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For younger learners

  • Early Years Foundation Stage

Special Numbers

In some senses, all numbers are special, though some are perhaps given more attention than others...

The Special Numbers pathway on wild.maths.org invites students to take a closer look at some familiar categories of number and operations, and perhaps discover that there's a lot more to averages, fractions and square numbers than they might have initially thought.

The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.


M, M and M

Age 11 to 14
Challenge Level Yellow star

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Keep it Simple

Age 11 to 14
Challenge Level Yellow star

Can all unit fractions be written as the sum of two unit fractions?

Twisting and Turning

Age 11 to 14
Challenge Level Yellow starYellow star

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

Unequal Averages

Age 11 to 14
Challenge Level Yellow starYellow star

Play around with sets of five numbers and see what you can discover about different types of average...

Power Mad!

Age 11 to 14
Challenge Level Yellow starYellow star

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Egyptian Fractions

Age 11 to 14
Challenge Level Yellow starYellow star

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Peaches Today, Peaches Tomorrow...

Age 11 to 14
Challenge Level Yellow starYellow star

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

The Greedy Algorithm

Age 11 to 14
Challenge Level Yellow starYellow starYellow star

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

Wipeout

Age 11 to 16
Challenge Level Yellow starYellow star

Can you do a little mathematical detective work to figure out which number has been wiped out?

Searching for Mean(ing)

Age 11 to 16
Challenge Level Yellow starYellow star

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?

Big Powers

Age 11 to 16
Challenge Level Yellow starYellow starYellow star

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Hollow Squares

Age 14 to 16
Challenge Level Yellow star

Which armies can be arranged in hollow square fighting formations?

Generating Triples

Age 14 to 16
Challenge Level Yellow star

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Plus Minus

Age 14 to 16
Challenge Level Yellow starYellow star

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

Fair Shares?

Age 14 to 16
Challenge Level Yellow starYellow star

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

What's Possible?

Age 14 to 16
Challenge Level Yellow starYellow star

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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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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