This lesson is split into two parts showing students how to solve one-step equations by using either multiplication or division.
Prior Knowledge: Once students have learned how to write equations, translate sentences into equations, translate equations into sentences and solve one-step equations using addition and subtraction, they are now ready to move onto solving simple equations using multiplication or division.
Common Core State Standards
A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Mathematical Practice(s): 6. Attend to precision
- I can apply order of operations and inverse operations to solve equations
- I can construct an argument to justify my solution process
In what ways can the problem be solved and why should one method be chosen over another?
Vocabulary: inverse operation, isolate, variable, constant, reciprocal, coefficient
LESSON - Solve by Multiplying
- Instruct that minus and negative are equivalent
GOAL-to isolated the specified variable
- Instruct that what is done on one side of the equation (= sign), must be done on the other side of the = sign.
I a. Problem: 2/3x = 5
Step 1: Identify the variable we are solving for: (x)
Step 2: To isolate that variable, you must multiply both sides by the reciprocal of 2/3, which is 3/2.
(3/2) (2/3)x = 5 (3/2)
Step 3: Multiply and simplify if necessary
1x = 5/1 * 3/2
x = 15/2
Note: You may leave the answer as an improper fraction or you can change it to a mixed number.
I b. Problem: 2/3x = 5 (Another option to solving this problem, especially for students who have difficulty with fractions). This combines multiplication and division.
Step 1: Same as above
Step 2: Multiply both sides by the denominator, this leaves you with just the numerator.
(3) 2/3x = 5 (3)
Step 3: Multiply: 2x = 15
Step 4: Divide both sides by the coefficient (2)
2x/2 = 15/2
Step 5: Simplify: x = 15/2
LESSON - Solve by Dividing
Problem: 6j = 24
Step 1: Identify the variable we are solving for: (j)
Step 2: Divide both sides by the coefficient (6)
6j/6 = 24/6
Step 3: Simplify: j = 4
* Reminder for students: that –x is the same as -1x & x is the same as 1x.
Guided Practice: 3-6 practice problems. You can do 1or 2 problems with the students at the board (Smart Board, Elmo, etc.) and then put them in small groups of no more than 3 to do the rest. These problems can be pulled from any textbook or other resource.
Independent Practice: Solving Equations BINGO. You can use problems from any textbook or resource. You can also use some problems from kutasoftware.com. They have worksheets with the answer key.
On the board or Smart Board, write the answers to the problems. Put some common mistake answers on the board also. Have the students place their answers anywhere on their Bingo board. You can have the students create their own Bingo board or you can use the template provided here.
Critical Thinking Problem: Have a discussion with the students about how they think they should solve this problem. Let them know that they have learned enough information to solve the problem but you have not given them the step by step process to solve it. Can they make a connection using prior knowledge to solve the problem?
Problem: - 3/8 k = 2/3 (This problem has fractions on both sides of the equation). Answer: -16/9
Closure/Review: Ask 1-3 questions relating to today’s lesson to be answered by the class as a whole. This will give you a general idea of the class’ understanding of today’s topic.
Exit Ticket: This is to be done the last 3-5 minutes of class and given to you (by hand or in a designated area of your room) as they leave class. Possible questions:
- Demonstrate the two ways of solving this problem: 3/4x = 3. 2) Solve: -5x = - 75 & -3x = 27