Creating and manipulating expressions and formulae

There are 198 NRICH Mathematical resources connected to Creating and manipulating expressions and formulae

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Finding factors

Age

14 to 16

Challenge level

Can you find the hidden factors which multiply together to produce each quadratic expression?

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Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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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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Christmas chocolates

Age

11 to 14

Challenge level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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Seven squares

Age

11 to 14

Challenge level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Favourite

Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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Favourite

More number pyramids

Age

11 to 14

Challenge level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Favourite

Mechanical integration

Age

16 to 18

Challenge level

To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.

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Favourite

Lens angle

Age

14 to 16

Challenge level

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

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Favourite

Perfectly square

Age

14 to 16

Challenge level

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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For younger learners

Creating and manipulating expressions and formulae

Finding factors

Pair products

Cubes within cubes revisited

Christmas chocolates

Seven squares

Think of two numbers

More number pyramids

Mechanical integration

Lens angle

Perfectly square