# Areas Investigation

## Investigate polygons with an area of 4 sq. units.

Use printable square spotty paper and a pencil for an alternative method of constructing the polygons.

## Investigate polygons with other areas.

#### How Many Squares? 2

A printable grid containing many copies of the design used in the second shape counting Starter.

The short web address is:

www.transum.org/go/?to=manysquares2

#### Areas of Composite Shapes

Find the areas of combined (composite) shapes made up of one or more simple polygons and circles.

The short web address is:

www.transum.org/go/?to=areacomposite

#### Formulae Pairs

Find the matching pairs of diagrams and formulae for area, perimeter and volume of basic shapes.

The short web address is:

www.transum.org/go/?to=formulaepairs

Investigations Home

"The following puzzle comes from the excellent Mr Barton's podcasts and was suggested by Will Emeny.

These two rectangles have an area of 10 square units.

In total, there are five different rectangles with vertices on grid points that have an area of 10 square units. Draw all five.

Prove there can be no more than five.

Draw all the rectangles that have an area of 12 square units. How do you know you've got them all?"

Transum,
Thursday, September 8, 2016

Do you have any starting points for mathematical investigations or comments about the investigations we have presented here?

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.

For Students:

For All: