course 3 think smart for the smarter balanced assessment › cms › lib011 › ca01802504... ·...

Scat

ter

P

lots

Go online for more! connectED.mcgraw-hill.com• Question Analysis Charts • Student Scoring Rubrics • Technology-Enhanced Questions • More Performance Tasks!

• Smarter Balanced Assessment Item Types

• Countdown to SBAC

• Chapter Tests in SBAC Format

• Chapter Performance Tasks, Rubrics, and Student Work Samples

• Benchmark Tests with Performance Tasks

Think Smart for the Smarter Balanced Assessment

Thin

k Smart for th

e Smarter Balan

ced Assessm

ent

Course 3

Course 3

www.mheonline.com connectED.mcgraw-hill.com

NAME DATE PERIOD SCORE

Cop

yrig

ht ©

McG

raw

-Hill

Edu

catio

n. P

erm

issi

on is

gra

nted

to r

epro

duce

for

clas

sroo

m u

se.

Course 3 • Chapter 8 • Volume and Surface Area 121

Program: SBAC Component: PT

PDF PassVendor: MPS Grade: Course 2

Chapter 8 Performance Task

Good Sports CompanyThe Okeke family owns and operates a sporting goods company called Good Sports. To create a trustworthy product, they must be precise during the manufacturing process.

Hakeem oversees the making ofbaseballs. Baseballs have threemain parts, as shown. Each partmust be made precisely toconform to league standards.

Core (cork spheresurrounded by rubber)

Wool layers

Cowhide covering

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

Part AThe diameter of the spherical core of the baseball measures approximately 1.31 inches. What is the volume of the core of the baseball? Round to the nearest hundredth.

Part BLayers of wool are wound tightly around each core, resulting in a sphere with a radius of approximately 1.41 inches. What is the volume of the wool? Round to the nearest hundredth.

Part CAfter the cowhide covering is sewn on, each baseball has a total diameter between 2.86 inches and 2.94 inches. What are the possible circumferences of a baseball? What are the possible volumes of a baseball? Write your answers as ranges, and round to the nearest hundredth.

121-122_SBAC_A_C3_C08_PT_793945.indd 121121-122_SBAC_A_C3_C08_PT_793945.indd 121 20/11/14 3:43 PM20/11/14 3:43 PM

Copyright ©

McG

raw-H

ill Education. Permission is granted to reproduce for classroom

use.

122 Course 3 • Chapter 8 • Volume and Surface Area

Program: SBAC Component: PT


Part DBaseballs are not the only products made by the company. Good Sports also produces plastic cones with a 3.5-inch diameter and an 8-inch slant height.

8 in.

3.5 in.x in.

7 in.

Amma is in charge of new product development. She thinks the company should also produce cones with a diameter of 7 inches. She wants to use the same amount of plastic to produce each cone. What is x, the slant height of the cone that Amma wants to build? Assume both cones are open on the bottom.

Part ETo conform to tennis standards, each tennis ball thecompany manufactures must measure between2.575 inches and 2.70 inches in diameter.

Kahlil is in charge of packaging and distribution.He packages 3 maximum-sized tennis balls in onecylindrical can. He wants to fit the tennis ballssnugly so that each ball touches the next oneand the sides of the can. What are thediameter d and the height h of each can?

Approximately what percentage of the containerwill be filled by the tennis balls? Round to the nearest tenth of a percent. Approximately how many cubic inches of empty space remain in the container? Round to the nearest hundredth.

d in.

h in.

121-122_SBAC_A_C3_C08_PT_793945.indd 122121-122_SBAC_A_C3_C08_PT_793945.indd 122 20/11/14 3:43 PM20/11/14 3:43 PM

Copyright ©

The McG

raw-H

ill Com

panies, Inc. Permission is granted to reproduce for classroom

Program: SBAC Component: Chapter 8


250 Course 3 • Chapter 8 • Performance Task Student Work Sample

Chapter 8 Performance Task Student Work Sample

250-253_SBAC_A_C3_EM_2-UPS_793945.indd 250250-253_SBAC_A_C3_EM_2-UPS_793945.indd 250 11/25/14 2:54 PM11/25/14 2:54 PM

Cop

yrig

ht ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to r

epro

duce

for

clas

sroo

m

Stud

ent

Wor

k S

ampl

e



Course 3 • Chapter 8 • Performance Task Student Work Sample 251



Copyright ©

The McG

raw-H

ill Com







Cop

yrig

ht ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to r

epro

duce

for

clas

sroo

m

Stud

ent

Wor

k S

ampl

e






Copyright ©

McG

raw-H

ill Education. Permission is granted to reproduce for classroom

use.

260 Course 3 • Chapter 8 • Performance Task Rubric

Program: SBAC Component: PTR


Chapter 8 Performance Task Rubric

Page 121 • Good Sports CompanyTask ScenarioStudents will use formulas and geometric reasoning to fi nd circumference, surface area, and volume related to cones, cylinders, and spheres to solve problems about sporting goods manufacturing.

CCSS Content Standard(s)

8.G.9

Mathematical Practices MP1, MP2, MP3, MP4, MP5, MP6

Depth of Knowledge DOK2, DOK3, DOK4

Part Maximum Points Scoring Rubric

A 1 Full Credit:d = 1.31 in., so r = 0.655 in.

V = 4 − 3 �πr�3 = 4 − 3 �π(0.655)3 ≈ 0.375�π ≈ 1.18 in3

No credit will be given for an incorrect or incomplete answer.

B 2 Full Credit:Total volume of the ball after the wool layers are added:

V = 4 − 3 �πr3 = 4 − 3 �π(1.41)3 ≈ 3.738�π ≈ 11.74 in3

Volume of wool layers alone:11.74 – 1.18 = 10.56 in3

Partial Credit (1 point) will be given for the correct volume of the core and wool combined OR the correct volume of only the wool.


C 2 Full Credit:Smallest baseball: C = π�d = 2.86�π ≈ 8.98 in.Largest baseball: C = π�d = 2.94�π ≈ 9.24 in.The circumference of a baseball is between 8.98 and9.24 inches.

Smallest baseball: d = 2.86, r = 1.43

V = 4 − 3 �πr3 = 4 − 3 �π(1.43)3 ≈ 12.25 in3

Largest baseball: d = 2.94, r = 1.47

V = 4 − 3 �πr3 = 4 − 3 �π(1.47)3 ≈ 13.31 in3

The volume of a baseball is between 12.25 and 13.31 cubic inches.

Partial credit (1 point) will be given for the correct range of circumferences OR the correct range of volumes.

No credit will be given for an incorrect answer.

260-261_SBAC_A_C3_C08_PTR_793945.indd 260260-261_SBAC_A_C3_C08_PTR_793945.indd 260 20/11/14 3:52 PM20/11/14 3:52 PM

Per

form

ance

Tas

k R

ubri

cs

Cop

yrig

ht ©

McG

raw

-Hill

Edu

catio

n. P

erm

issi

on is

gra

nted

to r

epro

duce

for

clas

sroo

m u

se.

Course 3 • Chapter 8 • Performance Task Rubric 261

Program: SBAC Component: PTR


Chapter 8 Performance Task Rubric, continued

Part Maximum Points Scoring Rubric

D 2 Full Credit:Because both cones are open at the bottom, the amount of plastic used is equal to the lateral area.Current cone: d = 3.5, r = 1.75

L.A. = πr� = π(1.75)(8) = 14π ≈ 43.98 in2

New cone: d = 7, r = 3.5Lateral area is equal to the current cone’s lateral area.

L.A. = πr�14π = π(3.5)(x)14 = 3.5x4 = x, so the slant height of the new cone is 4 in.

Partial credit (1 point) will be given for the correct lateral area OR the correct slant height.


E 4 Full Credit:Maximum diameter of a tennis ball = 2.7 in.Diameter of can = diameter of ball = 2.7 in.Height of can = height of 3 tennis balls = 3(2.7) = 8.1 in.

Radius of can or tennis ball: 2.7 ÷ 2 = 1.35 in.Can: V = πr2h = π(1.35)2(8.1) ≈ 46.377 in3

1 tennis ball: V = 4 − 3 �πr3 = 4 − 3 �π(1.35)3 ≈ 10.306 in3

3 tennis balls: V = 3(10.306) = 30.918 in3

Percentage of the can fi lled by tennis balls:

30.918 −−−− 46.377 ≈ 0.667, or 66.7%

Empty space in can: 46.377 – 30.918 ≈ 15.46 in3

Partial Credit (1 point) will be given for each of 4 answers: the correct can dimensions OR the correct percentage of can fi lled by tennis balls OR the correct mathematical reasoning and process for fi nding the percentage but based on incorrect calculations OR the correct amount of empty space in the can.

No credit will be given for an incorrect and incomplete answer.

TOTAL 11

260-261_SBAC_A_C3_C08_PTR_793945.indd 261260-261_SBAC_A_C3_C08_PTR_793945.indd 261 20/11/14 3:52 PM20/11/14 3:52 PM

Cop

yrig

ht ©

The

McG

raw

-Hill

Com

pani

es, I

nc. P

erm

issi

on is

gra

nted

to r

epro

duce

for

clas

sroo

m

Stud

ent

Wor

k S

ampl

e






course 3 think smart for the smarter balanced assessment › cms › lib011 › ca01802504... ·...

Documents