Solving Linear Equations
Algebra – Grade 9
Objective: Students will be able to solve linear equations and explain their thinking
processes orally and in writing. They will solve problems orally during the think-pairshare activity and turn in written work from that activity.
Introduce Vocab: (give examples/non-examples with each)
Integer: a number that when written in decimal form has only 0’s after the decimal place
Number Line: a scaled horizontal diagram of numbers, usually integers
Operation: an action done in a math problem, ex. add, subtract, multiply, divide
Order of Operations/PEMDAS: list telling which operations get performed first
Evaluate: calculating an expression with only known constants (no variables involved)
Solve: to determine what constant a variable represents in a specific problem
Term: a mathematical unit; terms are separated by + and – signs.
Coefficient: the constant associated with a term containing a variable
Review the Number Line (anticipatory set):
Write an incomplete number line on the board and have students raise their hands to give
answers to ?’s. Also have students raise their hands to answer: How did I move from 0 to
1? From 5 to 4? What happens when I move left/right on the number line?
Write another number line with some blank hatch marks. Again have students raise their
hands to fill in ?’s. Finally, have someone com up to the board to fill in the __. If
students have trouble after answering the above questions, fill in z-2 spot. Point out that
constants are always written under the hatch marks. While the variables don’t have to b
written above the hatch marks, they should be to make things easier.
Introduce Order of Operations/PEMDAS:
Write the letters P E MD AS vertically on the board. Ask class as a whole to say what
each letter stands for (they should remember from vocab). Explain that parentheses are
the most powerful, exponents are less powerful etc. Have you ever heard people talk
about attacking a problem? Well, how do you attack a math problem? With PEMDAS!
When you solve a linear equation, you need to get the variable alone on one side of the
equation; you need to break the other numbers away from it. (Your final answer should
look like x = # or z = #, etc.) To do this, you have to build up your strength by attacking
the weaker operations first. (When evaluating an equation, the opposite happens: the
stronger operations will be performed first.) When you are separating a variable from
other numbers, “attacking” an operation means performing the opposite operation to both
sides of the equation.
Ex.
Note: The “=” means those expressions represent the same
number on the number line.
According to PEMDAS, which operation is weakest, which one do we attack first?
(addition) How? (subtraction) With what number? (7). So when we subtract 7 from the
LHS, what will we get? (3x) Mark 3x on the number line. What does the ? have to be?
This is why we have to perform the same operation to both sides of the equation: the LHS
and the RHS move together—the “=” at each step means that the two sides of the
equation are the same number on the number line.
Remember, our overall goal is to get the variable alone by attacking the numbers on its
half of the equation one by one. What can we attack next? How?
Do another example: 5x – 8 = 82.
Checking Your Work:
Plug your solution for the variable into the original equation. Now you are evaluating the
problem, so the strongest operations are performed first.
Ask for questions—if none, ask students to come up with a question a student who didn’t
get all the notes might ask.
Think-Pair-Share:
Give students four problems of the form mx + b = c to solve individually (y/2 + 9 = 12,
4x +10 = 90, 2z/4 = 3, w/6 = 6). Have students solve and check two problems on the top
half of their papers with written explanations. They should solve and check two
problems on the bottom half without explanations. After a few minutes students switch
bottom halves and write in explanations on other people’s papers. After a few more
minutes they get together and see if their explanations agree. The top halves of their
papers will be collected.
Homework: For this assignment use the number line method with short explanation for
all problems even if you no longer feel it’s necessary. If you are stuck on a problem
instead of writing an explanation ask a SPECIFIC question. “Asking a question on a
problem you get wrong will get you more partial credit.” Also give students a more
difficult question that will not be graded but also ask them to use the number line method
and either give an explanation or a specific question: 2x – 7 = 7x + 3.
Modifications:
If some students are behind because of special needs or because they’re new, be available
for questions during the “think” activity. For students that are ahead: make sure they end
up in groups with students that may need to “conference” when they break into groups.
Also consider putting in a more challenging question for them to work on during the
individual thinking time.