Posing Questions and Making Conjectures - Upper Secondary

White Box

Stage: 2, 3, 4 and 5 Challenge Level:

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

Odds and Evens

Stage: 3 and 4 Challenge Level:

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Interactive Spinners

Stage: 3 and 4 Challenge Level:

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Pair Products

Stage: 4 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Difference Dynamics

Stage: 4 and 5 Challenge Level:

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Painting by Numbers

Stage: 5 Challenge Level:

How many different colours of paint would be needed to paint these pictures by numbers?

Impossible Triangles?

Stage: 5 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?