# 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?

### The Clue Is in the Question

##### Stage: 5 Challenge Level:

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:

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:

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:

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.

### Supercomputer

##### Stage: 4 Short Challenge Level:

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

### Little Difference

##### Stage: 4 Short Challenge Level:

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