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There are **42** NRICH Mathematical resources connected to **Introducing algebra**, you may find related items under Algebraic expressions, equations and formulae.

Problem
Primary curriculum
Secondary curriculum
### The Number Jumbler

The Number Jumbler can always work out your chosen symbol. Can you work out how?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Different Deductions

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Price Match

Can you find pairs of differently sized windows that cost the same?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Finding 3D Stacks

Can you find a way of counting the spheres in these arrangements?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Products

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Perimeter Expressions

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Your Number Was...

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Crossed Ends

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Times Shape

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Lines

A resource to try once children are familiar with number lines, and they have begun to use them for addition. It could be a good way to talk about subtraction. Leah and Tom each have a number line. Can you work out where their counters will land?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Secret Number

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Your Number Is...

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Break it Up!

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?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Up and Down Staircases

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Special Numbers

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Trebling

Can you replace the letters with numbers? Is there only one solution in each case?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Brown Family

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Think of Two Numbers

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plenty of Pens

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Super Shapes

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

Age 7 to 11

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and Two

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sweetie Box

Max and Bryony both have a box of sweets. What do you know about the number of sweets they each have?

Age 5 to 11

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Making Algebra Rich

Lynne suggests activities which support the development of primary children's algebraic thinking.

Age 5 to 11

Article
Primary curriculum
Secondary curriculum
### 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.

Age 5 to 16

Problem
Primary curriculum
Secondary curriculum
### Gran, How Old Are You?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Number Lines

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Forward Into Logo 8: More about Variables

Write a Logo program, putting in variables, and see the effect when you change the variables.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### First Forward Into Logo 6: Variables and Procedures

Learn to write procedures and build them into Logo programs. Learn to use variables.

Age 11 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cherry Buns

Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gift Stacks

Use the information to work out how many gifts there are in each pile.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sisters and Brothers

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Buckets of Thinking

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Augustus' Age

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Spell by Numbers

Can you substitute numbers for the letters in these sums?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Many Eggs?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cat Food

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Age 7 to 11

Challenge Level