Problems
Matchsticks
Stage: 2 Challenge Level: 
Reasoning about the number of matches needed to build squares that share their sides.
Ten Green Bottles
Stage: 2 Challenge Level:
Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?
Take the Right Angle
Stage: 2 Challenge Level:
How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.
The Mathemagician's Seven Spells
Stage: 2 Challenge Level:
"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?
Having the Time of Your Life
Stage: 2 Challenge Level:
In a minute the average heart pumps 4 litres of blood and beats 70 times. How many litres does it pump in a year?
Counting Counters
Stage: 2 Challenge Level:
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
Cuisenaire Rods
Stage: 2 Challenge Level:
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Polydron
Stage: 2 Challenge Level:
Continue this pattern made from squares and equilateral triangles. Can you describe the patterns?
Slow Coach
Stage: 2 Challenge Level:
How many of this company's coaches travelling in the opposite direction does the 10 am coach from Alphaton pass before reaching Betaville?
Logoland - Sequences
Stage: 3 Challenge Level:
Below are two diagrams concerned with a sequence of squares Part 1 Part 2 Both are based on the following procedure: TO SQUARE :S :N IF :S < 2 [ STOP] REPEAT 2 [ REPEAT :N [ FD :S RT 90 FD :S LT 90]. . . .
Sissa's Reward
Stage: 3 Challenge Level:
According to an old Indian myth, Sissa ben Dahir was a courtier for a king. The king decided to reward Sissa for his dedication and Sissa asked for one grain of rice to be put on the first square. . . .
Excel Investigation: Target Decimal
Stage: 3 and 4 Challenge Level:
Use an Excel spreadsheet to approximate a decimal using trial and improvement.
Excel Interactive Resource: Multiples Chain
Stage: 3 and 4 Challenge Level:
Use an interactive Excel spreadsheet to investigate factors and multiples.
Excel Technique: Logic Tests
Stage: 3 and 4 Challenge Level:
Learn how to use logic tests to create interactive resources using Excel.
Olympic Magic
Stage: 4 Challenge Level:
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Tablecloth
Stage: 4 Challenge Level:
Colour the squares of the square tablecloth so that each square is the same colour as all the symmetrically placed squares and a different colour from the rest of the squares.
Squaring the Circle and Circling the Square
Stage: 4 Challenge Level:
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Staircase
Stage: 5 Challenge Level:
Solving the equation x^3 = 3 is easy but what about solving equations with x to the power x^3 or x to the power x to the power x^3 or having a 'staircase' of powers?
Maltese Cross
Stage: 5 Challenge Level:
Sketch the graph of xy(x^2 - y^2) = x^2 + y^2 consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.
Escriptions
Stage: 5 Challenge Level:
For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
