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

Chapter 7 Performance Task

PERIOD

SCORE

A Party for Isabella

Reynaldo and his daughter Rosie are hosting a birthday party for Rosie's grandmother Isabella.

Reynaldo built horseshoe pits in his yard for the party. The object is to throw a horseshoe from

one end of the pit around a wooden stake at the other end. Rectangles ABCD and FGHJ show

the raised horseshoe pits. Points S (3.5, 3) and S (43.5, 3) show the locations of the wooden

1

2

stakes. Each unit on the grid represents 1 foot.

y 9

6B

C

G

H

3

S1

S2

A

D

F

J

x

O

3

6

9

12 15 18 21 24 27 30 33 36 39 42 45 48

-3

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

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

Part A

Diego wants to know how far apart the stakes are, so he transforms point S 1

to point S . Describe the transformation and give the distance. 2

Part B

Diego realizes his own yard isn't long enough for the horseshoe pit. Uncle Reynaldo says that in a similar game called quoits, the stakes are only 21 feet apart. Describe a translation that could be used to move point S and

2

rectangle FGHJ so that the new location of the stake, point S , is 21 units 3

from S . Identify the coordinates of the vertices of quadrilateral F'G'H'J' and 1

point S . Compare the size and shape of the new quadrilateral F'G'H'J' with 3

the preimage.

Part C

Rosie hangs a pi?ata from a tree

branch while Isabella watches.

The tree and Isabella cast

h ft

shadows as shown. How tall is

5 ft

the tree? Explain how you used

similar triangles.

8 ft

12 ft

Course 3 ? Chapter 7 ? Congruence and Similarity 119

Rosie and Diego decorate the

y

8

house. Half of the house's roof

and a side of the house are

Q P

represented on the coordinate plane. Rosie and Diego attach

Roof N

M L

4

lights to one side of the house's

2

roof, as shown by points L, M, N, P, and Q.

-14 -12 -10 -8 -6 -4 -2 O

x 2 4 6 8 10 12 14

-2

K -4

Part D

Reflect KL and LQ across the y-axis to show the other side of the house and the roof. Reflect the labeled points to show the lights Rosie and Diego will hang on the other side of the roof. Explain how the length of each preimage segment compares with the reflected image.

Part E

The pitch of a roof refers to the slope of the roof. Find the pitch of the left side of the roof. Then verify the slope by using a different set of points. Does it matter which points you choose? Explain.

Part F

Calculate the slope of L'Q'. How does the slope of LQ compare to the slope of its image L'Q' ? Make a conjecture about the slope of a line and the slope of its reflection across the y-axis. Support your conjecture with a separate example.

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

120 Course 3 ? Chapter 7 ? Congruence and Similarity

Chapter 7 Performance Task Rubric

Page 119 ? A Party for Isabella

Task Scenario

Students will use translations and reflections to describe the effects of transformations and to produce images on the coordinate plane. Students will also use similar triangles to indirectly measure objects and to identify the slope of a line to solve problems involving birthday party events.

CCSS Content Standard(s)

8.EE.6, 8.G.1, 8.G.1a, 8.G.1b, 8.G.2, 8.G.4, 8.G.5

Mathematical Practices MP1, MP2, MP3, MP4

Depth of Knowledge DOK2, DOK3, DOK4

Part

Maximum Points

Scoring Rubric

A

1

Full Credit:

S (3.5, 1

3)

(3.5

+

40,

3)

S (43.5, 2

3),

so

it

is

a

translation

40 units to the right. The distance between the stakes is

40 feet.

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

B

3

Full Credit:

Point S is 21 feet from point S , so point S is at (3.5 + 21, 3) or

3

1

3

(24.5, 3).

An alternative is to translate S (43.5, 3) 19 units to the left. 2

Vertices are 1.5 units left or right and 2 units up or down from S : 3

F'(23, 1), G'(23, 5), H'(26, 5), J'(26, 1).

The image is congruent to the preimage because it was created using a translation.

Partial Credit (1 point) will be given for each of these 3 answers: a correct translation OR correct coordinates OR a correct comparison.

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

C

2

Full Credit:

Two vertical objects and their shadows form two sides of right

triangles. The angles formed by the sun's rays are the same, so

the triangles are similar. To solve, use the property that

corresponding sides of similar triangles are proportional.

-5h = -182-, 8h = 60, h = 7.5; The tree is 7.5 feet tall.

Partial Credit (1 point) will be given for a correct explanation OR the correct height.

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

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

254

Course 3 ? Chapter 7 ? Performance Task Rubric

Chapter 7 Performance Task Rubric, continued

Part

D

Maximum Points

2

Scoring Rubric

Full Credit:

y 8

QQ

P

Roof N

M

4

P N M

L

2

-14 -12 -10 -8 -6 -4 -2 O -2

K -4

2 4 6 8 10

L x

12 14

K

E F TOTAL

Reflections do not change segment length, so KL = K'L' and LQ = L'Q'.

Partial Credit (1 point) will be given for a correct graph OR a correct comparison.

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

2

Full Credit:

Sample answer:

L(?12, 2) and Q(0, 6): slope = -06-?-?(?-212-) = -142- = -31

M(?9, 3) and N(?6, 4): slope = -?6-4-??-(3?-9-) = -31

The slope is the same for any two points on the line, so it does

not matter which points are chosen.

Partial Credit (1 point) will be given for the correct slopes for two sets of points but no explanation OR the correct slopes for only one set of points with a correct explanation.

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

3

Full Credit:

L'(12, 2) and Q'(0, 6): slope = -06-??-12-2 = ?-31

The slope shows the same relationship between the rise and run,

1:3, as for LQ, but because it is a reflection, the sign of the slope

is the opposite.

Sample answer: Conjecture/support: Reflecting a line with slope m across the y-axis results in a line with slope ?m. When line y = 2x is reflected across the y-axis, it forms line y = ?2x.

Partial credit (1 point) will be given for each of 3 answers: the correct slope OR an accurate comparison of the slopes OR a valid a conjecture with a supporting example.

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

13

Course 3 ? Chapter 7 ? Performance Task Rubric

255

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

Performance Task Rubrics

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