Course 3 Think Smart for the Smarter Balanced Assessment

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Course 3

Think Smart for the Smarter Balanced Assessment

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NAME

DATE

PERIOD

Chapter 4 Performance Task

Saving for College

Mr. 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 A

The 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?

SCORE

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Amount in Account ($)

Part B

The 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.

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

Savings Accounts

y

1050

1000 950 Compound Interest 900

850

800

750

700

650

600

550

500

x

0 2 4 6 8 10 12 14 16 18

Time (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.

Course 3 ? Chapter 4 ? Functions 113

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 C

After 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 D

The 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?

114 Course 3 ? Chapter 4 ? Functions

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Chapter 4 Performance Task Rubric

Page 113 ? Saving for College

Task Scenario

Students will interpret the equation y = mx + b as defining a linear function, create tables of values and graphs to represent linear functions, compare two functions represented in different 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 simplifies 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:

Simple Interest

x (years) y (total $)

0

500

1

520

3

560

6

620

12

740

18

860

Amount in Account ($)

Savings Accounts

y

1050

1000 950 Compound Interest

900

850

800

750

700

650

600

Simple Interest

550

500

x

0 2 4 6 8 10 12 14 16 18

Time (years)

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: m = 20.37, m = 23.91).

0?1

3?6

Partial Credit (1 point) will be given for each of these 3: the correct

table OR the correct graph OR an accurate comparison.

No credit will be given for an incorrect answer.

236

Course 3 ? Chapter 4 ? Performance Task Rubric

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

Chapter 4 Performance Task Rubric, continued

Part

C

Maximum Points

2

Full Credit: Sample answer:

Scoring Rubric

Distance from Home

Profit ($) Performance Task Rubrics

Copyright ? McGraw-Hill Education. Permission is granted to reproduce for classroom use.

D TOTAL

1

2 3 4 5

Time 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.

No credit will be given for an incorrect answer.

4

Full Credit:

Sample answer: The slope represents the

y 1,000

profit for selling each bracelet:

800

$2.25. The y-intercept

600

represents the amount spent

to start the business: ?$200.

400

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.

200

-200 0 -200

x 200 400 600 800 1,000

Bracelets Sold

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.

No credit will be given for an incorrect answer.

11

Course 3 ? Chapter 4 ? Performance Task Rubric

237

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