Areas Investigation

Investigate polygons with an area of 4 sq. units.

Paint
Paint
Paint
Paint
Paint
Paint
Undo Clear
Camera

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

Teacher notes for this and solutions to other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

A Transum subscription also gives you access to the 'Class Admin' student management system, downloadable worksheets, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

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.

Here are some other activities you may be interested in:

Featured Activity

ChristMaths

ChristMaths

Christmas activities make those December Maths lessons interesting, exciting and relevant. If students have access to computers there are some online activities to keep them engaged such as Christmas Ornaments and Christmas Light Up.

Suggested

Remainder Race

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.

The short web address is:

Transum.org/go/?to=remainder

Recently Updated

Xmas Light Sum

Xmas Light Sum

Arrange the coloured lights to create a balanced pattern where the total of each colour matches the target numbers. So far this activity has been accessed 3766 times and 218 Transum Trophies have been awarded for completing it.

Transum.org is a proud supporter of the kidSAFE Seal Program