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

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?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

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

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

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

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.

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?

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.

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?

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

Can you substitute numbers for the letters in these sums?

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?

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

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

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

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

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?

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?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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?

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

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?

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?

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

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

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

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?

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

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

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

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