Problems
Making Sticks
Stage: 1 Challenge Level: 
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?
Grouping Goodies
Stage: 1 Challenge Level:
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Multiplication Squares
Stage: 2 Challenge Level:
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.
Factor Lines
Stage: 2 Challenge Level:
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A Right Charlie
Stage: 2 Challenge Level:
Can you use this information to work out Charlie's house number?
Divide it Out
Stage: 2 Challenge Level:
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Scoring with Dice
Stage: 2 Challenge Level:
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?
LOGO Challenge 8 - Rhombi
Stage: 2, 3 and 4 Challenge Level:
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
Remainder
Stage: 3 Challenge Level:
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
X Marks the Spot
Stage: 3 Challenge Level:
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" .
Basket Case
Stage: 3 Challenge Level:
A girl goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Oh for the Mathematics of Yesteryear
Stage: 3 Challenge Level:
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. . . .
Excel Investigation: Ring on a String
Stage: 3 and 4 Challenge Level:
This investigation uses Excel to optimise a characteristic of interest.
Excel Interactive Resource: Make a Copy
Stage: 3 and 4 Challenge Level:
Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.
Excel Technique: Making a Table for a Function of Two Independent
Stage: 3 and 4 Challenge Level:
Learn how to make a simple table using Excel.
Excel Technique: Inserting an Increment Button
Stage: 3 and 4 Challenge Level:
Learn how to use increment buttons and scroll bars to create interactive Excel resources.
Excel Technique: Using Paste Special to Lift a Copy of Values
Stage: 3 and 4 Challenge Level:
Learn how to use advanced pasting techniques to create interactive spreadsheets.
Diagonals for Area
Stage: 4 Challenge Level:
Prove that the area of a quadrilateral is given by half the product of the lengths of the diagonals multiplied by the sine of the angle between the diagonals.
Number Rules - OK
Stage: 4 Challenge Level:
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...
Sine Problem
Stage: 5 Challenge Level:
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.
Diverging
Stage: 5 Challenge Level:
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.
Flexi Quads
Stage: 5 Challenge Level:
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?
Elsewhere...
Featured Solutions
Articles & Games
Multiplication Series: Number Arrays
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
Multiplication Series: Illustrating Number Properties with Arrays
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.
