Grade 8 Mathematics

GRADE 8 MATHEMATICS Smarter Balanced Assessment Questions Question Number 1 For each number, indicate whether it is rational or irrational. Answer Key Question 1 Item Claim #2 1 Domai Target n NS A

Exemplar: (shown at right) Rubric: (1 point) Student correctly classifies each number as rational or irrational (R,I,R,I,R). DOK CONTE NT MP Key 1 8.NS.A.1 N/A

See exemplar Question Number 2 A square with side length s has an area of 324 square centimeters. This equation shows the area of the square. What is the side length of the square in centimeters? Answer Key Question 2 Item Claim #3 1 Domai Target n EE

B DOK CONTE NT MP Key 1 8.EE.A.2 N/A 18 Key: 18 Rubric: (1 point) Student enters the correct side length. Question Number 3

The school is 100 meters from Jasons house. The following describes his most recent trip: He walked 50 meters toward school in 2 minutes. He realized he left a book at home. He turned around and walked home at the same speed. He spent 1 minute looking for his book. He walked all the way to school at twice his original speed. Draw a line that accurately represents Jasons trip. Answer Key Question 3 Item Clai m #5 1 Doma Targe in t F DOK F

Exemplar: (Shown at right) Rubric: (1 point) Student correctly graphs all three line segments. 2 CONTEN MP T 8.F.B.5 N/A Key See exemplar Question Number 4 Write each number on its correct position along the number line.

Answer Key Question 4 Ite m #1 Claim 1 Doma in NS Targ et A Exemplar: (shown at right) Rubric: (2 points) student places all three values at the correct positions on the number line

DOK 2 CONTE NT 8.NS.A.2 M P 6 Key See exemplar Question Number 5 Draw the image of the figure after the following transformation: A reflection over the x-axis A horizontal translation 7 units to the left

Answer Key Question 5 Item #6 Clai m 1 Domai Target n G G Exemplar: (shown at right) Rubric: (2 points) Student correctly reflects and translates all points. (1 point) Figure is reflected over the x-axis correctly; no DOK

2 CONTE NT 8.G.A.3 MP Key N/A See exemplar Question Number 6 A 13-foot ladder is learning on a tree. The bottom of the ladder is on the ground at a distance of 5 feet from the base of the tree. The base of the tree and the ground form a right angle as shown. Write the distance, in feet, between the ground and the top of the ladder.

Answer Key Question 6 Item #9 Clai m 1 Domai Target n G H DOK 2 CONTE NT 8.G.B.7 MP Key

N/A 12 Key: 12 or its equivalent Rubric: (1 point) Student enters the correct distance Question Number 7 The points show different locations in Joes town. Each unit represents 1 mile. Write the shortest distance, in miles, between Joes home and the park. Round your answer to the nearest tenth. Answer Key Question 7 Item Claim #10

1 Domai Target n G H DOK 2 CONTE NT 8.G.B.8 MP Key N/A 3.6 Key: 3.6

Rubric: (1 point) Student enters the distance rounded to the nearest tenth of a mile. Question Number 8 A cone with radius 4 feet is shown. Its approximate volume is 165 cubic feet. Write the height of the cone, in feet. Round your answer to the nearest hundredth. Answer Key Number 8 Item Claim #11 1

Domai Target n G I DOK 2 CONTE NT 8.G.C.9 MP Key 6 9.84 9.85 Key: 9.84-9.85 Rubric: (1 point) Student enters the correct height within the indicated range (to

accommodate different acceptable values of pi) Question Number 9 Joe solved this linear system correctly. 6x + 3y = 6 y = -2x + 2 These are the last two steps of his work. 6x 6x + 6 = 6 6=6 Which statement about this linear system must be true? a. x must equal 6 b. y must equal 6 c. There is no solution to this system. d. There are infinitely many solutions to this system. Answer Key Number 9 Item #13 Clai

m 1 Doma in EE Targe t D DOK 2 CONTE NT 8.EE.C. 8b MP Key N/A

D Key: D Rubric: (1 point) Student selects the correct statement Question Number 10 An empty corn silo in the shape of a cylinder is being filled with corn. The silo is filled at a constant rate for a total of 10 hours. The table shows the amount of corn, in cubic feet, in the silo at the given number of hours after filling started. Write the percent of the silo that is filled with corn at 10 hours. Answer Key Number 10 Ite m #2 5

Clai m 4 Doma in G, RP Targ et A DOK CONTENT MP Key 2 8.G.C.9,

7.RP.A.3 1, 4 90.9 91 Key: 90.9-91 Rubric: (2 points) Student enters a correct numerical value for the percent of volume that is filled at the end of 10 hours (accept values in the range 90.9-91) (1 point) Student gives the amount filled after 10 hours (8250) but forgets to find the percentage of the filled amount to the volume Question Number 11 The table shows the relationship between the average number of hours students study for a mathematics test and their average grade. Which type of function is most likely to model these data?

a.Linear function with positive slope b.Linear function with negative slope c. Non-linear function that decreases then increases Answer Key Number 11 Item Claim #23 4 Domai Target n F D DOK 2 CONTE NT

8.F.B.5 MP Key 4 D Key: D Rubric: (1 point) Student selects the correct type of function Question Number 12 Two figures are shown on the coordinate grid. Show that Figure A and Figure B are congruent by describing a sequence of basic transformations that maps Figure A onto Figure B. In your response, be sure to identify the transformations in the order they are Answer Key Number 12 Item

Claim #20 3 Doma in G Targe t B DOK 3 CONTE NT 8.G.A.2 MP

Key 1, See 2, exemplar st Exemplar 1: 1 transformation is to reflect over the 3 y-axis. 2nd transformation is to rotate 90 counter-clockwise about the origin. 3rd transformation is to translate right by 2 units. Exemplar 2: 1st transformation is to reflect over the x-axis. 2nd transformation is to rotate 90 clockwise about the origin. 3 rd transformation is to translate right by 2 units. Other correct series of transformation are possible. Rubric: (2 points) Student describes three transformations with sufficient detail to prove that Figure A and Figure B are congruent. (1 point) Student either describes all three transformation in general terms, without the degree of precision necessary to prove congruency (e.g. rotation, reflection, and translation) or correctly Question Number 13 Consider this equation: c = ax bx

Joseph claims that if a, b, and c are non-negative integers, then the equation has exactly one solution for x. Select all cases that show Josephs claim is incorrect. a. A b =1, c = 0 b. A = b, c 0 c. A = b, c=0 d. A = b, c 0 e. a b , c = f. a b, c = 0 Answer Key Number 13 Item Claim Doma in Targe t DOK

CONTE NT MP Key #18 3 EE D 3 8.EE.C.7 a 1, 3 See exemplar

Exemplar: (shown at right) Rubric: (1 point) Student correctly selects the second and third options. Question Number 14 Claire is filling bags with sand. All the bags are the same size. Each bag must weigh less than 50 pounds. One sand bag weighs 58 pounds, another sand bag weighs 41 pounds, and another sand bag weighs 53 pounds. Explain whether Claire can pour sand between sand bags so that the weight of each bag is less than 50 pounds. Answer Key Number 14 Item Claim

#31 2 Doma in Targe t 2A DOK 3 CONTE NT 6.SP.3 MP Key See Below

Sample top-score response: since the mean is more than 50, (58+41+53)/3=50 2/3 pounds, it is not possible to move sand between bags so that each sandbag weighs no more than 50 pounds. For full credit: The response demonstrates a full and complete understanding of solving problems of this type. The response contains the following evidence: Student provides sufficient support for the conclusion that it is not possible to have less than 50 pounds or less in each sandbag (e.g. Question Number 15 A sequence of transformations is applied to a polygon. Select all statements which indicate a sequence of transformations where the resulting polygon has an area greater than the original polygon. Reflect over the x-axis, dilate about the origin by a scale factor of , translate up 5 units Rotate 90 counterclockwise around the origin, dilate about the origin by a scale factor of Dilate about the origin by a scale factor of , rotate 180 clockwise around the origin, translate down 2 units

Dilate about the origin by a scale factor of 2, reflect over the y-axis, dilate about the origin by a scale factor of Answer Key Number 15 Item Claim #16 3 Doma in G Targe t G Exemplar: (shown at right) Rubric: (1 point) Student correctly selects the second and fourth statements.

DOK 3 CONTE NT 8.G.A.3 M P 2 Key See exemplar

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