This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

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### Finding factors

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

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### Factorising with Multilink

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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### Pair Products

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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### Pythagoras Perimeters

If you know the perimeter of a right angled triangle, what can you say about the area?

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### Difference of Two Squares

What is special about the difference between squares of numbers adjacent to multiples of three?

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### Square Number Surprises

There are unexpected discoveries to be made about square numbers...

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### Puzzling Place Value

Can you explain what is going on in these puzzling number tricks?

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### Plus Minus

Can you explain the surprising results Jo found when she calculated
the difference between square numbers?

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### What's Possible?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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### Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

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### Always Perfect

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

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### Perfectly Square

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

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### Multiplication square

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

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### 2-Digit Square

A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?

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### Harmonic Triangle

Can you see how to build a harmonic triangle? Can you work out the next two rows?

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*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*