Visualising and representing

problem
Terminology

Age

14 to 16

Challenge level

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
problem
Rati-o

Age

11 to 14

Challenge level

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
problem
Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
problem
Hidden rectangles

Age

11 to 14

Challenge level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
problem
Counting cards

Age

7 to 11

Challenge level

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
problem
Threesomes

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem
Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?
problem
Diagrams

Age

7 to 11

Challenge level

A group activity using visualisation of squares and triangles.
problem
Remainders

Age

7 to 14

Challenge level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
problem
LOGO challenge - triangles-squares-stars

Age

11 to 16

Challenge level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.