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Multiplying Monomials and Binomials

Why would $2m \times m^{2} = 3m^{2}$? Or $2m^{2}$?

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3 replies on “Multiplying Monomials and Binomials”

Oh, they’re so close! The student saw that 2m^2 was wrong but changed the wrong 2. Maybe they need m^2 = m*m reinforced. They can then think about 2*m*m*m.

mr bombasticsays:

I agree with Max that they need the definition of an exponent reinforced. But, they also need a better understanding of addition.

This student probably looks at 2A + A and thinks “combine like terms” to get 3A. But, they likely do not understand why 2A + A is 3A. They probably don’t know what a “term” is either, or why they need to be alike. As a result they are combining the 2m & m to get 3m. The exponent stays put because … they probably need a better understanding of order of operations as well.

As an aside, I wish the phrase “combine like terms” would go away.

I would suggest we write the terms out as 2m and mm, then we could put 2mmm in the box. We could do that in each box, and then write the result in a different color.
I don’t say “combine like terms,” as my students don’t understand it. I say “put things together if they have the same letters and exponents.” Back to apples and bananas.
We’re working hard on eliminating “crossmultiply” (I tell the kids it’s too much work), so I’ll work on eliminating CLT too. Thanks Mr. B.