Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

Can you substitute numbers for the letters in these sums?

Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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?

Challenge Level

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

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?

Challenge Level

Amy's mum had given her Â£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?

Challenge Level

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?

Challenge Level

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

Challenge Level

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

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.

Challenge Level

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

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

Challenge Level

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

Challenge Level

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.

Challenge Level

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?

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?

Challenge Level

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

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?

Challenge Level

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

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?

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

Challenge Level

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

Challenge Level

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