Algebra in the new curriculum

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?

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?

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

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.

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

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

What patterns can you make with a set of dominoes?

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?

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

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

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?

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?

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?

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

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

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

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?

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

This box does something to the numbers that go into it. If you know the numbers that come out, what might be going on inside the box?

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

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?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

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

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.

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

Are these statements always true, sometimes true or never true?

Are these statements always true, sometimes true or never true?

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.

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

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