# 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.

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.

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

#### Polygon Hunting

Find all the polygons that can be drawn by joining dots on this seven dot grid.

www.transum.org/go/?num=1011

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Investigations Home

Transum,

Tuesday, March 3, 2015

"The Areas Investigation grid above could be used to play a game. Two players take it in turns to draw a shape with an area of four. If a player is unable to think of a shape that hasn't been drawn before, then the other player wins. No reflections or rotations of shapes already drawn are allowed."

Will Emeny,

Thursday, September 8, 2016

"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?"

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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.

## Here are some other activities you may be interested in:

#### Hi-Low Predict

A version of the Play Your Cards Right TV programme. Calculate the probabilities of cards being higher or lower than the one shown. a fun way to practise applying probability and using fractions.

#### Remainder Race

A game involving chance and choice requiring an ability to calculate the remainder when a two digit number is divided by a single digit number.

Transum.org/go/?to=remainder

#### Fraction Foundations

Recognise simple fractions (halves, quarters and tenths) of whole numbers and shapes. So far this activity has been accessed 209 times and 37 Transum Trophies have been awarded for completing it.

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