Think Smart for the Smarter Balanced Assessment

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1 Course 3 Think Smart for the Smarter Balanced Assessment Smarter Balanced Assessment Item Types Scatter Plots Countdown to SBAC Chapter Tests in SBAC Format Chapter Performance Tasks, Rubrics, and Student Work Samples Benchmark Tests with Performance Tasks Go online for more! connected.mcgraw-hill.com Question Analysis Charts Student Scoring Rubrics Technology-Enhanced Questions More Performance Tasks!

2 NAME DATE PERIOD SCORE 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 = (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? Copyright McGraw-Hill Education. Permission is granted to reproduce for classroom use. 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 $) , x Time (years) Make a table of values for the simple interest equation from Part A. Graph the equation on the same graph. Compare and contrast the two types of interest. Include a discussion about the rates of change. Amount in Account ($) Savings Accounts y Compound Interest Course 3 Chapter 4 Functions 113

3 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? Copyright McGraw-Hill Education. Permission is granted to reproduce for classroom use. 114 Course 3 Chapter 4 Functions

4 Page 113 Saving for College Chapter 4 Performance Task Rubric 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 8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5 Standard(s) 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 $) x Time (years) The simple interest graph is increasing and is a linear function. It has a constant rate of change (m = 20). The compound interest graph is also increasing but is a nonlinear function and has a variable rate of change (for example: m 0 1 = 20.37, m 3 6 = 23.91). Partial Credit (1 point) will be given for each of these 3: the correct table OR the correct graph OR an accurate comparison. No credit will be given for an incorrect answer. Amount in Account ($) Savings Accounts y Compound Interest Simple Interest Copyright McGraw-Hill Education. Permission is granted to reproduce for classroom use. 236 Course 3 Chapter 4 Performance Task Rubric

5 Chapter 4 Performance Task Rubric, continued Copyright McGraw-Hill Education. Permission is granted to reproduce for classroom use. Part Maximum Points C 2 Full Credit: Sample answer: Scoring Rubric 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. D 4 Full Credit: Sample answer: y 1,000 The slope represents the profit for selling each bracelet: $2.25. The y-intercept represents the amount spent to start the business: $200. Break even: y = 0, so 0 = x 200 and x 88.89; they must sell 89 bracelets x 800 1, Make $1,000: y = 1,000, so 1,000 = 2.25x 200 and Bracelets Sold 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 $1,000 OR the correct sales on 1,000 bracelets. No credit will be given for an incorrect answer. TOTAL 11 Distance from Home 1 2 Profit ($) Performance Task Rubrics Course 3 Chapter 4 Performance Task Rubric 237

6 Chapter 4 Performance Task Student Work Sample Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom 238 Course 3 Chapter 4 Performance Task Student Work Sample

7 Chapter 4 Performance Task Student Work Sample Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom Student Work Sample Course 3 Chapter 4 Performance Task Student Work Sample 239

8 Chapter 4 Performance Task Student Work Sample Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom 240 Course 3 Chapter 4 Performance Task Student Work Sample

9 Chapter 4 Performance Task Student Work Sample Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom Student Work Sample Course 3 Chapter 4 Performance Task Student Work Sample 241