Creating and manipulating expressions and formulae

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

problem

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Perimeter expressions

Age

11 to 14

Challenge level

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

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Legs eleven

Age

11 to 14

Challenge level

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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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?

problem

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Multiplication square

Age

14 to 16

Challenge level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

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Matchless

Age

14 to 16

Challenge level

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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Training schedule

Age

14 to 16

Challenge level

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

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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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How much can we spend?

Age

11 to 14

Challenge level

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?

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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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For younger learners

Creating and manipulating expressions and formulae

Perimeter expressions

Legs eleven

Special numbers

Multiplication square

Matchless

Training schedule

Partitioning revisited

How much can we spend?

Finding factors

Pair products