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We have been getting some questions concerning the Common Core progression of performing operations with algebraic expressions. It appears that the addition of monomials and the multiplication of monomials by an integer starts in 6th grade, with problems similar to 10a+3a=13a and 5(6x)=30x. The distributive property leads into factoring expressions (generating equivalent expressions) similar to 4x+12. In 7th grade, it looks like this continues with rational coefficients. There is also some subtraction of binomials, problems like (5x+8)-(2x-9). Whole number exponents are introduced in grade 6, and work with exponents (laws of exponents) is in grade 8. Should students be encountering problems that look like (8×2)(4×5) (8 times x squared)(4 times x to the fifth).
People are questioning the depth or how far to take these algebraic expressions in 8th grade. What about the multiplication of two binomials ? I was just curious as to your thoughts about how the transition from 6th to the beginning of 9th should go with these algebraic expressions. Thank you for your time and I look forward to your response.I’ve wondered how far we will go with this as well. It takes a lot of practice to be able to reduce fractions in the form of (((3xy^-4z^5)^-3(4y^-2z^-3))/((7x^-2)^3)(y^6)^-7) and it is a challenge to answer the question, “When will we ever…”
Polynomials as a topic in their own right are not introduced until high school, and there the emphasis is on seeing them as a system (like the integers) of “numbers” that can be added, subtracted, and multiplied. Introducing monomials earlier and separately doesn’t fit well with this approach. In fact, I don’t see a good reason for introducing them at all, except possibly as a piece of terminology. And even there I’m not sure; you can talk about the monomials in a polynomial as terms in a sum. Certainly problems like the one Lane suggested are beyond the scope of Grade 8, and I would say that even the simpler multiplication of degree two monomials suggested by sbrockley is straying off track.
The focus of algebra in Grades 6–8 is linear expressions, equations and functions. The laws of exponents are limited to numerical expressions (8.EE.1).
To clarify, I’m wondering if, even at the high school level, we need to be reducing expressions like that.
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