Use the worksheet to record your answers to the Algebraic Expressions portfolio
activities. When you are finished, save your worksheet with your answers and submit it
for a portfolio grade.
Question 1
A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms oft showing
his total cost.
b. Choose a value for t greater than $12 and less than $13. Use one of the
expressions you wrote in part a) to find Conor's total cost, rounded to the
nearest penny. Show your work.
c. Suppose that Conor's total cost to see the movie is greater than $17.50 and less
than $20. What could be a value oft to make that possible?
Question 2
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d - 15 dollars 10%
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a. Write two expressions in terms of d to show how much Winona and Takoda
would pay in total if they bought their mother the set of power tools.
b. What does the expression 0.90(d- 5) refer to? How do you know? How else
could this expression be written?
c. Choose a value ford that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Question 3
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Population
Percentage
Change
Pleasantville X -2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the information from the second and third
columns to write two expressions showing the current estimated population of
the town in terms of x, y, or z.
b. Add a fourth row to the table showing the population information for the town
of Concord. Concord's population as of the last census wasp people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
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c. Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b) above, calculate the
estimated current population of Concord, rounding to the nearest whole number
if needed. Explain why you used the expression you did to make your
calculation.
Question 4
A'Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A'Leila knows that
a=(1⁄2)b.
a. Write two different expressions giving the perimeter of the donkey's pen.
b. Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you wrote.
c. Explain why you used that expression to evaluate the perimeter of the donkey's
pen.
Algebraic Expressions Portfolio Worksheet
Use the rubric to check your work on the portfolio.
Algebraic Expressions Portfolio Rubric
View Learning Coach Guide
Algebraic Expressions Portfolio
1. Have your student look over the portfolio rubric and complete the
portfolio activities on their own.
2. Make sure your student completes all the required parts of the
portfolio. Go over the rubric with your student.
3/5
9/29/23, 11 :43 AM
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Vega Viewer SPA
3. For Question 1, your student may need to review the different ways
of writing expressions given in the unit. Remind them that in parts
b) and c) the task is to evaluate the expression given the value
chosen for t.
4. For Question 2, your student should recall the different ways of
writing expressions that involve percentages. Remind them what the
meaning of a discount is. Discuss that the total cost of an item may
or may not be the most important consideration in what present to
buy, but that their paragraph should acknowledge the different costs
regardless.
5. For Question 3, your student again needs to recall the different ways
of writing expressions that involve percentages. You might want to
talk with them about the meaning of a positive or negative change in
population and how it reflects the number of people who live in a
town.
6. For Question 4, encourage your student to draw a model of the pen
to represent the dimensions.
4/5
To answer the questions in this Algebraic Expressions portfolio, you will need to follow the instructions and use the given information to write and evaluate expressions. Here's a breakdown of how you can approach each question:
Question 1:
a. To find Conor's total cost, you need to consider the cost of the ticket and the amusement tax. The expressions in terms of 't' would be:
- Cost of the ticket: t dollars
- Amusement tax: 0.15t dollars
b. Choose a value for 't' between $12 and $13. Let's say t = $12.50. To find Conor's total cost, use one of the expressions from part a:
- Cost of the ticket: $12.50
- Amusement tax: 0.15 * $12.50 = $1.875 (rounded to $1.88)
- Total cost: $12.50 + $1.88 = $14.38 (rounded to $14.38)
c. The total cost needs to be greater than $17.50 and less than $20. Let's use the expression from part a: t dollars.
- Substitute the greatest possible value: t = $19.99
Question 2:
a. To find the total cost for each present, you use the given expressions for the cost and the discount percentage. The expressions in terms of 'd' would be:
- Power tools: d dollars
- Water skis: (d + 15) dollars
- Jewelry: (d - 15) dollars
b. The expression 0.90(d - 5) represents the cost after a 10% discount. By multiplying 'd' by 0.90, we account for the 10% discount. The '5' is subtracted to adjust the discount amount. Another way to write this expression is 0.90d - 4.50.
c. Choose a value for 'd' between $25 and $100. Let's say d = $50. Calculate the total cost for each present using the expressions from part a:
- Power tools: $50
- Water skis: $50 + $15 = $65
- Jewelry: $50 - $15 = $35
Based on these costs, Winona and Takoda should buy the power tools because it has the lowest total cost.
Question 3:
a. Choose one of the towns and use the information to write expressions for its current estimated population. Let's choose Pleasantville. The expressions in terms of 'x' would be:
- Current estimated population: X + (-2%) * X (or X - 0.02X)
b. Add the population information for the town of Concord to the table. Let's say the population is 'p' people, and the percentage change is -3%. The expressions for the current estimated population of Concord would be:
- Current estimated population: p + (-3%) * p (or p - 0.03p)
c. Choose a value for 'p' between 5,000 and 10,000. Let's say p = 7,500. Calculate the current estimated population of Concord using the expression from part b:
- Current estimated population: 7,500 + (-3%) * 7,500 = 7,275 (rounded to 7,275)
The expression p - 0.03p was used to calculate the estimated population because it represents a 3% decrease in population.
Question 4:
a. To find the perimeter of the donkey's pen, you need to consider the lengths of its sides. The expressions for the perimeter would be:
- Perimeter 1: 2a + 2b yards
- Perimeter 2: 2b + 2(1/2)b = 2b + b = 3b yards
b. Choose a value for 'a' between 5 and 15. Let's say a = 10. Evaluate the perimeter of the pen using one of the expressions from part a:
- Perimeter 1: 2(10) + 2b = 20 + 2b yards
c. The expression used to evaluate the perimeter of the pen was 2a + 2b because it represents the formula for the perimeter of a rectangle with sides 'a' and 'b'.
Once you have answered all the questions and completed the worksheet, make sure to save it with your answers and submit it for grading.
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Question 1
A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms oft showing
his total cost.
b. Choose a value for t greater than $12 and less than $13. Use one of the
expressions you wrote in part a) to find Conor's total cost, rounded to the
nearest penny. Show your work.
c. Suppose that Conor's total cost to see the movie is greater than $17.50 and less
than $20. What could be a value oft to make that possible?
Question 2
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d - 15 dollars 10%
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a. Write two expressions in terms of d to show how much Winona and Takoda
would pay in total if they bought their mother the set of power tools.
b. What does the expression 0.90(d- 5) refer to? How do you know? How else
could this expression be written?
c. Choose a value ford that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Question 3
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Population
Percentage
Change
Pleasantville X -2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the information from the second and third
columns to write two expressions showing the current estimated population of
the town in terms of x, y, or z.
b. Add a fourth row to the table showing the population information for the town
of Concord. Concord's population as of the last census wasp people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
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c. Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b) above, calculate the
estimated current population of Concord, rounding to the nearest whole number
if needed. Explain why you used the expression you did to make your
calculation.
Question 4
A'Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A'Leila knows that
a=(1⁄2)b.
a. Write two different expressions giving the perimeter of the donkey's pen.
b. Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you wrote.
c. Explain why you used that expression to evaluate the perimeter of the donkey's
pen
Use the rubric to check your work on the portfoli
View Learning Coach Guide
Algebraic Expressions Portfolio
1. Have your student look over the portfolio rubric and complete the
portfolio activities on their own.
2. Make sure your student completes all the required parts of the
portfolio. Go over the rubric with your student.
3/5
9/29/23, 11 :43 AM
about:blank
Vega Viewer SPA
3. For Question 1, your student may need to review the different ways
of writing expressions given in the unit. Remind them that in parts
b) and c) the task is to evaluate the expression given the value
chosen for t.
4. For Question 2, your student should recall the different ways of
writing expressions that involve percentages. Remind them what the
meaning of a discount is. Discuss that the total cost of an item may
or may not be the most important consideration in what present to
buy, but that their paragraph should acknowledge the different costs
regardless.
5. For Question 3, your student again needs to recall the different ways
of writing expressions that involve percentages. You might want to
talk with them about the meaning of a positive or negative change in
population and how it reflects the number of people who live in a
town.
6. For Question 4, encourage your student to draw a model of the pen
to represent the dimensions.
4/5
Question 1:
a. Two expressions in terms of "t" showing Conor's total cost are:
1) Total cost = t + 0.15t, which simplifies to 1.15t
2) Total cost = t(1 + 0.15), which simplifies to 1.15t
b. Let's choose t = $12.75. Using the first expression from part a:
Total cost = 1.15 * $12.75 = $14.66 (rounded to the nearest penny)
c. To find a value of "t" that would make Conor's total cost greater than $17.50 and less than $20, we can set up the inequality:
17.50 < 1.15t < 20
Divide all parts of the inequality by 1.15:
15.22 < t < 17.39
So, a value of "t" between $15.22 and $17.39 would make this possible.
Question 2:
a. Two expressions in terms of "d" for the total cost of the power tools are:
1) Total cost = d - 0.15d, which simplifies to 0.85d
2) Total cost = d * (1 - 0.15), which simplifies to 0.85d
b. The expression 0.90(d - 5) refers to the total paid after a 10% discount is applied to the original cost of "d" dollars. The expression could also be written as 0.9d - 4.5.
c. Let's choose d = $50. Calculate the total cost of each present:
- Power tools: 0.85 * $50 = $42.50
- Water skis: ($50 + $15) * (1 - 0.25) = $52.50
- Jewelry: ($50 - $15) * (1 - 0.10) = $40.50
Based on the costs, Winona and Takoda should buy the jewelry because it has the lowest total cost.
Question 3:
a. Let's choose Pleasantville. The expressions for its current estimated population would be:
1) Current estimated population = X + (-2%) * X = X - 0.02X
2) Current estimated population = X * (1 - 0.02) = X * 0.98
b. Adding the population information for the town of Concord:
- Concord's population: P people
- Percentage change: -4% (negative integer not divisible by two)
The expressions for the current estimated population of Concord would be:
1) Current estimated population = P + (-4%) * P = P - 0.04P
2) Current estimated population = P * (1 - 0.04) = P * 0.96
c. Let's choose p = 7,500. Calculate the estimated current population of Concord:
- Current estimated population = 7,500 - 0.04 * 7,500 = 7,200 (rounded to the nearest whole number)
The expression P * 0.96 was used because it represents a 4% decrease in population.
Question 4:
a. Two expressions for the perimeter of the donkey's pen are:
1) Perimeter = 2a + 2b
2) Perimeter = 3b
b. Let's choose a =