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:
…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.
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.
