Problems
The School Trip
Stage:1 Challenge Level:
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
How Old?
Stage:1 Challenge Level:
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Tug-of-war Contest
Stage:2 Challenge Level:
It was the annual summer sports day at Tuggem School. The contestants for the Tug-of-War were limbering up. Use the information to discover who wins the third heat of the Tug-of-War contest.
Oranges and Lemons
Stage:2 Challenge Level:
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Making Cuboids
Stage:2 Challenge Level:
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Plates of Biscuits
Stage:2 Challenge Level:
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
Rocco's Race
Stage:2 Challenge Level:
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
Throw a 100
Stage:2 Challenge Level:
Can you score 100 by throwing rings on this board? Is there more than way to do it?
World of Tan - Fractions
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outlines of the chairs?
On Target
Stage:2 Challenge Level:
You have 5 darts and your target score is 44. How many different ways could you score 44?
Two and Two
Stage:2 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
2D-3D
Stage:3 Challenge Level:
Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of. . . .
Muggles Magic
Stage:3 Challenge Level:
You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.
DOTS Division
Stage:4 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Our Ages
Stage:4 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be exactly (n-1) times her age. In m2 years I shall be exactly (n-2) times her age. After that I shall never again be an exact multiple of. . . .
Schlafli Tessellations
Stage:3, 4 and 5 Challenge Level:
are somewhat mundane they do pose a demanding challenge in terms of 'elegant' LOGO procedures. This problem considers the eight semi-regular tessellations which pose a demanding challenge in terms of. . . .
Gnomon II
Stage:4 Challenge Level:
A gnomon is an L shape. Each Fibonacci number has its gnomon with area corresponding to the number. Draw dotted lines dividing each gnomon into two parts illustrating the Fibonacci rule.
There's a Limit
Stage:4 and 5 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
Ellipses
Stage:4 and 5 Challenge Level:
Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.
Parabella
Stage:4 and 5 Challenge Level:
This is a beautiful result involving a parabola and parallels.
Proof Sorter - Geometric Series
Stage:5 Challenge Level:
This is an interactivity in which you have to sort into the correct order the steps in the proof of the formula for the sum of a geometric series.
