Problems
Let's Investigate Triangles
Stage:1 Challenge Level:
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many more different triangles can they make?
Claire's Counting Cards
Stage:1 Challenge Level:
Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .
Dodecamagic
Stage:2 Challenge Level:
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
Back to School
Stage:2 Challenge Level:
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
Mystery Matrix
Stage:2 Challenge Level:
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A-magical Number Maze
Stage:2 Challenge Level:
This magic square has operations written in it, to make it into a maze. Start wherever you like and go through every cell and go out through the exit marked in cell 8 with a total of 15!
World of Tan - an Appealing Stroll
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outline of the child walking home from school?
Adding All Nine
Stage:3 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Chocolate Maths
Stage:3 Challenge Level:
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
Tetra Square
Stage:3 Challenge Level:
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
More Mathematical Mysteries
Stage:3 Challenge Level:
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
Hex
Stage:3 Challenge Level:
Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.
Overlaid
Stage:2, 3 and 4 Challenge Level:
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
One or Both
Stage:3 Challenge Level:
Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?
American Billions
Stage:3 Challenge Level:
Find the ten digit number in which the number formed by the first two digits from the left is divisible by 2, the number formed by the first three digits from the left is divisible by 3...
Reciprocal Triangles
Stage:5 Challenge Level:
Prove that the sum of the reciprocals of the first n triangular numbers is approximately equal to 2 when n is large and tends to 2 as n tends to infinity.
Golden Triangle
Stage:5 Challenge Level:
Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
Sangaku
Stage:5 Challenge Level:
The square ABCD is split into three triangles by the lines BP and CP. Find the radii of the three inscribed circles to these triangles as P moves on AD.
Proof Sorter - the Square Root of 2 Is Irrational
Stage:5 Challenge Level:
Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
