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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.
Key Words
• Expression
• Equation
• Variable
• Inverse Operations
Example 1
Checking Possible Solutions
Tell whether the number is a solution of n + 5 = 14.
a. 9
SOLUTION
a. n + 5 = 14
9 + 5 =? 14
14 = 14
Write equation.
Substitute 9 for n.
14 = 14, so 9 is a solution.
Example 1
Checking Possible Solutions
Tell whether the number is a solution of n + 5 = 14.
b. 7
SOLUTION
b. n + 5 = 14
7 + 5 =? 14
12 = 14
Write equation.
Substitute 7 for n.
12 = 14, so 7 is a not a solution.
Example 2
Translating Verbal Sentences
Verbal sentence
Equation
a. The difference of twice a number
and 3 equals – 4.
2y – 3 = – 4
b. The product of 9 and a number
is 36.
9y = 36
c. –3 is equal to twice the sum of
a number and 2.
–3 = 2( y + 2 )
Example 3
Using Mental Math to Solve Equations
Equation
Question
Solution
Check
a. 9 + x = 12
Nine plus what
number equals
12?
3
9 + 3 = 12
b. n – 5 = 10
What number
minus 5 equals
10?
15
15 – 5 = 10
c. 4t = 20
Four times
what number
equals 20?
5
4(5) = 20
Example 3
Equation
m
= 12
d.
3
Using Mental Math to Solve Equations
Question
Solution
What number
divided by 3
equals 12?
36
Check
36
= 12
3
Guided Practice
for Examples 1, 2, and 3
Tell whether the number is a solution of the equation.
1. 3x = 12; 4
ANSWER
solution
2. 7 = 13 – n; 5
ANSWER
not a solution
6
3.
= 3; 2
y
ANSWER
solution
4. Write as an equation: The difference of 5 and
twice a number is 17.
ANSWER
5 – 2n = 17
Guided Practice
for Examples 1, 2, and 3
Solve the equation using mental math.
5. 7x = 35
ANSWER
5
6. 15 = m – 6
ANSWER
21
7. 12 + a = 32
ANSWER
20
24
8.
= 6
n
ANSWER
4