Posing Questions and Making Conjectures - Upper Secondary

White Box

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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

Pair Products

Stage: 4 Challenge Level: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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

Impossible Triangles?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Which of these triangular jigsaws are impossible to finish?

The Clue Is in the Question

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Producing an Integer

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Eulerian

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 37 - 2014
Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Leaning Over

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?

Posing Questions and Making Conjectures - Short Problems

Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.

Posing Questions and Making Conjectures - Short Problems

Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Posing Questions and Making Conjectures.

Supercomputer

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 28 - 2014
What is the units digit of the given expression?

Little Difference

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 30 - 2014
What is the value of $2006 \times 2008 - 2007 \times 2007$?