Grade 11 Math Fashion Show Performance Task Teacher Booklet
Title:
Grade:
Claim(s):
Assessment Target(s):
Standard(s):
Mathematical Practice(s):
Bloom's Taxonomy Level:
DOK Level:
Score Points:
Difficulty:
Resources:
Notes:
Task Overview:
Teacher
Preparation/Resource
Requirements:
Copyright
Fashion Show
11
Claim 4: Modeling and Data Analysis Students can analyze complex, real-world scenarios and can
construct and use mathematical models to interpret and
solve problems.
Claim 3: Communicating Reasoning
Students can clearly and precisely construct viable
arguments to support their own reasoning and to critique the
reasoning of others.
Claim 2: Problem Solving
Students can solve a range of complex well-posed problems
in pure and applied mathematics, making productive use of
knowledge and problem solving strategies.
Claim 4
A. Apply mathematics to solve problems arising in everyday
life, society, and the workplace.
D. Interpret results in the context of a situation.
Claim 3
B. Construct, autonomously, chains of reasoning that will
justify or refute propositions or conjectures. E. Distinguish correct logic or reasoning from that which is
flawed and—if there is a flaw in the argument—explain what
it is.
Claim 2
A. Apply mathematics to solve well-posed problems in pure
mathematics and arising in everyday life, society, and the
workplace.
Item 1- N.Q.1 C2TA
Item 2- S.ID.4 C4TA
Item 3- A.REI.5, A.REI.6 C3TB
Item 4- A.REI.6 C3TE
Item 5- A.CED.2, A.CED.3 C4TA, C4TD
Item 6- A.CED.2, A.CED.3 C4TD, C4TA
N.Q.1, A.CED.2, A.CED.3, S.ID.4, A.REI.5, A.REI.6
1, 2, 3, 4, 5, 7, 8
Analyzing - 4
Strategic Thinking/Reasoning - 3
14 points possible
Medium
N/A
N/A
The student assumes the role of a project manager for a
school fashion show. In class and individually, the student
completes tasks in which he/she reviews the costs and
profits associated to a fashion show fundraiser. Finally, the
student uses data to interpret the feasibility of certain
results.
None required
2015 Key Data Systems
©
1
Grade 11 Math Fashion Show Performance Task Teacher Booklet
Time Requirements:
Prework:
Approximately 60-80 minutes
None
The junior class has decided to have a fashion show in order to raise money for a
class field trip. Your job is to act as a project manager and help the students
design the stage and plan the show then determine the desired profit and use
data to evaluate the reasonableness of doubling the actual profits.
Part A
1. The stage is equipped with curtains that hide the sets. The image shows
the layout of the stage from above. Curtain 1 is 20 feet high from top to
bottom.
Sample TopScore
Response
(Session 1)
What is the minimum area of Curtain 1?
A.
B.
C.
D.
18 square feet
30 square feet
216 square feet
600 square feet
D. 600 square feet
Copyright
2015 Key Data Systems
©
2
Grade 11 Math Fashion Show Performance Task Teacher Booklet
2. The students designing the outfits plan to make unisex outfits that
stretch to fit students who are within 2 inches of the mean hip
measurement. Assume that the hip measurements for teenage boys and
girls in the 11th grade resembles a normal distribution.
If the mean hip measurement is 34 inches with a standard deviation of
2 inches, what percent of the students will be able to try out to model
the clothes?
A.
B.
C.
D.
34
36
68
95
C. 68
Sample TopScore
Response
(Session 1)
Copyright
2015 Key Data Systems
©
3
Grade 11 Math Fashion Show Performance Task Teacher Booklet
Part B
3. The costume jewelry and accessories for the show are bought from sales
racks at two different stores on different days. Use x to represent the
price of each item on the sales rack at the first store and y to represent
the price of each item on the sales rack at the second store.
On the first day, the students spent $30 on 4 items from the first store
and 7 items from the second store. On the second day, the students
spent $22 on 3 items from the first store and 5 items from the second
store. On the third day, the students need to buy 10 items from the first
store and 17 items from the second store.
The class treasurer believes that he can figure out the amount of money
that the students need on the third day without actually knowing the
price of each item. Justify the treasurer's claim. Then check your answer
by creating and solving a system of linear equations based on the first
day and the second day to confirm the amount of money that the
students need to purchase the items on the third day. Explain your
reasoning.
The treasurer is correct. You do not need to know the cost of
the items to find the total spent on the third day. This can be
figured out by adding the cost of the first day to twice the cost
of the second day; $30 + 2($22) = $74. The students will need
$74. I can use this method because the number of items
purchased on the third day match the number of the items on
the first but two times the number of items purchased on the
second day.
When solving the system of linear equations, we have
4x + 7y = $30 and 3x + 5y = $24. Solving algebraically, we
can use elimination and 12x + 21y = $90 and 12x + 20y = $88.
If I subtract the second equation from the first equation, I get
y = $2. If I then substitute the y-value into the first equation,
4x + 7($2) = $30, I get 4x = $16 and x = $4. I can then check
the calculation by substituting the x- and y-values into the
second equation; 10($4) + 17($2) = $74. The solution
confirms that the students need $74 to buy the items on the
third day.
Copyright
2015 Key Data Systems
©
4
Grade 11 Math Fashion Show Performance Task Teacher Booklet
4. Two of the juniors volunteered to drive to the stores, but they wanted to
be reimbursed for the time they spend driving to the stores and the
number of miles traveled in their cars. The drivers did not charge for the
cost of driving back to the school.
The two drivers planned to charge a different amount for the time spent
and the distance traveled because they drove different sized vehicles.
The students wrote linear equations to account for the cost of driving
based on the time it took to drive to the stores, x, and the number of
miles traveled, y.
Student A charged $2.25x + $2.00y, and Student B charged
$2.75x + $1.50y. Student A determined that she will charge $28.50.
Student B determined that he will charge $32.00.
The treasurer needs to find the time and distance traveled for record
keeping. He believes that it took the students 3 minutes of travel time.
Determine the actual travel time, in minutes, and the number of miles
traveled for each driver. Then identify the flaw in the treasurer's
assumption. Explain your reasoning.
The treasurer switched the variables. Three represents the
distance traveled (3 miles), and 10 is the amount of minutes
the students spent traveling. The system of equations is
$2.25x + $2.00y = $28.50 and $2.75x + $1.50y = $32.00. I
can multiply the first equation by 3 to get
$6.75x + $6.00y = $85.50 and then multiply the second
equation by 4 to get $11.00x + $6.00y = $128.00. From there,
I can subtract the first equation from the second equation to
get $4.25x = $42.50. If I divide both sides of the equation by
$4.25, I get x = 10. Next, I can substitute 10 into the first
equation, $2.25(10) + $2.00y = $28.50. Then I subtract
$2.25(10) from both sides of the equation to get
$2.00y = $6.00. If I divide both sides of the equation by $2.00,
the result is y = 3. The solution is x = 10 and y = 3. Therefore,
it takes 10 minutes to drive to the stores and there are 3 miles
traveled.
Copyright
2015 Key Data Systems
©
5
Grade 11 Math Fashion Show Performance Task Teacher Booklet
5. The juniors sold the student tickets for $3 and the adult tickets for $8.
Use s to represent the number of student tickets that were sold and a to
represent the number of adult tickets that were sold. In total, 300
tickets were sold. After paying back the investors, the profit was $775.
If the juniors initially received a total of $210 from investors, how many
tickets of each type did the students sell? Explain how you calculated
the values.
There were 283 student tickets sold and 17 adult tickets sold.
I used the equations s + a = 300 and $3s +$8a = $985. I
calculated the value by solving the first equation for s, so that
s = 300 - a. Then, I substituted the expression for s in for s in
the second equation. $3(300 - a) + $8a = $985. From there, I
simplified to find that $900 - $3a + $8a = $985. I combined
the like terms and found that $5a = $85. I divided both sides
by $5 and determined that a = 17. Next, I plugged the a-value
into my expression for s and found that s = 300 - 17 = 283.
6. Use the information from the last question to complete the following
task.
Is it mathematically possible to double the profits while still selling only
300 tickets? Write a model that can be used to determine the answer,
and then use the actual sales to make an argument about the feasibility
of doubling the profits while keeping the ticket prices the same for the
second show. Are the required number of ticket sales reasonable given
the data from the first show?
Yes, it is possible to double the profits while still selling only
300 tickets. The following system of equations should be used
as the model: s + a = 300, $3s +$8a = $1760. Doubling the
profit means doubling the $775, which becomes $1550, but we
still need to include the investment, which moves the total to
$1760. Solving the system results in needing to sell 172 adult
tickets and 128 student tickets. Based on the data from the
first show, the majority of the sales were to students. I do not
believe that the fashion show would be able to double the
profit because too many adult tickets need to be sold.
End of Performance Task
Copyright
2015 Key Data Systems
©
6
Grade 11 Math Fashion Show Performance Task Teacher Booklet
Rationales for Part A:
Rationales Question 1:
A.
B.
C.
D.
Student(s) may not have realized that 18 is the length of one of the sides.
Student(s) may not have realized that 30 is the other dimension of the curtain.
Student(s) may not have realized that 216 square feet is the area of Section A.
Correct answer
Rationales Question 2:
A. Student(s) may not have realized that they need to count the students who fall within
the range on both sides of the mean.
B. Student(s) may not have realized that finding a value that is one standard deviation
away does not result in the solution.
C. Correct answer
D. Student(s) may not have realized that they wanted the percent within one standard
deviation, not the percent within two standard deviations.
Scoring Rubric for Part B:
Scoring Rubric Question 3:
The student demonstrates a thorough understanding of how to solve a
system of linear equations. The student justifies the class treasurer's
argument then correctly evaluates the system of equations and explains the
process they used to confirm their answer.
The student demonstrates a good understanding of how to solve a system of
linear equations. The student justifies the class treasurer's argument then
correctly evaluates the system of equations but does not explain the process
they used to confirm their answer.
The student demonstrates a limited understanding of how to solve a system
of linear equations. The student understands how a quadratic function should
look but does not understand what they need to do in order to justify the
treasurer's belief.
The student demonstrates little to no understanding of how to solve a system
of linear equations. The student does not justify the treasurer's argument,
does not correctly evaluate the system of equations, and does not explain
the process used to confirm their answer.
3 Points:
2 Points:
1 Point:
0 Points:
Copyright
2015 Key Data Systems
©
7
Grade 11 Math Fashion Show Performance Task Teacher Booklet
Scoring Rubric Question 4:
The student demonstrates a thorough understanding of how to solve a
system of linear equations. The student explains the flaw in the class
treasurer's assumption, identifies the solutions as 10 minutes for traveling to
the stores and 3 miles traveled, and explains the process they used to solve
the system of equations.
The student demonstrates a good understanding of how to solve a system of
linear equations. The student explains the flaw in the class treasurer's
assumption, identifies the solutions as 10 minutes for traveling to the stores
and 3 miles traveled, but does not explain the process they used to solve the
system of equations.
The student demonstrates a limited understanding of how to set up a system
of linear equations. The student correctly explains what the 10 and the 3
represent but does not identify the solutions and does not provide an
explanation.
The student demonstrates little to no understanding of how to solve a system
of linear equations. The student does not explain the flaw in the assumption,
does not identify the solutions, and does not explain the process they used to
solve the system of equations.
3 Points:
2 Points:
1 Point:
0 Points:
Scoring Rubric Question 5:
The student demonstrates a thorough understanding of how to set up and
evaluate a system of equations. The student correctly identifies the system
as s + a = 300, $3s +$8a = $985, states the solution set of 283 student
tickets sold, and 17 adult tickets sold and explains the steps they used to
solve for the values.
The student demonstrates a good understanding of how to set up and
evaluate a system of equations. The student correctly identifies the system
as s + a = 300, $3s +$8a = $985 but does not state the number of tickets of
each type that were sold or does not provide an explanation.
The student demonstrates a limited understanding of how to set up and
evaluate a system of equations. The student uses an incorrect system, such
as s + a = 300, $3s +$8a = $775 but does provide an explanation.
The student demonstrates little to no understanding of how to set up and
evaluate a system of equations. The student does not identify the correct
system, does not state the solution, and does not explain the steps they used
to solve for the value.
3 Points:
2 Points:
1 Point:
0 Points:
Copyright
2015 Key Data Systems
©
8
Grade 11 Math Fashion Show Performance Task Teacher Booklet
Scoring Rubric Question 6*:
The student demonstrates a thorough understanding of how to set up and
evaluate a system of equations. The student correctly identifies the system
3 Points:
as s + a = 300, $3s +$8a = $1760 and states the solution set of 128 student
tickets sold and 172 adult tickets sold is a mathematical solution but is not a
reasonable outcome given the actual sales from the first show.
The student demonstrates a good understanding of how to set up and
evaluate a system of equations. The student correctly identifies the system
2 Points:
as s + a = 300, $3s +$8a = $1760 but does not explain the steps or
evaluate the reasonableness of the solution.
The student demonstrates a limited understanding of how to set up and
evaluate a system of equations. The student uses an incorrect system, such
1 Point:
as s + a = 300, $3s +$8a = $1970 but explains the steps or evaluates the
reasonableness.
The student demonstrates little to no understanding of how to set up and
evaluate a system of equations. The student does not correctly identify the
0 Points:
system, does not state the solution, and does not explain whether the
solution is reasonable.
*A student should receive full credit for this question if they correctly calculate with the incorrect
numbers from the previous question(s).
Copyright
2015 Key Data Systems
©
9