Sixth Grade Acceleration Intervention
Unit: Simplifying Expressions
Theme: Entertainment
Day 6 Lesson
Objective
Students will simplify algebraic expressions represented as physical models by
combining like terms.
Students will write and evaluate an algebraic expression to represent unknown quantities.
Materials
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Overhead projector or document camera
Scissors
“Aquarium Mix Up Cards” resource sheets (cut prior to lesson)
“Equation Cards” resource sheets (cut prior to lesson)
“Written Response Record Sheet” resource sheets (one per student)
Aquarium Warm Up (10 minutes)
Arrange students into groups of three or four and present the class with the following
scenario: “The Mathtastic Family and the Factastic Family are taking a trip to the
aquarium. The aquarium charges a price per person plus a flat fee of $25 for the dolphin
show per family. The Mathtastic Family consists of six family members and they decide
to see the dolphin show. The Factastic Family of four wants to go to the aquarium, but
they want to skip the dolphin show to have lunch. Their lunch ends up costing them a
total of $40. Write an expression to represent the total cost of both families trip to the
aquarium combined.”
Answer: Answers may vary depending on format written by students. 6c + 25 + 4c + 40
or 10c + 65
After students write their expression, have them answer the following questions:
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1. How did you develop your expression?
2. What does your variable represent?
3. What would be the total cost of the trip to the aquarium if the tickets cost $20 per
person?
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Answers:
1. Explanations may vary.
2. Cost per ticket to the aquarium
3. 10(20) + 65 = $265.00
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Note: If students did not combine the number of family members and/or costs of the
dolphin show and lunch cost, remind them to always simplify their expression to make it
easier to work with. Encourage students to use a variable that is appropriate for the
problem, rather than just using “x.”
“Aquarium Mix Up” Activity (10 minutes)
After students have combined the expressions and found the total cost, explain that they
will now be compare the cost between several different families and their costs on their
trips to the aquarium.
Pass out the “Aquarium Mix Up Cards.” Each student will receive either a scenario or an
expression. Give the students a few minutes to find their partner by matching their
scenario to the correct expression, or vice versa.
Have groups read their scenario and explain how they knew their expression matched.
Answer: The original “Aquarium Mix Up Cards” resource sheet can be used as the
answer key.
“Which Costs More?” Activity (15 minutes)
Use the same partners from the “Aquarium Mix Up” activity.
After the students have found their match, display the following scenario using the
document camera or overhead projector:
“All of your families are going to the aquarium on Saturday. The weekend rate is $25 per
ticket. Find the total cost for your family to attend the aquarium.”
Give students time with their partners to work on evaluating their expressions. Students
need to show their work on a piece of paper to use with the “High Five” activity.
High Five Activity (20 minutes)
To review the answers to the “Which Costs More?” activity, have students walk around
the room in pairs and high five with another group that is finished. Once a group is
formed, students will check each other’s work. (Note: If there is a discrepancy, students
may come check their work with the answer key below.)
After the group has agreed on the correct answer to both problems, the pair with the more
expensive aquarium cost has to take a seat. The group with the cheaper cost continues on
to “high five” another group and the process continues until the family with the cheapest
cost is left standing.
Answers:
1. 5c + 25 = 5(25) + 25 = 125 + 25 = $150
2. 3c + 30 = 3(25) + 30 = 75 + 30 = $105
3. 2c + 52 = 2(25) + 52 = 50 + 52 = $102
4. 4c + 25 = 4(25) + 25 = 100 + 25 = $125
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5. 6c +10 = 6(25) +10 = 150 +10 = $160
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6. 5c + 40 = 5(25) + 40 = 125 + 40 = $165
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7. 7c " 20 = 7(25) " 20 = 175 " 20 = $155
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8. 4c + 35 = 4(25) + 35 = 100 + 35 = $135
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9. c + 73 = 25 + 73 = $98
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10. 5c +15 = 5(25) +15 = 125 +15 = $140
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! Next, have students discuss why that family had the cheapest cost.
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! Moonlight Special Activity (20 minutes)
Collect all of the “Aquarium Mix Up” cards and redistribute them around the room. Give
the students time to find their new partner by matching the scenario with the correct
algebraic expression.
Once the students have the correct partners, place the following scenario using the
document camera or overhead projector:
“All of your families have now decided to go to the aquarium on Friday afternoon instead
to receive the Moonlight Ticket Special of $15 per person. Find the total cost for your
family to attend the aquarium.”
Once the pairs have their expressions, have them complete the “High Five” activity again
to check their work and find the cheapest family cost. If groups have the same cost, they
both keep going, until they get knocked out. (Note: Use the answer key below if groups
have any discrepancies.)
Answers:
1. 5c + 25 = 5(15) + 25 = 75 + 25 = $100
2. 3c + 30 = 3(15) + 30 = 45 + 30 = $75
3. 2c + 52 = 2(15) + 52 = 30 + 52 = $82
4. 4c + 25 = 4(15) + 25 = 60 + 25 = $85
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5. 6c +10 = 6(15) +10 = 90 +10 = $100
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6. 5c + 40 = 5(15) + 40 = 75 + 40 = $115
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7. 7c " 20 = 7(15) " 20 = 105 " 20 = $85
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8. 4c + 35 = 4(15) + 35 = 60 + 35 = $95
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9. c + 73 = 15 + 73 = $88
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10. 5c +15 = 5(15) +15 = 75 +15 = $90
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Once the last pair is standing, discuss why they thought this family was the cheapest.
Was it the same family as the last time when the price of the ticket was $25? Why or
why not?
Exit Ticket (10 minutes)
Pass out the “Expression Cards” and “Written Response Record Sheet” to each student.
Have the students create a scenario when they would use the given algebraic expression
to represent. Then, have them write an extension question where students would have to
evaluate the expression. They must include a title, scenario, extension questions, and
answer key. (Note: Answers will vary.)
Closure (5 minutes)
When students have finished making their questions, have them fold their question sheet
in half to hide the answer key. Then, have the students pair up and exchange scenarios
with each other. Each student should solve the problem, and then check their answer
with the answer key.
If time permits, have students volunteer to read their question and discuss the reactions
from their partner.
Aquarium Mix Up Cards
The Multiplication Family of five
decides to go to the aquarium and see
the dolphin show which costs a flat
fee of $25 for the entire family.
5c + 25
The Division Family of three decides
to go to the aquarium; instead of
going to the dolphin show, they
decided to eat lunch. Their lunch
costs a total of $30.
3c + 30
The Addition Family of two decides
to go to the aquarium and see the
dolphin show for a flat fee of $25 for
the entire family. They also decided
to buy a dolphin stuff animal for $20
and a pack of dolphin pens for $7.
2c + 52
The Subtraction Family of four
decides to go to the aquarium and see
the dolphin show for a flat fee of $25
for the entire family.
4c + 25
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The Squared Family of six decides to
go to the aquarium, but instead of
seeing the dolphin show, the family
opts to see the jellyfish exhibit for a
flat fee of $10 for the entire family.
6c +10
The Parenthesis Family of five
decides to go to the aquarium, but
instead of seeing the dolphin show,
the family opts to see the jellyfish
exhibit for a flat fee of $10 for the
entire family. They also decided
afterwards to share a snack, which
costs $30 total.
5c + 40
The Exponent Family of six decides
to go to the aquarium, but instead of
going to the dolphin show, they
decide to let the youngest sibling
bring a friend with them. The friend
brings with her a coupon good for
$20 off their total purchase.
7c " 20
The Slope Family of four decides to
go to the aquarium and see the
dolphin show for a flat fee of $25 for
the entire family. Afterwards, they
decide to also attend the jellyfish
exhibit, which costs an additional
$10 for the entire family.
4c + 35
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Mr. Matho decides to go to the
aquarium by himself. He sees the
dolphin show, which costs him $25
and see the jellyfish exhibit, which
costs him $10. He also decides to
buy lunch for $10. Finally, he buys a
dolphin key chain for $8 and a
dolphin stuff animal for $20 as
souvenirs.
c + 73
The Pi Family of five decides to go
to the aquarium and see the dolphin
show at a flat fee of $25 for the
entire family. They also have a
coupon good for $10 off their
purchase.
5c +15
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Expression Cards
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5y "10
24g +16
2x + 4
x +10
10 p " 20 !
20k + 9
15v " 5
3 f + 30
20 f "10
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10h " 4
4v +12 !
7.5h + 20
30n +10
22y +12
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25m
5x +12
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7k + 8 !
50d + 25
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6b +14 !
2g + 6
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Written Response Record Sheet
Title: ________________________________
Scenario:
Extension Question:
Answer Key:
Correct Expression: _____________________
Extension Question Answer: ______________________________
Written Explanation: