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### Number and algebra

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### Working mathematically

### For younger learners

### Advanced mathematics

# Construction - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction.

Printable worksheets containing selections of these problems are available here.
### Folded A4

### Defined Distances

### Contact Circles

### Snail's Pace

### Triangular Wheel

### 3-sided

### Either Side

### Pink and White

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### Seven Squares - Group-worthy Task

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This is part of our collection of Short Problems.

You may also be interested in our longer problems on Construction.

Printable worksheets containing selections of these problems are available here.

Age 11 to 14

ShortChallenge Level

What shapes can be made by folding an A4 sheet of paper only once?

Age 11 to 14

ShortChallenge Level

Mark writes four points on a line at different lengths. What is the distance between the two points furthest apart?

Age 14 to 16

ShortChallenge Level

These four touching circles have another circle hiding amongst them...

Age 14 to 16

ShortChallenge Level

A snail is at the corner of a cube. What proportion of the cube's surface can the snail reach within an hour?

Age 14 to 16

ShortChallenge Level

An equilateral triangle is rolled along a line. What is the length of the path traced out by one of its vertices?

Age 14 to 16

ShortChallenge Level

How many triangles can Jack draw with two sides of lengths $6$cm and $8$cm and an area of $7$cm$^2$?

Age 14 to 16

ShortChallenge Level

A disc with a pencil inside it is rolled around the outside and inside of a wire equilateral triangle. What shape is drawn by the pencil?

Age 14 to 16

ShortChallenge Level

The white square slides once around the pink square. Through what distance does the point P on the white square move?

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?