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.
SuggestedHow Many Squares? 2
A printable grid containing many copies of the design used in the second
shape counting Starter. |
RelatedAreas of Composite Shapes
Find the areas of combined (composite) shapes made up of one or more simple
polygons and circles. |
Similar ActivityPolygon Hunting
Find all the polygons that can be drawn by joining dots on this seven dot grid. |
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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.
Featured ActivityRiver Crossing Three interactive versions of the traditional river crossing puzzles. The objective is to get all of the characters to the other side of the river without breaking any of the rules. |
SuggestedRemainder 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. |
Recently UpdatedShape Sorter Drag each shape into the correct bin according to their types and symmetries. So far this activity has been accessed 210 times and 99 Transum Trophies have been awarded for completing it. |
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?"