Doing a poor job with basic measurement concepts.

Then the book has no chance of doing a proper job with area, or with anything else that relies on multiplication.

Doing a poor job establishing what m Г— n means altogether.

Some drawbacks I have seen in the way some math textbooks teach A = L Г— W: This is what is meant by вЂњArea equals length times width.вЂќ The number of unit squares needed to tile a rectangle equals the number of length units that fit along one side multiplied by the number of length units that fit along an adjacent side. This argument is pretty obviously sound for any rectangle whatsoever with whole-number side lengths, so we can say that for any such rectangle: Remembering what Г— means, the total number of squares must then equal 7 Г— 5. For example, the 7 strips would turn into 7 groups of 5 squares each. If we draw both sets of lines, then each of the strips gets divided into squares (question: why perfect squares?). We might have done the same thing on either of the two adjacent sides, which would have resulted in the number of strips being 5. There are as many strips in the rectangle as there are length units in the side. If one side of the rectangle consists of 7 length units, then we can draw lines to divide the rectangle equally into 7 strips. In the context of a rectangle with, say, length 7 units and width 5 units, what are the groups, and what are the things? Today letвЂ™s confine our analysis of the formula to whole numbers, because IвЂ™m thinking about the formula today from the perspective of a young student who hasnвЂ™t yet absorbed fractional quantities or fraction operations.В For whole numbers, the simple interpretation of m Г— n is that it stands for the number of things in m groups of n things each.

The reason the formula works has to do with what the Г— symbol means.

W is the number of length units when you measure an adjacent side of the rectangle.

L is the number of length units when you measure one side of the rectangle.

A is the number of unit squares needed to tile the rectangle.

Has a student ever asked you why multiplying length by width gives the area of a rectangle? In this blog post, Standards co-author Jason Zimba describes the area formula on a conceptual level and highlights some weaknesses in the ways textbooks introduce the formula. EditorвЂ™s Note: This blog post originally appeared on Jason ZimbaвЂ™s personal blog on August 10, 2016.

Area formula for rectangle