Problems
One Big Triangle
Stage:1 Challenge Level:
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Super Value Shapes
Stage:2 Challenge Level:
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
April Fool Your Mathematical Senses
Stage:2 Challenge Level:
There is a little trick to many, but not all, of these problems. Read them carefully and think twice! Then try these tricky quickies on your friends and family.
World of Tan - Soup
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Sticky Triangles
Stage:2 Challenge Level:
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
What's it Worth?
Stage:3 Challenge Level:
Each symbol has a numerical value. The total for the symbols is written at the end of each row and column. Can you find the missing total that should go where the question mark has been put?
Spirals and Wallpapers
Stage:3 Challenge Level:
A spiral is defined as: ...a curve formed by a point moving around a fixed point and constantly moving away from or approaching the fixed point. (p110. HBJ Dictionary of Mathematics compiled by Ken. . . .
Is it Magic or Is it Maths?
Stage:3 Challenge Level:
Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .
Making Rectangles, Making Squares
Stage:3 Challenge Level:
How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?
3388
Stage:3 Challenge Level:
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Hot Pursuit
Stage:3 Challenge Level:
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Nine Colours
Stage:3 Challenge Level:
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
Square Mean
Stage:4 Challenge Level:
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Qqq..cubed
Stage:4 Challenge Level:
It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .
AMGM
Stage:4 Challenge Level:
Choose any two numbers. Call them a and b. Work out the arithmetic mean and the geometric mean. Which is bigger? Repeat for other pairs of numbers. What do you notice?
Tricircle
Stage:4 Challenge Level:
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
Parabolic Patterns
Stage:4 and 5 Challenge Level:
The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.
Snooker Frame 2
Stage:5 Challenge Level:
It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?
Orthogonal Circle
Stage:5 Challenge Level:
Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.
