ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.4

Task Type: ☐ I ☐ II ☒ III Math Practice: ☒1 ☐ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

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Mateo was given a book of 50 “Easy” level Sudoku puzzles for his birthday May 12. His goal is to complete the book by summer break which starts June 1 this year.

1. About how many puzzles does he need to complete each day to reach his goal? 2. What is a reasonable estimate for how long it takes to complete one puzzle?

Use your response to #2 to complete #3

3. He finishes his goal. How long did it take him to complete his book? Express your answer in hours and minutes.

Please provide the correct response below: Please provide comments/clarifications below:

Answer 1. 50÷18 = 2 or 3 each day Answer 2. 20 – 30 minutes (no wrong answer here) Answer 3. 50 x 30 = 1500 minutes = 25 hours (depends on #2 answer)

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.3

Task Type: ☐ I ☐ II ☒ III Math Practice: ☒1 ☒ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

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Meg plants a redwood tree in 1960. The first 23 years it grew to 161 feet. In 2003 it was 361 feet tall. Lightning hit the tree in 2009 and killed the tree. How tall was the tree when it died? Explain your answer using all assumptions you used.

Please provide the correct response below: Please provide comments/clarifications below:

411 ft. tall 161÷23 = 7; 200÷20 = 10 First 23 years = 7 ft per year Next 20 years = 10 ft per year Average 8.4 ft per year 50.37 ft. I assumed average rainfall and growth

161 200 +50 411 feet tall

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.2

Task Type: ☐ I ☐ II ☒ III Math Practice: ☐1 ☒ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

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Find the equation that does not belong with the other two in its row. 23x + 7 = 11 7x + 4 = 3x + 4(x + 1) -x – 15 = 4x – 20

3(x – 4) = 4x – x +12 1

4 x = 3

4 x - 1

2 x + 8 1

2 x – 8 = 2(1

4x – 4)

2(x – 4) + 2 = 1

2x 8x + 5 = 2(4x +5) 1

3 x + 5 = 1

3 (x – 15)

Please provide the correct response below: Please provide comments/clarifications below:

They would click on the correct response. Row 1. Equation 2 Row 2. Equation 2 Row 3. Equation 1

Row 1 – one solution, infinite solution, one solution Row 2 – infinite solution, no solution, infinite solution Row 3 – one solution, no solution, no solution

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.4

Task Type: ☐ I ☐ II ☒ III Math Practice: ☒1 ☒ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

Please write the complete item in the box below:

John was given the task of estimating the square roots of 5 non-perfect square numbers: √8, √52, √63, √127, √149. He thinks if he totals these numbers and then finds the square root of that sum, it would be equivalent to the sum of the square roots. Use estimation to determine if John’s theory is correct. Explain your answer.

Please provide the correct response below: Please provide comments/clarifications below:

√8 ≈ 3 √52 ≈ 7 √63 ≈ 8 √127 ≈ 11 √149 ≈ 12

8 + 52 + 63 + 127 + 149 = 399 √399 ≈ 20; 20 ≠41 Theory is incorrect because the sum of the roots is 41 and the sum of numbers is 399 and √399 is about 20, not 41.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.4-1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☒6 ☒7 ☐8

Please write the complete item in the box below:

Solve expressing your answer in scientific notation.

(-1.08 x 102) ÷ (6 x 10-2)

Please provide the correct response below: Please provide comments/clarifications below:

-1.8 x 103

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.2

Task Type: ☐ I ☐ II ☒ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☒6 ☒7 ☐8

Please write the complete item in the box below:

John is making square picture frames for his paintings. He wants the frame to be 6 inches shorter than twice its width. John needs the perimeter to be 144 inches for each frame. What will the dimensions be, in inches, for each picture frame? Show your work.

Please provide the correct response below: Please provide comments/clarifications below: Width = 22 inches Length = 38 inches

2w – 6 = l 2(22) – 6 = l 44 -6 = l 38 = l

2w + 2l = 144 2w + 2(2w – 6) = 144

2w +4w – 12 = 144 6w – 12 = 144 6w = 132 W = 22

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.1

Task Type: ☐ I ☐ II ☒ III Math Practice: ☒1 ☐ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

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The desk is 30 inches high. Math textbooks are 1.25 inches thick and dictionaries are 2 inches thick.

1. Construct a table that contains the total height of a stack of books (up to 10 of each) on top of the desk.

2. Write an expression that can be used to determine total height (H) of any combination of math texts (M) and dictionaries (D).

3. Use your expression and/or table to determine the following: a. How tall would a stack of 6 math books and 8 dictionaries be when stacked

on the desk? 4. What different combinations of books would measure exactly 4 feet tall?

Please provide the correct response below: Please provide comments/clarifications below:

Responses: 1. See table 2. 1.25m + 2d + 30 = H. 3. 1.25(6) + 2(8) + 30 = 53.5 in. 4. 9 dictionaries, 0 math or 4 dictionaries, 8

math

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MATH: 6-8

Height of Books on Desk

10 50 51.25 52.5 53.75 55 56.25 57.5 58.75 60 61.25 62.5 9 48 49.25 50.5 51.75 53 54.25 55.5 56.75 58 59.25 60.5 8 46 47.25 48.5 49.75 51 52.25 53.5 54.75 56 57.25 58.5 7 44 45.25 46.5 47.75 49 50.25 51.5 52.75 54 55.25 56.5 6 42 43.25 44.5 45.75 47 48.25 49.5 50.75 52 53.25 54.5 5 40 41.25 42.5 43.75 45 46.25 47.5 48.75 50 51.25 52.5 4 38 39.25 40.5 41.75 43 44.25 45.5 46.75 48 49.25 50.5 3 36 37.25 38.5 39.75 41 42.25 43.5 44.75 46 47.25 48.5 2 34 35.25 36.5 37.75 39 40.25 41.5 42.75 44 45.25 46.5 1 32 33.25 34.5 35.75 37 38.25 39.5 40.75 42 43.25 44.5 0 30 31.25 32.5 33.75 35 36.25 37.5 38.75 40 41.25 42.5 0 1 2 3 4 5 6 7 8 9 10

Math Texts

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.D.2

Task Type: ☐ I ☐ II ☒ III Math Practice: ☒1 ☒ 2 ☐ 3 ☒ 4 ☒5 ☐6 ☒7 ☐8

Please write the complete item in the box below:

Joe and Fred are going camping and wanted to purchase some snacks. Joe bought one bag of chips and three candy bars for $9.75. Fred bought two bags of chips and two candy bars for $9.50.

1. What is the price for a single bag of chips? 2. What does one candy bar cost?

Explain your answers.

Please provide the correct response below: Please provide comments/clarifications below:

Answer 1 - $2.50 Answer 2 - $2.25 C = chips; b = candy bar C + 3b = 9.75 2c + 2b = 9.50 C = -3b + 9.75

2 (-3b + 9.75) + 2b = 9.50 -6b +19.50 + 2b = 9.50 -4b +19.50 = 9.50 B = $2.50 per candy bar C + 3(2.50) = 9.75 C + 7.50 = 9.75 C = $2.25 per bag of chips

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.7a (8.C.2)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Show steps in solving this equation for x.

3(2x – 4) = 12(12 x – 1)

What conclusions can you draw for the solution set?

Please provide the correct response below: Please provide comments/clarifications below:

6x – 12 = 6x – 12 +12 +12 6 𝑥6

= 6 𝑥6

X = X infinitely many solutions

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.7b

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☒ 2 ☐ 3 ☐ 4 ☒5 ☒6 ☒7 ☐8

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Solve:

12 (45 x + 6) = 3

5 x – 8

Please provide the correct response below: Please provide comments/clarifications below:

2/5 x + 3 = 3/5 x – 8 2/5 x +11 = 3/5 x 11 = 1/5 x 55 = x

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.5-1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☒1 ☐ 2 ☐ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Graph the relationship between the amount of brown M&Ms in a bag and the rest of the other colors as shown in this table: Brown 3 10 13 20 Other 9 30 39 60

What does the slope of your graph represent?

Please provide the correct response below: Please provide comments/clarifications below:

Answers may vary: 1. How many other M&Ms there are for each

brown one. 2. Unit rate 3. There are three others for every brown. 4. There are 3 times as many others than there

are brown.

5. Browns are 1/3 of the bag.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.4-2

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☒6 ☒7 ☒8

Please write the complete item in the box below:

Your calculator shows this answer on the screen: 6.37E6.What standard notation amount is this?

a. 637,000,000 b. 63,700.000 c. 6,370,000,000 d. 6,370,000

Please provide the correct response below: Please provide comments/clarifications below:

6.37 x 106 = 6,370,000 Answer D

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.4-1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☒6 ☒7 ☐8

Please write the complete item in the box below:

Subtract:

2.45 x 106 – 45

a. 2,000,000 b. 2,449,995 c. 20,000,000 d. 24,449,955

Please provide the correct response below: Please provide comments/clarifications below:

2,449,955 = Answer B Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.F.1-1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☒ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Determine if which relation is a function.

a)

b) x 6 7 8 7 9

x 1 2 1 2

y 75 80 86 87 99

y 6 5 4 5

c) Input Output

d) x y

0 0

-2 -4

e) (7, -1) (9, -7) (7, 0) (12, -1) (15, 0)

1 -1

-1 -3

2 0

1 -1

-1 1

2 0

Please provide the correct response below: Please provide comments/clarifications below:

C, D are functions These are not functions:

a. 7→80 7→87 b. 1→6 1→4 e. 7→ -1 7→0

Check grammar of the prompt; add Check al that apply.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2018

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.3

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☒ 4 ☐5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

A blue whale weighs approximately 4 x 104 pounds. A tadpole weighs about 2 x 10-2. About how many times heavier is a whale than a tadpole?

a. 20 million b. 2 thousand c. 2 million d. 200 thousand

Please provide the correct response below: Please provide comments/clarifications below:

40,000 ÷ .02 = 2 million Answer C

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.G.4 (8.C.3.2)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☐ 2 ☒ 3 ☐ 4 ☒5 ☒6 ☐7 ☐8

Please write the complete item in the box below:

Cy says that these 2 figures are congruent. Justify or refute his statement by describing a sequence of rotations, reflections, translations and/or dilations to support your conclusion.

Please provide the correct response below: Please provide comments/clarifications below:

Answers will vary but should include a rotation, reflection, dilation, and translation. The sequence may vary. The axis of the reflection may vary.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.G.2 (8C.3.2

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☐ 2 ☒ 3 ☐ 4 ☒5 ☒6 ☐7 ☐8

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There is a sailing race at Lake Pleasant. The sail on each boat must be congruent. Describe the sequence of translations, reflections, rotations, and/or dilations which could prove that boat A’s sail is congruent to boat B.

Please provide the correct response below: Please provide comments/clarifications below:

Answers may vary. Should/could include a reflection ad a translation. Can include a rotation. Cannot include dilation.

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MATH: 6-8

A B

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☒7 ☐8

Please write the complete item in the box below:

Solve:

(5-3) ( 59

55 ) =

Please provide the correct response below: Please provide comments/clarifications below:

5 Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.8b (8.C.2)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Solve the given system of equations and justify your reasoning. -3x + y = 2 -9x +3y = 18

Please provide the correct response below: Please provide comments/clarifications below:

No solution because they are parallel lines. Justification: The slopes are equal but they have different y intercepts. Acceptable response could include a graph showing that the lines are parallel.

-3x +y = 2 Y = 3x + 2 -9x + 3y = 18 3y = 9x + 18 Y = 3x + 6 They have the same slope.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.5-2

Task Type: ☒ I ☐ II ☐ III Math Practice: ☒1 ☐ 2 ☐ 3 ☒ 4 ☒5 ☒6 ☐7 ☒8

Please write the complete item in the box below:

Compare the table of miles per gallon to the given equation. Which vehicle goes farther on 15 gallons of gasoline? Car A Gallons 2 5 8 12 Distance 56 140 224 336

Car B Y = 3/x X = number of gallons Y = distance travelled What is the unit rate in miles per gallon of the vehicle that goes the farthest?

Please provide the correct response below: Please provide comments/clarifications below:

Car B 31 mpg

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☒7 ☐8

Please write the complete item in the box below:

Solve:

(5-3) (55) =

Please provide the correct response below: Please provide comments/clarifications below:

52 and 25 Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.1

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☐ 2 ☐ 3 ☐ 4 ☐5 ☐6 ☒7 ☐8

Please write the complete item in the box below:

Solve:

(a4) ( 𝑎2

𝑎−3) =

Please provide the correct response below: Please provide comments/clarifications below:

The answer is a9 Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/10/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.EE.8a (8.C.1.2)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☒ 2 ☒ 3 ☐ 4 ☒5 ☒6 ☒7 ☐8

Please write the complete item in the box below:

Solve this system of equations by graphing. 6x + 4y = 12 7x + 5y = 15 Correct response:

Please provide the correct response below: Please provide comments/clarifications below:

(0,3) Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.F.1-2

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☒ 2 ☐ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Roger solves the solution y = 2x – 4 and y = x – 1 and finds the solution (3,2). Use a graph to show Roger’s solution is reasonable. Correct response:

Please provide the correct response below: Please provide comments/clarifications below:

Roger’s solution is correct. Click here to enter text.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.F.1-2

Task Type: ☒ I ☐ II ☐ III Math Practice: ☐1 ☒ 2 ☐ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

Using the graph showing profit as a function of popsicle sales, answer the following questions:

a. What is the minimum number of popsicles that must be sold before they begin showing a profit?

b. How much profit is produced when 100 popsicles are sold?

Please provide the correct response below: Please provide comments/clarifications below:

Answer A. 60 popsicles must be sold Answer B. $41.00

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.G.2 (8.C.5.2)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☒ 2 ☒ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

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Rotate figure ABCD about the origin CCW 90° and then reflect it over the y-axis.

Please provide the correct response below: Please provide comments/clarifications below:

Student will create figure on the graph as shown in the answer.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/11/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.G.B (8.C.5.3)

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☒ 2 ☒ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

Please write the complete item in the box below:

How can you show that the slope of a line is the same between any two points on the line?

Please provide the correct response below: Please provide comments/clarifications below:

You can calculate the slope of a line for different pairs of points and see that the slope is the same. The legs of the right triangle represent the change in y and the change in x that make the constant slope ration.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Date: 6/12/2013

Grade: ☐ 6 ☐ 7 ☒ 8 Mathematics Standard: 8.C.5.2

Task Type: ☐ I ☒ II ☐ III Math Practice: ☐1 ☒ 2 ☒ 3 ☐ 4 ☒5 ☐6 ☐7 ☐8

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In the coordinate plane, ∆ABC is similar to ∆ADE. What is the value of x?

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X = 6

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MATH: 6-8