This post is continued from first part.
I remind students that it could be stated as 6y=36—it doesn’t matter.
More examples follow with my help diminishing after about the second, so they are working independently. They should do their work in their notebooks. I walk around the room to see what they’re doing, offering help and guidance when needed and answering questions.
Examples:
This last may be confusing because of a zero on the left hand side. Remind them zero is a number, and to solve it as they have problems with non-zero numbers.
Mixing up examples with simpler equations is important, so I include a few:
For the last in the example, I show how to check if the answer is correct without looking up the answer in the back of the book:
Checking the answer is done by substituting 3 for c in the original equation:
Common Mistake. One mistake I’ve seen often is that students will forget that in an equation like 6y = 36, one divides both sides by 6. I’ve seen students subtract 6 from both sides in the belief that 6y – 6 = y. Students need to be reminded that this is not true. If we have 5 × 3 – 5 , the answer is not 3, but 10. The term 6y signifies that 6 is being multiplied by y. To undo multiplication, we divide.
Homework. The homework should be a mix of simple equations where there are variables on both sides, but a number on only one side, and more complex equations with both numbers and variable terms on both sides. Problems with fractions and fractional coefficients (like (2/3)x) will be addressed in the next lesson. Including it in this lesson is too much information; I know, I’ve done it.