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?

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.

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

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

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?

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

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?

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

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

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.

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

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?

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

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?

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.

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?

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?

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?

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

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

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?

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

A geometry lab crafted in a functional programming language. Ported to Flash from the original java at web.comlab.ox.ac.uk/geomlab

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