Problems
Buzzy Bee
Stage:1 Challenge Level:
Buzzy Bee was building a honeycomb. She decided to decorate the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
Part the Polygons
Stage:2 Challenge Level:
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Which Scripts?
Stage:2 Challenge Level:
There are six numbers written in five different scripts. Can you sort out which is which?
Super Shapes
Stage:2 Short Challenge Level:
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Heptagon Triangles
Stage:2 Challenge Level:
How many different triangles can you find in this shape? How many of each type of triangle is there? What other shapes can you find?
Shapes on the Playground
Stage:2 Challenge Level:
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what each of them drew using the clues?
Pick up the Sticks
Stage:2 Challenge Level:
I was making shapes with cocktail sticks. I used 28 to make 4 heptagons. Then I used the same number to make 4 octagons and a square. Can you do it?
World of Tan - Working Men
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Making Boxes
Stage:2 and 3 Challenge Level:
What size square corners should be cut from this piece of paper to make a box with the largest possible volume?
Converging Means
Stage:3 Challenge Level:
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the. . . .
The Genie in the Jar
Stage:3 Challenge Level:
This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .
Some Spirals and Tessellations
Stage:3 Challenge Level:
Aspiral is a curve formed by a point moving around a fixed point and constantly moving away from or approaching the fixed point. This month, building on the idea that many sets of things can be. . . .
Mathland Election
Stage:3 Challenge Level:
A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
Euler's Squares
Stage:4 Challenge Level:
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square. Three of the numbers that he found are a = 18530, b=65570, c=45986. Find the fourth number, x. You. . . .
Diophantine N-tuples
Stage:4 Challenge Level:
Take any whole number q. Calculate q^2 - 1. Factorize q^2-1 to give two factors a and b (not necessarily q+1 and q-1). Put c = a + b + 2q . Then you will find that ab+1 , bc+1 and ca+1 are all. . . .
Lawnmower
Stage:4 Challenge Level:
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .
Gnomon I
Stage:4 Challenge Level:
A gnomon is an L shape. Each Fibonacci number has its gnomon with the area corresponding to the number. Draw them and show that they obey the Fibonacci rule.
More Parabolic Patterns
Stage:4 and 5 Challenge Level:
The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.
Proof Sorter - Quadratic Equation
Stage:4 and 5 Challenge Level:
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Pythagorean Golden Means
Stage:5 Challenge Level:
Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio.
