Reflection: Checks for Understanding Variables on both sides?... No Problem - Section 2: New Info

Students will always do the following when subtracting a quantity from both sides of an equation. (similarly when performing any other operation on both sides)

3x + 6 = -5x - 12                                                                                                                                                                                 -3x          -3x

In this case the student subtracted 3x from both sides, but notice that the student placed the expression being subtracted directly under the 3x and the 5x. This is fine. But does the student understand that he/she is subtracting 3x from the entire left side and the entire right side?

I find too many students do this disconnected from the the concepts of equivalence and combination of like terms. . Each time I see this I suspect the latter. I ask questions like "why not place the -3x under the 6 and the 12?" The student should respond that it doesn't matter because one will end up combining like terms anyhow. Too many times I find that students become confused with this question. I then make them see that they are actually subtracting from the entire side and asking them to simplify 3x + 6 - 3x, so that can see that the result on the left side is 6.

This misconception is clearly visible when students decide to divide by a value on both sides and do as follows:   given 12x  = 30 - 3x

﻿12x = 30 - 3x                                                                                                                                                   3               3

Subtracting from both sides. Search for the misconception.
Checks for Understanding: Subtracting from both sides. Search for the misconception.

Variables on both sides?... No Problem

Unit 2: Solving Linear Equations
Lesson 6 of 10

Big Idea: Equations may look difficult, but once students see and know what to do, they become confident, and actually enjoy solving these.

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Standards:
Subject(s):
Math, solving equations, Algebra, Linear and Nonlinear Equations, two step equations, variables on both sides
60 minutes

Mauricio Beltre

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