1. Equations and Mental Math
Standard: AF 1.1 Write and solve one-step linear equations in one variable.
Objective: Students will use mental math to write and solve one-step linear equations in one variable by performing inverse operations, identifying missing quantities, using graphic organizers, writing reflective summaries, and scoring an 80% proficiency on exit slip quizzes and online assessments.

2. Key Words
Expression
Equation
Variable
Inverse Operations

3. Tell whether the number is a solution of . n + 5 = 14
Example 1
Checking Possible Solutions
Tell whether the number is a solution of n + 5 = 14
a. 9
SOLUTION
Write equation. n + 5 = 14 a.
Substitute 9 for n. 9 + 5 14 = ? 14 =
14 = 14, so 9 is a solution.

4. Tell whether the number is a solution of . n + 5 = 14
Example 1
Checking Possible Solutions
Tell whether the number is a solution of n + 5 = 14
b. 7
SOLUTION
Write equation. n 5 = 14 b. +
Substitute 7 for n. 7 5 14 + = ? 12 = 14
12 = 14, so 7 is a not a solution.

5. The difference of twice a number and 3 equals 4. – 2y – 3 = 4
Example 2
Translating Verbal Sentences
Verbal sentence
Equation a.
The difference of twice a number
and 3 equals 4. – 2y – 3 = 4
The product of 9 and a number
is 36. b. 9y = 36
–3 is equal to twice the sum of
a number and 2. c. –3 = ( ) 2 + y

6. Nine plus what number equals 12? 3 9 + = 12
Example 3
Using Mental Math to Solve Equations
Equation
Question
Solution
Check a. 9 + x = 12
Nine plus what number equals 12? 3 9 + = 12
What number minus 5 equals 10? b. n – 5 = 10 15 – 5 = 10
Four times
what number equals 20? c. 4t = 20 5
4(5) = 20

7. What number divided by 3 equals 12? 3
Example 3
Using Mental Math to Solve Equations
Equation
Question
Solution
Check m 36 = 12 3 d. = 12
What number divided by 3 equals 12? 3

8. Tell whether the number is a solution of the equation.
Guided Practice
for Examples 1, 2, and 3
Tell whether the number is a solution of the equation. 1. 3x =
12; 4
ANSWER
solution 7 = 13 2. – n; 5
ANSWER
not a solution 3. y 6 = 3; 2
ANSWER
solution
Write as an equation: The difference of 5 and twice a number is 17. 4.
ANSWER 5 – 2n = 17

9. Solve the equation using mental math.
Guided Practice
for Examples 1, 2, and 3
Solve the equation using mental math. 7x = 35 5.
ANSWER 5 15 = m 6. – 6
ANSWER 21 12 + a 7. = 32
ANSWER 20 8. n 24 = 6
ANSWER 4