Fundamentals of Area

Area is a topic where students are likely to have remembered a process (you multiply the lengths to get the area) but may not have a secure understanding of what area actually is.  It is worth spending time discussing what we mean by area.  I would prefer my students memorise “Area is the amount of space inside a 2D shape” rather that “Area is length times width”.

Counting the Squares is a good place to start even with students who feel like they know how to calculate area.   The concept of 1cm² as a quantity, an amount of something that bigger shapes have more of is powerful.  Estimation can be useful.  Physical pieces of 1cm² card and a series of rectangles, some with grids, some without is worth doing.

Reinforcing units is important.  Reminding students of the commutative law and rewriting 2cm x 3cm as 2 x 3 x cm x cm can help explain why we write cm² and link it back to algebra.  You could even play with 3cm x 2m.  Does make sense to say that this area would be 6 cmm?

A key step in the process is moving from:

Screen Shot 2016-07-14 at 09.57.31.png…without losing sight of the underlying concept that the rectangle is made up of 12 little squares, each one 1cm².

Moving on to rectilinear shapes, I like this question as a way of challenging thinking.

Screen Shot 2016-07-14 at 09.04.55.png

 

The first misconception here would be multiplying 3 x 4 to get 12.  But of course the correct answer is “we don’t have enough information”, an answer which shows depth of understanding and one which I would like my students to be presented with more often.

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