Doodles Do Algebra – Lesson 68

Update: This Lesson Is Part of Book 3 of Doodles Do Algebra: “The Basic Math of Algebra” available on Amazon.

Worksheet:

Available in the book, “The Basic Math of Algebra, Book 3 of Doodles Do Algebra“

Today’s lesson is yet more practice dividing monomials but the last two questions ask your child to divide polynomials. The key is for him to recognize the similarity between $a^2/a$ and $(x+y)^2/(x+y)$. These are they same type of problem, only in the first one the thing you are dividing is a single term, a, and in the second problem you are dividing a polynomial (x+y). You can write the division out for him (x+y)*(x+y)/(x+y) and show him that (x+y)/(x+y)=1 just like a/a=1 and 2/2=1 and when you say it you say, “how often is (x+y) contained in (x+y)? Once, so (x+y) divided by (x+y) equals 1” This is really all a matter of abstracting the concepts so the type of math you did when all you had were numbers is the same as the math you use with letters or combinations of added and subtracted and multiplied and fractionated letters. All along through this math series I try to write explanations in plain English, as best as I can instead of the terminology of the mathematician. The best math teacher I ever had was a Russian who told us he helped design the math behind the Chernyobl reactor before he defected to the US – he used to stand on his chair and point around the room to describe partial differential equations and the technique was so absolutely effective that I still hear him talking and see him jumping and pointing in my head when I do that sort of math. The basic key, I think, is to reach a child’s base of understanding of the concept. It does not matter if he uses the right terminology at the start and fundamentally it does not matter if his explanation would make sense to a mathematician – your child is a child, and often with homeschoolers, he is a young child exploring an advanced math. The first hurdle is deep understanding and then terminology can come later.

1. $5a^2x3y^4$
2. $3c^4x^2c^4v^4$
3. $-2c^2x^2v^3$
4. $-15c^4e^3y^2$
5. $(x+y)$
6. $(a+b)$