Course 3 Think Smart for the Smarter Balanced …...236 Course 3 • Chapter 4 • Performance Task Rubric Chapter 4 Performance Task Rubric Page 113 • Saving for College Task Scenario

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Course 3 • Chapter 4 • Functions 113

Program: SBAC Component: C04_PT

PDF PassVendor: MPS Grade: Course 3

Chapter 4 Performance Task

Saving for CollegeMr. and Mrs. Sanchez plan for a college education when their baby is born. They have already saved $500 and want to invest that money in a savings account at a local bank until their child is 18 years old. One account that the bank offers provides 4% interest to parents for college tuition.

Write your answers on another piece of paper. Show all your work to receive full credit.

Part AThe bank offers two accounts. One account has a 4% simple interest rate. Simple interest I can be found with I = prt, using the principal p, the decimal rate r, and the time t in years. The equation y = 500 + 500(0.04)x represents investing $500 in this account, where y is the total amount in the account and x is the number of years invested. Explain the equation. Does the equation represent a function? Is it linear?

Part BThe bank also has an account offering 4% monthly compound interest, which means that the interest will be applied to both the original principal and any interest accumulated each month. The table and graph show how the total amount in the account y will change over x years.

Make a table of values for the simple interest equation from Part A. Graph the equation on the same graph. Compare and contrast the two types of interest. Include a discussion about the rates of change.

2 4 6 8 10 12 14 16 18

600550500

650700750

Am

ou

nt

in A

cco

un

t ($

)

800850900950

10001050

Time (years)

0

Savings Accounts

y

x

Compound Interest

Compound Interest

x (years) y (total $)

0 500

1 520.37

3 563.64

6 635.37

9 716.24

12 807.39

18 1,025.99

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114 Course 3 • Chapter 4 • Functions

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The amount in the savings account is not the only way to save money. The Sanchez family wants to raise at least $1,000 more. So they decide to make and sell bracelets in addition to their regular jobs.

Part CAfter work one day, Mrs. Sanchez plans to stop at the crafts store and at the bank. The crafts store is about halfway from her work to her home. The bank is right around the corner from her home. She estimates that it will take her longer at the crafts store to buy jewelry components than it will at the bank. Sketch a qualitative graph to represent Mrs. Sanchez’s drive home, where the y-axis indicates the distance from the home. Number each segment, and provide a key to show what each segment represents.

Part DThe Sanchez family creates the equation y = 2.25x – 200 to show the amount y in dollars they will make as profit after selling x bracelets. Graph the equation. What do the slope and y-intercept represent? How many bracelets will they have to sell to break even? How many bracelets will they have to sell to make the $1,000? How much will they make after selling 1,000 bracelets?

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236 Course 3 • Chapter 4 • Performance Task Rubric

Chapter 4 Performance Task Rubric

Page 113 • Saving for College

Task ScenarioStudents will interpret the equation y = mx + b as defi ning a linear function, create tables of values and graphs to represent linear functions, compare two functions represented in diff erent ways, determine and interpret the rate of change and initial value of a function, and make a qualitative graph to solve problems about saving money for a college education.

CCSS Content Standard(s)

8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5

Mathematical Practices MP1, MP2, MP3, MP4, MP6

Depth of Knowledge DOK2, DOK3

Part Maximum Points Scoring Rubric

A 2 Full Credit:Sample answer: The equation shows that $500 is the initial amount in the bank account. The interest is added to that amount to get the total amount in the account after x years.

The equation simplifi es to y = 20x + 500, which is in the form y = mx + b. So, it is a linear function.

Partial Credit (1 point) will be given for explaining the equation OR reasoning that it is a linear function.

No credit will be given for an incorrect answer.

B 3 Full Credit:Sample table:

The simple interest graph is increasing and is a linear function. It has a constant rate of change (m = 20). The compound interest graph is also increasing but is a nonlinear function and has a variable rate of change (for example: m0–1 = 20.37, m3–6 = 23.91).

Partial Credit (1 point) will be given for each of these 3: the correct table OR the correct graph OR an accurate comparison.


2 4 6 8 10 12 14 16 18

600550500

650700750

Am

ou

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in A

cco

un

t ($

)

800850900950

10001050

Time (years)

0

Savings Accounts

y

x

Simple Interest

Compound Interest

Simple Interest

x (years) y (total $)

0 500

1 520

3 560

6 620

12 740

18 860

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Course 3 • Chapter 4 • Performance Task Rubric 237

Chapter 4 Performance Task Rubric, continued

Part Maximum Points Scoring Rubric

C 2 Full Credit: Sample answer:

Key:

1. Mrs. Sanchez drives halfway home to get to the crafts store.

2. She spends time at the crafts store shopping.

3. She continues on to the bank, which is close to home.

4. She spends less time at the bank than at the crafts store.

5. Finally, she drives the rest of the way home.

Partial Credit (1 point) will be given for creating the graph but failing to create a key.


D 4 Full Credit: Sample answer:

The slope represents the profi t for selling each bracelet: $2.25. The y-intercept represents the amount spent to start the business: –$200.

Break even: y = 0, so 0 = 2.25x – 200 and x ≈ 88.89; they must sell 89 bracelets.

Make $1,000: y = 1,000, so 1,000 = 2.25x – 200 and x ≈ 533.3; they must sell 534 bracelets.

Sell 1,000 bracelets: y = 2.25(1,000) – 200 = 2,050; they will make $2,050.

Partial Credit (1 point) will be given for each of these 4: the correct graph and explanation of slope and y-intercept OR the correct break-even sales OR the correct number of bracelets for $1,000 OR the correct sales on 1,000 bracelets.


TOTAL 11

1

2

34

5

Time

Dis

tan

ce f

rom

Ho

me

-200

-200

2000 400 600 1,000800

200

400

600

Pro

fit

($)

800

1,000

Bracelets Sold

y

x

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238 Course 3 • Chapter 4 • Performance Task Student Work Sample

Chapter 4 Performance Task Student Work Sample

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Course 3 • Chapter 4 • Performance Task Student Work Sample 239



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240 Course 3 • Chapter 4 • Performance Task Student Work Sample



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Course 3 Think Smart for the Smarter Balanced …...236 Course 3 • Chapter 4 • Performance Task Rubric Chapter 4 Performance Task Rubric Page 113 • Saving for College Task Scenario