1. Match the written description to an expression.
Learning Objective
We will write equations.
What are we going to do?
CFU
Activate Prior Knowledge
The sum is the answer to an addition problem.
The difference is the answer to a subtraction problem.
The product is the answer to a multiplication problem.
The quotient is the answer to a division problem.
An expression is a mathematical phrase written with numbers and variables connected by operations.
Match the written description to an expression.
Expressions
1. What is 5 less than 10?
10 • 5
Students, you already know how to read a written description of simple expressions. Now, we will read written descriptions to write equations.
Make Connection
2. What is the sum of 10 and 5?
10 ÷ 5
3. What is the product of 10 and 5?
10 – 5
4. What is 10 divided by 5?
10 + 5

2. x + 4 = 7 5•n = n – 8 x + 4 = 7 5•n = n – 8 Examples
Concept Development
An equation declares an equal relationship1 between two expressions.
Examples
expression
x + 4 = 7
expression
5•n = n – 8
Which is an equation? How do you know?
A x + 8
B x + 8 = 23
CFU 1
To write an equation, translate2 the written sentences to mathematical symbols.
• In math, the word “is” means “equals =.”
Which is the correct equation from the written sentence? “The sum of a number (y) and 7 is the product of 6 and that number (y).”
A y + 7 = 6 • y
B y • y
In your own words, what is an equation?
An equation is ____________.
CFU 2
“The sum of a number (x) and 4 is 7. ”
x + 4 = 7
Go to
Skill Dev 1
“The product of 5 and a number (n) is 8 less than
the same number (n). ”
5•n = n – 8
1 the way things are connected
2 change from one language to another
Vocabulary
Go to
Skill Dev 2

3. = = = = = = = = x + 4 = 7 = = = = = = = = Equation
Skill Development/Guided Practice 1
expression
x + 4 = 7
Equation
An equation declares an equal relationship between two expressions.
• In math, the word “is” means “equals =.”
Read the written sentence carefully.
Identify3 the variable and known amounts. (underline)
Identify the operation clue words. (circle)
Determine where the equal sign will be written. Hint: “is” means “equals =.“
Interpret4 the written description to write the equation.
Read the equation aloud.
Write equations. 1 2 3 4 a b
How did I/you identify the variable, known amounts, and operations?
How did I/you determine where the equal sign would be written?
How did I/you write the equation?
CFU 1 2 3
Written Description
Equation
1. The sum of a number (a) and 7 is 98.
2. The sum of 36 and a number (c) is 12.
3. A number (x) less than 13 is 63.
4. 7 less than a number (k) is 19.
5. The product of a number (e) and 17 is 3.
6. The product of 16 and a number (f) is 96.
7. A number (d) divided by 60 is 15.
8. 75 divided by a number (b) is 5. = = = = = = = = = = = = = =
3 find (synonym)
4 explain what it means
Vocabulary = =
Back to
Concept Dev

4. Skill Development/Guided Practice 2
expression
x + 4 = 7
Equation
An equation declares an equal relationship between two expressions.
• In math, the word “is” means “equals =.”
Read the written sentence carefully.
Identify the variable and known amounts. (underline)
Identify the operation clue words. (circle)
Determine where the equal sign will be written. Hint: “is” means “equals =.“
Interpret the written description to write the equation.
Read the equation aloud.
Write equations. 1 2 3 4 a b
How did I/you identify the variable, known amounts, and operations?
How did I/you determine where the equal sign would be written?
How did I/you write the equation?
CFU 1 2 3
Written Description
Equation
1. The sum of a number (a) and 13 is 14 minus the same number (a).
2. The product of a number (c) and 7 is 42 divided by the same number (c).
3. A number (f) less than 27 is 82 divided by that same number (f).
4. 22 less than a number (m) is 19 times that same number (m). = = = = = = = =

5. 1 2 Writing an equation will help you solve real-world problems.
Relevance
An equation declares an equal relationship between two expressions. 1
Writing an equation will help you solve real-world problems.
The trip to San Francisco will cost $1000. If Joey wants to split the cost with his friends so that they only have to pay $200 each, how many people will be traveling to San Francisco? 2
Writing an equation will help you do well on tests.
Sample Test Question:
23. The product of 8 and a number (p) is 96. Which equation shows this relationship?
A 8p = 96
B 8 + p = 96
C 8 – p = 96
D 8•96 = p
Does anyone else have another reason why it is relevant to write an equation that represents a written description? (Pair-Share) Why is it relevant to write an equation that represents a written description? You may give me one of my reasons or one of your own. Which reason is more relevant to you? Why?
CFU

6. = = x + 4 = 7 = = Equation Read the written sentence carefully.
expression
x + 4 = 7
Equation
An equation declares an equal relationship between two expressions.
• In math, the word “is” means “equals =.”
Skill Closure
Read the written sentence carefully.
Identify the variable and known amounts. (underline)
Identify the operation clue words. (circle)
Determine where the equal sign will be written. Hint: “is” means “equals =.“
Interpret the written description to write the equation.
Read the equation aloud.
Write equations. 1 2 3 4 a b
Written Description
Equation
1. The sum of a number (x) and 18 is 36.
2. 11 less than a number (y) is 62. = = = =
Constructed Response Closure
Thaddeus wrote an equation from the description below. Do you agree with his answer? Why or why not?
5 times a number (t) is 15.
Summary Closure
What did you learn today about writing an equation that represents a written description? (Pair-Share)

7. y = mx + b y-intercept slope
Practice (continued)
The slope of a line (m) is the ratio of the change in y to the change in x.
The y-intercept (b) is the point at which the line passes through the y-axis.
Determine the slope of the line. (write)
Determine the y-intercept. (write)
Derive the equation of the line. (write)
Interpret the equation.
“The equation of the line with a slope of ___ and a y-intercept of ___ is ________.”
Derive the equation of a line. 1 2 3 4
How did I/you determine the slope of the line?
How did I/you determine the y-intercept?
How did I/you derive the equation of the line?
CFU 1 2 3
y = mx + b
slope
y-intercept
1. Write the equation of a line with a slope of -2 and y-intercept of (0, 5).
2. Write the equation of a line with a slope of 4 and y-intercept of (0, -3).
3. Write the equation of the line represented by the table below.
4. Write the equation of the line represented by the table below.
m = -2
m = 4
y = -2x + 5
y = 4x - 3
b = 5
b = -3 3 -2 -1 -4 1 4 x y 2 1 4 -2 7
m = x y 4 -2 -3 -4
m = =
- 2
+ 3
b = 4
- 4
- 1
b = -3
y = - x + 4 3 2
y = x - 3 1 4

8. y = mx + b y-intercept slope
Practice (continued)
The slope of a line (m) is the ratio of the change in y to the change in x.
The y-intercept (b) is the point at which the line passes through the y-axis.
Determine the slope of the line. (write)
Determine the y-intercept. (write)
Derive the equation of the line. (write)
Interpret the equation.
“The equation of the line with a slope of ___ and a y-intercept of ___ is ________.”
Derive the equation of a line. 1 2 3 4
How did I/you determine the slope of the line?
How did I/you determine the y-intercept?
How did I/you derive the equation of the line?
CFU 1 2 3
y = mx + b
slope
y-intercept
5. Write the equation of the line passing through (-2, -1) and (2, 5).
6. Write the equation of the line passing through (6, 2) and (-3, -4).
-1 - 5
-2 - 2 -6 -4 3 2
2 - (-4)
6 - (-3) 6 9 2 3
m = = =
m = = =
y = x + b 3 2
y = x + b 2 3
-1 = (-2) + b 3 2
-4 = (-3) + b 2 3
-1 = -3 + b
-4 = -2 + b +3 +3 +2 +2
2 = b
-2 = b
y = x + 2 3 2
y = x - 2 2 3

9. y = mx + b y-intercept slope Slope: ______________
Practice (continued)
y = mx + b
slope
y-intercept
How did I/you determine what the question is asking?
How did I/you determine the math concept required?
How did I/you determine the relevant information?
How did I/you solve and interpret the problem?
How did I/you check the reasonableness of the answer?
CFU 2 1 3 4 5
11. Henrietta is saving money while working a summer job. At the beginning of summer, she has $40 in her bank account. She saves $30 more every 4 weeks. Write an equation to show the relationship between money saved (d) and weeks worked (w).
Slope: ______________
y-intercept: __________
Equation: ___________
12. Wayne is driving and notices traffic ahead is coming to a stop. He is going 70 miles per hour and slows 50 miles per hour every 6 seconds. Write an equation to show the relationship between his speed (s) to the number of seconds (t) that pass.
$80 +4 80
(0, 70)
+30
$70
d = w + 40 30 4 70
$60 60
y = - x + 70 50 6
$50
-50 50
Money Saved (d)
$40
(0, 40)
Speed (s) 40
$30 30
$20 20 +6
$10 10 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 30 4
Weeks Works (w)
Seconds (t)
m =
m =
-50 6
b = 40
b = 70
d = w + 40 30 4
s = t + 70 50 6

10. Review
1. Substitute and then evaluate 2𝑥−8 for each given value of x below.
𝑥=−6
𝑥=−2
𝑥=5
𝑥=9
2(−6)−8
−12−8
−20
2. Substitute and then check the solution.
Is 𝑥=5 the solution to −15𝑥+13=88?
Is 𝑥=−5 the solution to −15𝑥+13=88?
Is 𝑥=0 a solution to 9𝑥−7<−22?
Is 𝑥=−10 a solution to 9𝑥−7<−22?
Is 𝑥=9,𝑦=1 a solution to 2𝑥−3𝑦=15?
Is 𝑥=0,𝑦=−5 a solution to 2𝑥−3𝑦=15?
Is 𝑥=3,𝑦=1 a solution to 𝑦<4𝑥−11?
Is 𝑥=5,𝑦=3 a solution to 𝑦<4𝑥−10?

11. Solve Two-Step Equations
1. 2𝑥−8=10
2𝑥−8+𝟖=10+8
2𝑥 2 = 18 2
𝑥=9
2. 3𝑥−11=28
3. 5𝑥+15=−30
4. 6𝑥+14=−58
5. −3𝑥−5=28
6. −4𝑥+7=43
7. −2𝑥−5=−49
8. −8𝑥−4=−100
9. 7𝑥+15=106
10. −5𝑥−16=−81
11. 9𝑥+1=145
𝑥−12=−144
13. −10𝑥+14=−40
𝑥−14=70
15. −9𝑥+9=84
16. –𝑥−18=20
17. 8𝑥+50=−96
𝑥+21=−100
19. −14𝑥+14=98
𝑥−7=−55