Problems
Same Shapes
Stage:1 Challenge Level:
How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?
Dicey
Stage:2 Challenge Level:
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
It Figures
Stage:2 Challenge Level:
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Green Cube, Yellow Cube
Stage:2 Challenge Level:
How can you paint the faces of these eight the cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?
Map Folding
Stage:2 Challenge Level:
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. Label these rectangles on both sides of the paper. How many different ways can you fold it up?
World of Tan - Junk
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outline of this junk?
Base Puzzle
Stage:3 Challenge Level:
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.
Clock Squares
Stage:3 Challenge Level:
Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.
Happy Octopus
Stage:3 Challenge Level:
This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 ... Find all the fixed points and cycles for the happy number sequences in base 8.
Soma - So Good
Stage:3 Challenge Level:
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
Route to Root
Stage:4 Challenge Level:
A sequence of numbers x1, x2, x3, ... starts with x1 = 2, and, if you know any term xn, you can find the next term xn+1 using the formula: xn+1 = (xn + 3/xn)/2 . Calculate the first six terms of. . . .
First Forward Into Logo 10
Stage:3, 4 and 5 Challenge Level:
What happens when a procedure calls itself?
Major Trapezium
Stage:4 Challenge Level:
A small circle in a square in a big circle in a trapezium. Using the measurements and clue given, find the area of the trapezium.
Napkin
Stage:4 Challenge Level:
A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .
Cushion Ball
Stage:4 and 5 Challenge Level:
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
Pentagon from 1926
Stage:4 and 5 Challenge Level:
Find the vertices of a pentagon given the midpoints of its sides.
Triple Decker Sandwich
Stage:4 and 5 Challenge Level:
There are 150 8-sandwiches like 6 1 5 1 8 4 7 6 5 2 4 3 2 8 7 3 with 1 number between the 1's, 2 between the 2's etc. Can you find sandwiches where each digit occurs three times rather than twice?
