Transcript x - Hood River County School District

Lesson 3.2
Core Focus on
Introductory Algebra
Solving Equations using
Mental Math
Warm-Up
Copy and complete each table. Determine if each number in
the table is a solution of the equation.
x
6
7x = 42
7(6) = 42
Solution?
YES
7
8
7(7)  42
7(8)  42
NO
NO
x
26 − x = 15 Solution?
NO
10 26 − 10  15
YES
11 26 − 11 = 15
NO
12 26 − 12  15
Lesson 3.2
Solving Equations Using
Mental Math
Solve one-step equations using mental
math.
Good to Know!
In this lesson, you will learn a problem-solving strategy to solve
equations using mental math. You will be given equations and
asked to find the solution to each equation.
The steps to mentally solve an equation are:
GUESS
CHECK
REVISE
Example 1
Use the Guess, Check and Revise method to solve the equation.
a. y + 7 = 15
GUESS  CHECK  REVISE  CHECK
y=9
9 + 7 = 15
16  15
Too high. Pick a
lower number.
y=8
8 + 7 = 15
15 = 15
y = 8 is the
solution.
Example 1 Continued…
Use the Guess, Check and Revise method to solve the equation.
b. 6x = 30
GUESS  CHECK
x=5
6(5) = 30
30 = 30
The first guess
worked. x = 5
Example 2
Two sisters, Kylie and Sara, went shopping for school clothes.
Sara spent $105.11 and Kylie wasn’t sure how much she spent.
The sisters spent a total of $187.68. Write an equation and use it
to estimate how much Kylie spent on clothes.
Let k stand for the amount Kylie spent.
Kylie’s Clothes +
k
+
Sara’s Clothes = Total Cost
105.11
=
Round to the nearest whole number.
187.68
k + 105 = 188
GUESS  CHECK  REVISE  CHECK
k = 80
80 + 105 = 188
185  188
k = 83
83 + 105 = 188
188 = 188
Explore!
Record-Setting
Step 1 Helen grew her fingernails out so each nail is 24.2 cm long. The longest
fingernail on record is 76.7 cm. Write an addition equation and use it to
estimate how much longer Helen’s nails need to be to tie the record.
Step 2 John Evans balanced a 352 pound car on his head. Ryan worked his way up to
balancing a 151 pound car on his head. Write an addition equation and use it to
determine how many more pounds Ryan needs to balance on his head to tie the
record.
Step 3 A Japanese pig named Kotetsu has the record for the highest jump by a pig.
His jump measured 27.5 inches. An American pig jumped 12.2 inches. Write
an addition equation and use it to estimate how many more inches the
American pig needs to tie the record.
Step 4 Mac gathered 1,498 people for an Irish Dance. This is about
6,100 people fewer than the record set in Cork, Ireland on
September 10, 2005. Write a subtraction equation and use it
to estimate how many people attended the Irish Dance in
Ireland in 2005.
Communication Prompt
How do you use the Guess, Check and Revise method
to solve an equation?
Exit Problems
Solve each equation using the Guess, Check and Revise
method.
1. 4 + y = 13
y=9
2. 8x = 48
x=6
3. 21 − m = 3
m = 18
d
4.
8
3
d = 24