Unit 2 Lesson 18: Classwork (Keep)
Name _________________
Writing, Evaluating, and Finding Equivalent Expressions with Rational #’s
Objective: 7.EE.2. Understand that rewriting an expression in different forms in a problem context can shed
light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that
“increase by 5%” is the same as “multiply by 1.05.”
Variable: an unknown amount represented by a letter
In the expression m + 5, m is the variable.
Variable Expressions: Consist of numbers, variables, and operations
m+5
Key Words
n–3
3x
c
5
Situation you might find in a problem
Algebraic
Expression
plus, additional,
$10 plus $2 for each additional minute
10 + 2m
increased, sum of,
Sally’s grade increased by 7 points
g+7
more than,
5 more than Sam’s
s+5
less than **
2 dollars less than John
j–2
fewer than
5 fewer dogs than cats
c-5
times, twice
2 times (twice) the number of coins
2c
each
the tickets cost $3.00 each
3t
per
pays $12 per hour
12h
of
8% of the bill is tax
0.08b
half
half the area
a
2
off
price of something on sale for 25% off
p – 0.25p
Ex: John’s father asked him to compare several different cell phone plans and
identify which plan will be the least expensive for the family. Use the information
contained in the table below to answer the following questions.
Cell Phone Plans
All members of the family may not want identical plans, therefore we will let x
represent the number of phone lines, 𝑦 represent the number of phone lines with
unlimited texting, and 𝑧 represent the number of phone lines with Internet access.
Write an algebraic expression for each cell phone plan:
Company A ___________________________
Company B ___________________________
Company C ___________________________
In the expression 70 + 20x + 15y + 15z, the number 70 is a ________________
and 20, 15, and 15 are all _____________________________.
Using the expressions on the previous page, find the cost of each company’s phone
plan if:
a. Four people want a phone line, four people want unlimited texting, and the
family needs two Internet lines.
Company A
Company B
Company C
70 + 20x + 15y + 15z
70 + 20(4) + 15(4) + 15(2)
70 + 80 + 60 + 30
$240
90 + 15x + 10y + 20z
90 + 15(4) +10(4) + 20(2)
90 + 60 + 40 + 40
$230
200 + 10x
200 + 10 (4)
200 + 40
$240
Which cell phone company should John’s family use? Why?
John’s family should use Company B because the phone plan
is less expensive.
b. Four people want a phone line, four people want unlimited texting, and all
four people want internet lines.
Company A
70 + 20x + 15y + 15z
Company B
90 + 15x + 10y + 20z
Company C
200 + 10x
Which cell phone company should John’s family use? Why?
John’s family should use Company______________________
___________________________________________________.
c. Two people want a phone line, two people want unlimited texting and the
family needs two Internet lines.
Company A
70 + 20x + 15y + 15z
Company B
Company C
90 + 15x + 10y + 20z
200 + 10x
Which cell phone company should John’s family use? Why?
Ex: Three friends went to the movies. Each purchased a medium-sized popcorn
for 𝑝 dollars and a small soft drink for 𝑠 dollars. a. Write the expression that
represents the total amount of money (in dollars) the three friends spent at the
concession stand.
b. If the concession stand charges $6.50 for a medium-sized popcorn and $4.00 for
a small soft drink, how much did the three friends spend on their refreshments all
together? (SW)
http://www.engageny.org/sites/default/files/resource/attachments/g7-m2-student_materials.pdf
Evaluating Equivalent Expressions
Evaluate if x = 2, y = -1
Evaluate if y = 1
4( x + 2y )
4 ( 2 + 2(-1))
4(2-2)
4( 0)
0
5 (3 – 4y)
Evaluate if x = 5, y = -2
-3(x + 4y)
1
2
Evaluate if x = - , y = 1
1 - Need help
2 - Starting to understand
4x + 8y
4 (2) + 8 (-1)
8 + (-8)
0
2(4x – 3y)
3 - Understanding fairly well
4 - I could teach it to others!
Unit 2 Lesson 18: HW
Name _________________
Writing, Evaluating, and Finding Equivalent Expressions with Rational #’s
1. Sally is paid a fixed amount of money to walk her neighbor’s dog every day
after school. Each month, when she is paid, she puts aside $20 to spend and
saves the remaining amount. Write an expression that represents the amount
Sally will save in 6 months if she earns m dollars each month. If Sally is
paid $65 each month, how much will she save in 6 months?
2. A football team scored 3 touchdowns, 3 extra points and 4 field goals. Write
an expression to represent the total points the football team scored.
Write another expression that is equivalent to the one written above.
If each touchdown is worth 6 points, each extra point is 1 point, and each
field goal is 3 points, how many total points did the team score?
3. Write three other (different) expressions that are equivalent to 8𝑥−12.
Unit 2 Lesson 18
Name __________________________
HW #4. Profit is defined as earnings less expenses (earnings – expenses). At the
local hot air balloon festival, the Ma & Pops Ice Cream Truck sells ice cream pops,
which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the
festival’s organizers for a vendor permit. The table below shows the earnings,
expenses, and profit earned when 50, 75, and 100 ice cream pops were sold at the
festival.
a.
Write an expression that represents the profit (in dollars) Ma & Pop earned
by selling ice cream pops at the festival.
b.
Write an equivalent expression.
c.
How much did Ma & Pops Ice Cream Truck profit if it sold 20 ice cream
pops? What does this mean? Explain why this might be the case.
d.
How much did Ma & Pops Ice Cream truck profit if it sold 75 Ice Cream
Pops? What does this mean? Explain why this might be the case.
Evaluating Algebraic Expressions HW
Name: ______________
**SW neatly on separate paper**
Find the value of each expression. (Use PEMDAS)
1) 16 – 4 x 3 + 2
2) 15 + 3 2
3) 15  (–3) + 4 (8)
4) 4(9 + –3)
5) 4 x 2 2 – 2 x 2
6) 5 2 – 3(5) – 8
Find the value of each expression if n = 3.
7) 6n
8) 4(n + 5)
10) (6 – n) 2 + 13
11)
n2  6
3
9) 4n – 12
12) 8(16 – n)
Find the value of each expression if t = –3, u = 2, and v = 5.
13) 5t – v
14) 5t – u 2
15) t + 3u – v
16) (v – u) 2 + t
17) 3tv + 8u
18) t(v – u)
Find the value of each expression if a = 5, b = 3, and c = 7.
19) a 2 + c 2
20) 6b 2
21) a 2 – b
22) a 2 – b
23) (a + c) 2
24) 5(a – b)
2
Solve.
25) The science lab is in the shape of a rectangle. The lab is 32 feet long
by 25 feet wide. Use P = 2(l + w) to find the perimeter of the lab.
Evaluating Algebraic Expressions
Name_______________________
Show work for all parts each question on a separate piece of paper.
1) Evaluate each expression for x = 3, –2, ¼, and –2 ½
Ex:
a) –4x
–4x
–4x
–4x
–4(3)
–4(–2)
–12
8
–4x
–4( ¼ )
–1
–4(–2 ½)
10
b) 4x + 10
4x + 10
4x + 10
4x + 10
4x + 10
c) 6 – 2x
6 – 2x
6 – 2x
6 – 2x
6 – 2x
2) Evaluate each expression for x = –6.5, 2.5, and –1 ½
a) 6x
6x
6x
6x
b) 2x + 4x
2x + 4x
2x + 4x
2x + 4x
c) 8x – 2x
8x – 2x
8x – 2x
8x – 2x
d) What do you notice about each of the parts to question #2?