# Construction - September 2005, All Stages

## Problems

### Chairs and Tables

##### Stage: 1 Challenge Level:

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

### Mrs Trimmer's String

##### Stage: 1 Challenge Level:

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

### Complete the Square

##### Stage: 1 Challenge Level:

Complete the squares - but be warned some are trickier than they look!

### Dotty Relationship

##### Stage: 2 Challenge Level:

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

##### Stage: 2 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

### Yin Yang

##### Stage: 2 Challenge Level:

Can you reproduce the Yin Yang symbol using a pair of compasses?

##### Stage: 3 Challenge Level:

Can you mark 4 points on a flat surface so that there are only two different distances between them?

### Property Chart

##### Stage: 3 Challenge Level:

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

### Shapely Pairs

##### Stage: 3 Challenge Level:

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

### Three Tears

##### Stage: 4 Challenge Level:

Construct this design using only compasses

### Triangle in a Triangle

##### Stage: 4 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the inner triangle?

### Half a Triangle

##### Stage: 4 Challenge Level:

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

### Trig Rules OK

##### Stage: 5 Challenge Level:

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

### Pentabuild

##### Stage: 5 Challenge Level:

Explain how to construct a regular pentagon accurately using a straight edge and compass.

### Vecten

##### Stage: 5 Challenge Level:

Join in this ongoing research. Build squares on the sides of a triangle, join the outer vertices forming hexagons, build further rings of squares and quadrilaterals, investigate.