Introducing algebra

There are 44 NRICH Mathematical resources connected to Introducing algebra

problem

Favourite

Trebling

Age

7 to 11

Challenge level

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

problem

Favourite

Table patterns go wild!

Age

7 to 11

Challenge level

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.

problem

Favourite

Doplication

Age

7 to 11

Challenge level

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?

problem

Favourite

Special numbers

Age

11 to 14

Challenge level

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?

problem

Favourite

Your number was...

Age

11 to 14

Challenge level

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?

problem

Favourite

Up and down staircases

Age

7 to 11

Challenge level

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?

problem

Favourite

Perimeter expressions

Age

11 to 14

Challenge level

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

problem

Favourite

Two and two

Age

7 to 16

Challenge level

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

problem

Favourite

Break it up!

Age

5 to 11

Challenge level

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?

problem

Favourite

Shape products

Age

11 to 14

Challenge level

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

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Introducing algebra

Trebling

Table patterns go wild!

Doplication

Special numbers

Your number was...

Up and down staircases

Perimeter expressions

Two and two

Break it up!

Shape products