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?

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.

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

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

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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?

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

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?

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?

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

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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?

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?

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.

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

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?

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

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?

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.

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

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?

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