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Secondary processes > PM - Posing Questions. Making Conjectures

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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

##### Age 11 to 14 Challenge 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.

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 11 to 14 Challenge Level:

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

##### Age 14 to 18 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?

##### Age 16 to 18 Challenge Level:

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

##### Age 7 to 18 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.

##### Age 16 to 18 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. . . .

##### Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish?