Posing Questions and Making Conjectures

Posing Questions and Making Conjectures is part of our Working Mathematically collection.

Magic Letters

Age 11 to 14Challenge Level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Interactive Spinners

Age 11 to 14Challenge Level

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

Summing Consecutive Numbers

Age 11 to 14Challenge Level

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Tilted Squares

Age 11 to 14Challenge Level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Odds and Evens

Age 11 to 14Challenge Level

Are these games fair? How can you tell?

What Numbers Can We Make?

Age 11 to 14Challenge Level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Posing Questions and Making Conjectures - Short Problems

Age 11 to 16

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

Pair Products

Age 14 to 16Challenge Level

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

Pick's Theorem

Age 14 to 16Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Difference Dynamics

Age 14 to 18Challenge 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

Age 16 to 18Challenge Level

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

The Clue Is in the Question

Age 16 to 18Challenge Level

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Impossible Triangles?

Age 16 to 18Challenge Level

Which of these triangular jigsaws are impossible to finish?