List

Algebra in the New Curriculum

What's X got to do with it?
article

What's x got to do with it?

By following through the threads of algebraic thinking discussed in this article, we can ensure that children's mathematical experiences follow a continuous progression.
Making Algebra Rich
article

Making algebra rich

Lynne suggests activities which support the development of primary children's algebraic thinking.
Ip Dip
problem
Favourite

Ip dip

Age
5 to 11
Challenge level
filled star empty star empty star

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Heads and Feet
problem
Favourite

Heads and feet

Age
5 to 7
Challenge level
filled star filled star empty star
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Super Shapes
problem
Favourite

Super shapes

Age
7 to 11
Challenge level
filled star empty star empty star

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Plenty of Pens
problem
Favourite

Plenty of pens

Age
7 to 11
Challenge level
filled star empty star empty star

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Shape Times Shape
problem
Favourite

Shape times shape

Age
7 to 11
Challenge level
filled star empty star empty star

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Sticky Triangles
problem
Favourite

Sticky triangles

Age
7 to 11
Challenge level
filled star filled star filled star
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Next Domino
problem
Favourite

Next domino

Age
5 to 7
Challenge level
filled star empty star empty star
Which comes next in each pattern of dominoes?
A City of Towers
problem
Favourite

A city of towers

Age
5 to 7
Challenge level
filled star empty star empty 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?

Break it up!
problem
Favourite

Break it up!

Age
5 to 11
Challenge level
filled star empty star empty star

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Chairs and Tables
problem
Favourite

Chairs and tables

Age
5 to 7
Challenge level
filled star empty star empty star

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Street Sequences
problem

Street sequences

Age
5 to 11
Challenge level
filled star empty star empty star
Investigate what happens when you add house numbers along a street in different ways.
Repeating Patterns
problem
Favourite

Repeating patterns

Age
5 to 7
Challenge level
filled star empty star empty star
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
Cube bricks and daisy chains
problem

Cube bricks and daisy chains

Age
5 to 7
Challenge level
filled star empty star empty star

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

Triple Cubes
problem
Favourite

Triple cubes

Age
5 to 11
Challenge level
filled star empty star empty star

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Poly Plug Pattern
problem
Favourite

Poly plug pattern

Age
5 to 7
Challenge level
filled star empty star empty star

Create a pattern on the small grid. How could you extend your pattern on the larger grid?

Domino Patterns
problem
Favourite

Domino patterns

Age
5 to 7
Challenge level
filled star empty star empty star

What patterns can you make with a set of dominoes?

Circles, Circles
problem
Favourite

Circles, circles

Age
5 to 11
Challenge level
filled star empty star empty star

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Counting Stick Conjectures
problem

Counting stick conjectures

Age
5 to 11
Challenge level
filled star empty star empty star
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
Missing Middles
problem
Favourite

Missing middles

Age
5 to 7
Challenge level
filled star filled star empty star
Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes?
Hundred Square
problem
Favourite

Hundred square

Age
5 to 11
Challenge level
filled star filled star empty star

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Three Ball Line Up
problem
Favourite

Three ball line up

Age
5 to 7
Challenge level
filled star filled star empty star
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Caterpillars
problem
Favourite

Caterpillars

Age
5 to 7
Challenge level
filled star filled star empty star
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
School fair necklaces
problem
Favourite

School fair necklaces

Age
5 to 11
Challenge level
filled star filled star empty star
How many possible symmetrical necklaces can you find? How do you know you've found them all?

The "What if..?" questions are such an important part of mathematical thinking. Knowing what to ask means that you understand something about the structure of the problem, and being able to see similarities and differences means you're starting to generalise.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Take one example
article

Take one example

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Break it up!
problem
Favourite

Break it up!

Age
5 to 11
Challenge level
filled star empty star empty star

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Strike it out
problem
Favourite

Strike it out

Age
5 to 11
Challenge level
filled star empty star empty star

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Sitting round the party tables
problem
Favourite

Sitting round the party tables

Age
5 to 11
Challenge level
filled star empty star empty 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.
The add and take-away path
problem
Favourite

The add and take-away path

Age
5 to 7
Challenge level
filled star empty star empty star
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Count The Digits
problem
Favourite

Count the digits

Age
5 to 11
Challenge level
filled star empty star empty star
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
What was in the Box?
problem
Favourite

What was in the box?

Age
5 to 7
Challenge level
filled star empty star empty star
This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Always, Sometimes or Never?
problem
Favourite

Always, sometimes or never?

Age
5 to 11
Challenge level
filled star empty star empty star

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Next-door Numbers
problem

Next-door numbers

Age
5 to 7
Challenge level
filled star empty star empty star
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Ring a Ring of Numbers
problem
Favourite

Ring a ring of numbers

Age
5 to 7
Challenge level
filled star filled star empty star
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
How Odd
problem
Favourite

How odd

Age
5 to 7
Challenge level
filled star filled star empty star
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
School fair necklaces
problem
Favourite

School fair necklaces

Age
5 to 11
Challenge level
filled star filled star empty star
How many possible symmetrical necklaces can you find? How do you know you've found them all?

The "What if..?" questions are such an important part of mathematical thinking. Knowing what to ask means that you understand something about the structure of the problem, and being able to see similarities and differences means you're starting to generalise.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Take one example
article

Take one example

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
Money Bags
problem
Favourite

Money bags

Age
5 to 11
Challenge level
filled star filled star empty star
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Make 37 Poster
problem
Favourite

Make 37

Age
5 to 11
Challenge level
filled star filled star empty 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?

School fair necklaces
problem
Favourite

School fair necklaces

Age
5 to 11
Challenge level
filled star filled star empty star
How many possible symmetrical necklaces can you find? How do you know you've found them all?
Factors and Multiples Game
game
Favourite

Factors and multiples game

A game in which players take it in turns to choose a number. Can you block your opponent?

Exploring Wild & Wonderful Number Patterns
problem

Exploring wild and wonderful number patterns

Age
7 to 11
Challenge level
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EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Diagonally Square
problem

Diagonally square

Age
7 to 11
Challenge level
filled star empty star empty star
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Magic Vs
problem
Favourite

Magic Vs

Age
7 to 11
Challenge level
filled star empty star empty star

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

Follow the numbers
problem
Favourite

Follow the numbers

Age
7 to 11
Challenge level
filled star empty star empty star

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

Take three numbers
problem
Favourite

Take three numbers

Age
7 to 11
Challenge level
filled star empty star empty star

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

Division Rules
problem
Favourite

Division rules

Age
7 to 11
Challenge level
filled star empty star empty star
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Neighbourly Addition
problem

Neighbourly addition

Age
7 to 14
Challenge level
filled star empty star empty star
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Got It
problem
Favourite

Got it

Age
7 to 14
Challenge level
filled star filled star empty star

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Three neighbours
problem
Favourite

Three neighbours

Age
7 to 14
Challenge level
filled star filled star empty star
Take three consecutive numbers and add them together. What do you notice?
This Pied Piper of Hamelin
problem
Favourite

This Pied Piper of Hamelin

Age
7 to 11
Challenge level
filled star filled star empty star

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Six Ten Total
problem
Favourite

Six ten total

Age
7 to 11
Challenge level
filled star filled star empty star
This challenge combines addition, multiplication, perseverance and even proof.
Six Numbered Cubes
problem
Favourite

Six numbered cubes

Age
7 to 11
Challenge level
filled star filled star empty star
This task combines spatial awareness with addition and multiplication.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Break it up!
problem
Favourite

Break it up!

Age
5 to 11
Challenge level
filled star empty star empty star

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Street Sequences
problem

Street sequences

Age
5 to 11
Challenge level
filled star empty star empty star
Investigate what happens when you add house numbers along a street in different ways.
Holes
problem
Favourite

Holes

Age
5 to 11
Challenge level
filled star empty star empty star

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

Count The Digits
problem
Favourite

Count the digits

Age
5 to 11
Challenge level
filled star empty star empty star
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
Counting Stick Conjectures
problem

Counting stick conjectures

Age
5 to 11
Challenge level
filled star empty star empty star
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
Unravelling Sequences
problem

Unravelling sequences

Age
7 to 11
Challenge level
filled star empty star empty star
Can you describe what is happening as this program runs? Can you unpick the steps in the process?
Tables Without Tens
problem

Tables without tens

Age
7 to 11
Challenge level
filled star empty star empty star
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
Times Tables Shifts
problem
Favourite

Times tables shifts

Age
7 to 11
Challenge level
filled star empty star empty star

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Domino sets
problem
Favourite

Domino sets

Age
7 to 11
Challenge level
filled star empty star empty star

How do you know if your set of dominoes is complete?

Button-Up Some More
problem
Favourite

Button-up some more

Age
7 to 11
Challenge level
filled star filled star empty star

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Sticky Triangles
problem
Favourite

Sticky triangles

Age
7 to 11
Challenge level
filled star filled star filled star
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?


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