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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Posing Questions and Making Conjectures

### Magic Letters

### Summing Consecutive Numbers

### Spaces for Exploration

### How Much Can We Spend?

### Interactive Spinners

### Tilted Squares

### What Numbers Can We Make?

### Can They Be Equal?

### Where Can We Visit?

### Consecutive Negative Numbers

### Posing Questions and Making Conjectures - Short Problems

### Charlie's Delightful Machine

### Arithmagons

### Cuboid Challenge

### Searching for Mean(ing)

### A Little Light Thinking

### Pair Products

### Pick's Theorem

### Multiplication Arithmagons

### Impossible Triangles?

## Related Collections

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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

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?

Age 11 to 14

Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

Age 11 to 14

Challenge Level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

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

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

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 11 to 14

Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 11 to 14

Challenge Level

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Age 11 to 14

Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Age 11 to 16

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

Age 11 to 16

Challenge Level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Age 11 to 16

Challenge Level

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 16

Challenge Level

What's the largest volume of box you can make from a square of paper?

Age 11 to 16

Challenge Level

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Age 14 to 16

Challenge Level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

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 14 to 16

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 14 to 16

Challenge Level

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Age 16 to 18

Challenge Level

Which of these triangular jigsaws are impossible to finish?