**"Length"**

## Square Fence

*By toni On 23 March, 2013 · 7 Comments*

A fence is built around a square field.

Suppose another fence is built exactly one metre longer so the path between the two fences is the same width along the edges of the field. How wide would this path be?

Would a mouse be able to run along it?

Could a farmer drive […]

## Not-So-Square Fence

*By toni On 22 March, 2013 · 5 Comments*

A fence is built around a square field.

Suppose another fence is built exactly one metre longer so the path between the two fences is the same width all the way round including at the corners of the field.

How wide would this path be?

Would a mouse be able to run along it? […]

## Belt Around The Earth

*By AA On 22 March, 2013 · 2 Comments*

A wire belt is tied tightly around the Earth at the equator. Suppose the belt is made exactly one metre longer and held around the Earth at the equator so that it is the same distance away from the Earth everywhere. Would a mouse be able to crawl under the new belt? How do […]

Draw chords to cut a regular hexagon

(a) into two pieces which, when put together, make a parallelogram;

(b) into three pieces which, when put together, make a rhombus;

(c) into four pieces which, when put together, make two equilateral triangles.

(d) What angles can you find in each of your shapes?

(e) If […]

## Seven Squares

*By toni On 5 January, 2013 · 3 Comments*

Seven squares are drawn inside each other. The centre points of each side of the outer square are joined to make a smaller square inside it and so on.

The centre square has the area of 1 (one) square unit.

Draw the diagram. You can download square dotty paper here.

What is […]

## Years 9 – 10 Tet Trouble

*By toni On 18 January, 2012 · Leave a Comment*

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units.

Is it possible for a tetrahedron to have edges of lengths 10, 20, 25, 45, 50 and 60 units?

Can you write general rules for someone else to use to check whether […]

## Roundabout

*By toni On 18 January, 2012 · Leave a Comment*

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square.

Describe the path (or locus) of the centre of the circle and its length.

Try this on the NRICH interactivity.

## Years 9 to 13 – There and Back Again

*By toni On 18 January, 2012 · Leave a Comment*

Bilbo decides to leave his hobbit-hole and go on an adventure. He walks 100 km South, then 100 km East, then finally 100 km North, at which point he is surprised to find that he has arrived back home!

Many people would think that because of this Bilbo must live at the North Pole. […]

## Little Man

*By toni On 18 January, 2012 · Leave a Comment*

Little Man is much smaller than you and me. Here is a picture of him standing next to an ordinary mug.

Can you estimate how tall he is? How tall do you think Little Man’s mug might be?

My mug is 10 centimetres tall and it holds 300 millilitres but mugs come in different […]

## Wedge on Wedge

*By toni On 17 January, 2012 · Leave a Comment*

Two right-angled triangles are joined as shown in the diagram.

The green triangle has side lengths of 65, 52 and 39 cm and the blue triangle has side lengths of 52, 48 and 20 cm.

An object is dropped vertically from the top of the green triangle hitting the base by […]

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