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Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
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Geometry and measure

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Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
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Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
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For younger learners

  • Early Years Foundation Stage

Finding All Possibilities Lower Primary

These activities ask you to find all possible solutions.  If you work in a systematic way, you will be sure not to leave any out!

Robot Monsters

Age 5 to 7
Challenge Level Yellow star

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Two Dice

Age 5 to 7
Challenge Level Yellow star

Find all the numbers that can be made by adding the dots on two dice.

Same Length Trains

Age 5 to 7
Challenge Level Yellow star

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Button-up

Age 5 to 7
Challenge Level Yellow star

My coat has three buttons. How many ways can you find to do up all the buttons?

Three Ball Line Up

Age 5 to 7
Challenge Level Yellow starYellow star

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

6 Beads

Age 5 to 7
Challenge Level Yellow starYellow star

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

A City of Towers

Age 5 to 7
Challenge Level Yellow star

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Ladybirds in the Garden

Age 5 to 7
Challenge Level Yellow starYellow star

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Triangle Animals

Age 5 to 7
Challenge Level Yellow starYellow star

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Inside Triangles

Age 5 to 7
Challenge Level Yellow star

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Beads and Bags

Age 5 to 11
Challenge Level Yellow star

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Let's Investigate Triangles

Age 5 to 7
Challenge Level Yellow star

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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Homes

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

Stairs

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Train Carriages

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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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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