge level

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?
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Favourite

Partitioning Revisited

Age

11 to 14

Challenge level

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
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Favourite

Crossed Ends

Age

11 to 14

Challenge level

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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Favourite

How Much Can We Spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?