Problems
World of Tan - Transform This...into...that
Stage: Challenge Level: 
Can you fit the tangram pieces into these outlines?
Skip Counting
Stage: 1 Challenge Level:
Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
Halloween Investigation
Stage: 2 Challenge Level:
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
Hubble, Bubble
Stage: 2 Challenge Level:
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
Trick or Treat
Stage: 2 Challenge Level:
Mrs. Smith had emptied packets of chocolate-covered mice, plastic frogs and gummi-worms into a cauldron for treats. What treat is Trixie most likely to pick out?
Penta Place
Stage: 2 Challenge Level:
Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?
A Bit of a Dicey Problem
Stage: 2 Challenge Level:
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Appearing Square
Stage: 3 Challenge Level:
Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .
Thirty Nine, Seventy Five
Stage: 3 Challenge Level:
We have exactly 100 coins. There are five different values of coins. We have decided to buy a piece of computer software for 39.75. We have the correct money, not a penny more, not a penny less! Can. . . .
Serendipity
Stage: 3 Challenge Level:
As is often the case when looking for something, you become distracted by other more exciting ideas. Such was the case recently when retrieving some old tiling patterns. How could I have overlooked. . . .
Rhombicubocts
Stage: 3 Challenge Level:
Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices. . . .
Aba
Stage: 3 Challenge Level:
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
Framed
Stage: 3 Challenge Level:
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Disappearing Square
Stage: 3 Challenge Level:
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
Unit Fractions
Stage: 3 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
Common Divisor
Stage: 4 Challenge Level:
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Converse
Stage: 4 Challenge Level:
Clearly if a, b and c are the lengths of the sides of a triangle and the triangle is equilateral then a^2 + b^2 + c^2 = ab + bc + ca. Is the converse true, and if so can you prove it? That is if. . . .
Fitting In
Stage: 4 Challenge Level:
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .
Cubics
Stage: 4 and 5 Challenge Level:
Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.
Pent
Stage: 4 and 5 Challenge Level:
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Three Ways
Stage: 5 Challenge Level:
Given that x + y = -1 find the largest value of xy (a) by coordinate geometry (b) by calculus (c) by algebra.
Elsewhere...
Featured Solutions
Articles & Games
Using Questioning to Stimulate Mathematical Thinking
Good questioning techniques have long being regarded as a fundamental tool of effective teachers. This article for teachers looks at different categories of questions that can promote mathematical thinking.
Using Questioning to Stimulate Mathematical Thinking: Addendum
In the process of working with some groups of teachers on using questions to promote mathematical thinking, the following table was developed. It provides examples of generic questions that can be used to guide children through a mathematical investigation, and at the same time prompt higher levels of thinking.
