Breaking a large rectangle into two (and the distributive property)

While I feel that most of the Common Core math standards are fairly good, here's one place where I disagree with them (3.MD.7.c).

It has to do with the topic when a larger rectangle is broken into TWO parts, and then children write a math sentence from it such as (3 × 4) + (3 × 2).

This is in 3rd grade in the CCS. I feel it is a bit too difficult for that level, and would better fit 4th or even 5th grade.

Someone just wrote me recently concerning this topic, wondering WHY do we do all this in the first place. Here's my answer.


The reason for breaking the rectangle into two is to get students familiar with this:

7 × (2 + 8) = 7 × 2 + 7 × 8

which is (essentially) the distributive property.

The idea is to familiarize the students with how multiplication works with addition, and we use an AREA MODEL to show or prove that.

I decided to edit a video for this topic to help the person who asked...



The video just explains HOW we do the rectangle thing, not why. The why is what I just stated above. The distributive property is then studied further in 6th and 7th grades and in algebra.

For those grades, you can check out these videos... maybe they will give you a "sneak peek" as to what the 3rd grade stuff is preparing students for:

https://www.youtube.com/watch?v=3bTKLuUvIoY
https://www.youtube.com/watch?v=6TSs2jRLHPI
https://www.youtube.com/watch?v=hzXfan5T0MQ
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