Areas Investigation

Investigate polygons with an area of 4 sq. units.

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

Investigate polygons with other areas.

Suggested

How Many Squares? 2

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

Related

Areas of Composite Shapes

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

Similar Activity

Polygon Hunting

Polygon Hunting

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

The short web address is:

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.

Area 10

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?"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

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.

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