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Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
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Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
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  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Ordered Ways of Working Upper Primary

Having an ordered way of going about these activities will really help.  This might mean using the information given in a particular order or perhaps approaching the task in a methodical way which reveals patterns, helping you reach a solution.

Sitting Round the Party Tables

Age 5 to 11
Challenge Level Yellow star

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

A Mixed-up Clock

Age 7 to 11
Challenge Level Yellow star

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

What Do You Need?

Age 7 to 11
Challenge Level Yellow star

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

A Square of Numbers

Age 7 to 11
Challenge Level Yellow star

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Light the Lights Again

Age 7 to 11
Challenge Level Yellow starYellow star

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Prison Cells

Age 7 to 11
Challenge Level Yellow starYellow star

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Two Primes Make One Square

Age 7 to 11
Challenge Level Yellow starYellow star

Can you make square numbers by adding two prime numbers together?

Tea Cups

Age 7 to 14
Challenge Level Yellow starYellow starYellow star

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Counting Cards

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Curious Number

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Make 37

Age 7 to 11
Challenge Level Yellow starYellow star

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

First Connect Three

Age 7 to 11
Challenge Level Yellow star

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

Multilink Cubes

If you had 36 cubes, what different cuboids could you 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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