Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you use this information to work out Charlie's house number?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

Learn how to use advanced pasting techniques to create interactive spreadsheets.

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

Learn how to make a simple table using Excel.

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

This investigation uses Excel to optimise a characteristic of interest.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials, but it can also assist them in forming useful mental pictures to support memory and reasoning.