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Number and algebra

  • The Number System and Place Value
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For younger learners

  • Early Years Foundation Stage

Number and Place Value

These activities are part of our Primary collections, which are problems grouped by topic.

Take Three Numbers

Age 7 to 11
Challenge Level Yellow star

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Which Scripts?

Age 7 to 11
Challenge Level Yellow star

There are six numbers written in five different scripts. Can you sort out which is which?

The Deca Tree

Age 7 to 11
Challenge Level Yellow star

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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?

Round the Four Dice

Age 7 to 11
Challenge Level Yellow star

This activity involves rounding four-digit numbers to the nearest thousand.

Number Differences

Age 7 to 11
Challenge Level Yellow star

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Round the Three DiceLive

Age 7 to 11
Challenge Level Yellow star

What happens when you round these three-digit numbers to the nearest 100?

Swimming Pool

Age 5 to 11
Challenge Level Yellow star

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Reasoned Rounding

Age 7 to 14
Challenge Level Yellow star

Four strategy dice games to consolidate pupils' understanding of rounding.

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?

Dicey Operations in Line

Age 7 to 11
Challenge Level Yellow star

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Tug Harder!

Age 7 to 11
Challenge Level Yellow star

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Count Me In

Age 7 to 11
Challenge Level Yellow star

How do you know whether you will reach these numbers when you count in steps of six from zero?

Sea LevelLive

Age 7 to 11
Challenge Level Yellow star

The picture shows a lighthouse and some underwater creatures. Can you work out the distances between some of the different creatures?

Magic Vs

Age 7 to 11
Challenge Level Yellow star

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Four-digit Targets

Age 7 to 11
Challenge Level Yellow star

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Space Distances

Age 7 to 11
Challenge Level Yellow star

This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.

The Remainders Game

Age 7 to 14
Challenge Level Yellow star

Play this game and see if you can figure out the computer's chosen number.

Roman Numerals

Age 7 to 11
Challenge Level Yellow star

Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

Coded Hundred Square

Age 7 to 11
Challenge Level Yellow star

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Representing Numbers

Age 7 to 11
Challenge Level Yellow star

Find as many different ways of representing this number of dots as you can.

Nice or Nasty

Age 7 to 14
Challenge Level Yellow star

There are nasty versions of this dice game but we'll start with the nice ones...

Satisfying Four Statements

Age 7 to 11
Challenge Level Yellow star

Can you find any two-digit numbers that satisfy all of these statements?

Number Match

Age 5 to 11
Challenge Level Yellow star

A task which depends on members of the group noticing the needs of others and responding.

Planning a School Trip

Age 7 to 11
Challenge Level Yellow star

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Less Is More

Age 7 to 11
Challenge Level Yellow star

Use your knowledge of place value to try to win this game. How will you maximise your score?

Three Neighbours

Age 7 to 14
Challenge Level Yellow starYellow star

Take three consecutive numbers and add them together. What do you notice?

What Distance?

Age 7 to 11
Challenge Level Yellow starYellow star

Can you use addition and subtraction to answer these questions about real-life distances?

Ordering Journeys

Age 7 to 11
Challenge Level Yellow starYellow star

How would you put these journey lengths in order?

Number Lines in Disguise

Age 7 to 14
Challenge Level Yellow starYellow star

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Square Subtraction

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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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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