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

Grade: ☒ 6 ☐ 7 ☐ 8 Mathematics Standard: 6.EE.A.3/6.C.1.1 - evidence

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

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Write an equivalent expression for 6x – 4 – 3x

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

6x – 4 – 3x = 6x – 3x – 4 = 3x -4 If you had 6x’s and you took away 3x’s you would be left with 3x’s. The 4 would be the same because there re no like terms to combine it with.

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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: 6.EE.A.3/Evidence 6.C.1.1

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

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Using models, numbers, and/or words, explain why 6(x + 2) = 6x + 12. Possible Response:

x x x x x x

x + x + x + x + x + x = 6x

2 2 2 2 2 2 2 + 2 + 2 + 2 + 2 + 2 = 12

So, 6x + 12

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6 groups of x + 2 items in each group. See sample above.

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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: 6.EE.A.1/Evidence 6.EE.1-2

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

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Evaluate the following expression in simplest form:

148 – ( 23 )2 + 9.4

Check all that apply

a. 156 4345

b. 156 8690

c. 156.96

d. 156.84

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

A and C are correct Response B not in simplest form Response D is incorrect – subtracted fraction from whole number incorrectly

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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: 6.EE.A.1/Evidence 6.EE.1-2

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

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Evaluate the expression below:

1242 − 5(92)5

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

167.4 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: 6.EE.A.1/Evidence 6.EE.1-1

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

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Mr. and Mrs. Brant had three children. Each child got married and had 3 children of their own. Those children also got married and had 3 children. Write the situation above as a numerical expression using exponential notation showing how many children were in the Brant lineage.

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3∙3∙3 = 33 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: 6.EE.A.3/Evidence 6.C.1.1

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

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The expression 17c + 20c + 453 is the cost of gas, food, and lodging for c students on a field trip. Use the information above to answer the questions below.

1. Simplify the expression 17c + 20c + 453. Use models, words, and/or numbers to express your answer.

2. Which of the following answers could be used to find the total cost of the field trip

for 90 students? Check all that apply. a. 37(90) + 453 b. 17(100) – 17(10) + 20(90) + 453 c. 17(90) + 453(90) + 20(90) d. 17(9∙10) +20(9∙10) + 450 + 3 e. 17(50) + 17(40) + 20(90) + 453 f. 37(9) + 37(9) + 400 + 50 + 3

Please provide the correct response below: Please provide comments/clarifications below: 17c + 20c + 453 = 37c + 453 A, B, D, and E

C is incorrect because multiplied 453∙90 F is incorrect because 9 + 10 do not add up to 90

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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: 6.EE.2a/6.EE.A.2a/Evidence 6.C.1.1/6.EE.A.4

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

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Look at the problems below. The answer the questions below it.

26n∙8 26(n+8)

1. Zoraida and Bachel were discussing the problems above. Zoraida said they would have the same solution. Bachel disagreed. Use models, numbers, and/or words to explain who was correct.

2. Express both problems as verbal expressions.

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

Response 1. Bachel was correct. 26n∙8 = 8 groups of 26n. 26(n +8) = 26n + 208 = 208 added to 26 groups of n.

Response 2: 26n∙8 → the product of 26 and n multiplied by 8 26(n+8) → the sum of n and 8 multiplied by 26 or the sum of 26 times n and 26 multiplied by 8

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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: 6.NS.C.7b/Evidence 6.NS.5? there is none at this level for this standard

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

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Red the inequality below: -4.75 > -8.90 Which of the following read world contexts apply to the inequality? Check all that apply.

a. Sally Scubadiver is at 4.75 feet underwater which is higher than Sam Scubadiver who is at 8.90 feet underwater.

b. Dave’s debt went down from January when he owed $8.90 to March when he owed $4.75.

c. The temperature yesterday was -4.75° which is warmer than two days ago when it was -8.9°F.

d. Maria finished the race 4.75 seconds behind the winner. The next person finished the race 8.9 seconds after Maria.

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

Correct Answers: A, C, D Click here to enter text.

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MATH: 6-8

☐ Accept ☐ Accept with Edits ☐ Reject

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

Grade: ☒ 6 ☐ 7 ☐ 8 Mathematics Standard: Click here to enter standard.

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

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For every 2 hours Lalani works, she gets paid $22.46. The week, Lalani worked 7 hours. Create a table to show how much money she earned this week. Lalani owes her mother $85.00. She told her mom that she earned $89.84 this week. Will Lalani be able to pay off her debt? Why or why not?

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

x Y 2 22.46 4 44.92 6 67.38 7 78.61

X represents the # of hours; y the money earned. For every 2 hours, she earned $22.46. So for 6 hours I multiplied 22.46 by 3 because 6 has 3 groups of 2 hours. Then I found out she earned $11.23 in one hour so I added that to get 7 hours and $78.61.

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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: 6.EE.C.9/Evidence 6.C.8.2

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

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Talktime International Calling charges a flat service fee of $2.50 plus $0.25 per minute to place a call to any country in Europe. Show the relationship between the amount of time the call lasts and the cost of the call in an equation, table, and graph. Equation: _______________ Explain how you created the equation above. Table:

x y

a. What do x and y represent? b. How can you use your equation to fill in the table?

Graph:

a. How can your equation help you create this graph? b. What is the relationship you notice between the length of the call and the cost? c. How much would a 75 minute call cost? d. Which strategy did you use to solve the problem? Why?

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

Equation: 0.25x +2.50 = y X represents the number of minutes on the call plus the service charge of $2.50 for every call. Table: x = # of minutes; y = cost You can plug in the # of minutes for x to find out the cost (y).

Graph: The equation helped me create the table which gave me the coordinates to plot. The longer one speaks, the higher the cost. 75 minutes x 0.25 + 2.50 = $21.25; I multiplied the # of minutes and the cost per minute and added the base cost of $2.50.

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MATH: 6-8

Graph:

0

0.5

1

1.5

2

2.5

3

3.5

4

1 2 2 4 5

Cost of Phone Call

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

Grade: ☒ 6 ☐ 7 ☐ 8 Mathematics Standard: 6.EE.2C-1/6.EE.A.2C/Evid. 6.C.1.1/6.EE.A.4

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

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Read the expression below and then answer the questions below it. 27.62n + 13

20 + 14.34m – 26 97

100 n + 0.52 – 10.42m

1. Can you combine 14.34m and – 10.42m? Use models, numbers, and words to

explain your reasoning.

2. Evaluate the expression above if n = 3 and m = 6. Choose all that apply.

a. 43.03 b. 25.61 c. 15.79 d. 15 79

100

e. 43 3100

f. 25 61100

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

Answer 1. Yes – key - ∎ = -2m 14.34m = ∎∎∎∎∎∎∎ -10.42m = ∎∎∎∎∎ All are like terms so you can combine. Answer 2. B, F

A,E – added decimal incorrectly C,D – mixed up the values for m and n

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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: 6.EE.A.2C/Evidence 6.EE.2C-2

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

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Abraham is planting the triangular garden below. 13.2 ft. 9.9 ft.

Using the formula A = 𝑏ℎ2

figure out how many square feet of ground he has planted his garden in.

a. 11.55 ft2 b. 130.68 ft2 c. 23.10 ft2 d. 65.34 ft2

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

Correct Answer is D. 65.34 ft2

A – added then divided by 2 B- Forgot to divide by 2 C – Added base and height

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MATH: 6-8

16.5 ft. b= 9.9 ft.

h = 13.2 ft.

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

Grade: ☒ 6 ☐ 7 ☐ 8 Mathematics Standard: 6.NS.ba/Evidence 6.C.4

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

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The outdoor temperature in the evening was 6.5°. During the night, it dropped to the opposite. Use a number line and words to show the nighttime temperature. Possible Response: Nighttime Day time -6.5 0 6.5

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

The nighttime was the opposite of the daytime. The daytime was 6.5 – the opposite is -6.5.

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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: 6.NS.C.7B/Evidence 6.C.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:

Read the inequality below: -15.25 > - 20.52 Answer the questions below:

1. Using a number line and words, explain why the inequality above is true. 2. Create a real life context for this inequality.

Correct Response: -20.52 -15.25

-21 -20.5 -20 -19.5 -19 -18.5 -18 -17.5 -17 -16.5 -16 -15.5 -15

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

Because -15.25 is further right on the number line, it is greater than -20.52. Answers will vary.

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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: 6.NS.C.7C/Evidence 6.C.4

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

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Look at the number lines below and the answer the questions. Number Line #1

0 1 2 3 4 5 6 7 8 9 10 Number Line #2

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

1. Write the mathematical expression indicated by the length of the arrow above each. Number Line #1 _____________ Number line #2 _________________

2. Explain why both answers are the same.

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

I9I = 9 (#1) I-9I = 9 (#2) The answers are the same because each number line steps 9 units away from 0 which is the absolute value of 9 and -9.

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MATH: 6-8

ADE Summer Item Writing Institute Performance-Based Assessment Name: Click here to enter item author. Date: Click here to enter a date.

Grade: ☒ 6 ☐ 7 ☐ 8 Mathematics Standard: 6.NS.C.7a/Evidence 6.C.5

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

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Look at the number line below:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

1. Using numbers, symbols, and words, write 3 inequalities showing the relationship between the plotted points on the number line.

2. Choose one of your inequalities and explain why it is correct.

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

-8<4 4 > -8 Negative 8 is less than positive 4 Positive 4 is greater than negative 8

Answers will vary for #2. Example explanation: 4 is greater than -8 because 4 is further right on the number line than -8.

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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: 6.NS.C.5/6.NS.C.6C/Evidence 6.C.4

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

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A package delivery woman was delivering packages in a high rise building. She delivered her first package to the 16th floor. Then she descended 6 floors to deliver her next package. She then found a package that needed to be delivered 4 floors above her current floor. After that one was delivered, she travelled down 7 floors and for the last package she ascended 9 floors. Use a vertical number line and words to model and explain which floor she delivered to last.

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

She started at the 16th floor and went down 6 floors to the 10th floor. Then she went back up 4 floors to the 14th floor. After that she went down 7 floors to the 7th floor. Then finally she went up 9 floors back to the 16th floor where she started. She ended at the 16th floor.

Student should show appropriate vertical number line diagram to match the given scenario.

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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: 6.C.4

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

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Which of the following shows a pair of opposite numbers? Check all that apply.

A. B.

C. D. Jax says that D is one of the correct answers. Doreen tells him that 0 has no value so it is unable to be its own opposite. Who is correct and why?

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

B, D Jax is correct because 0 is equidistant from itself.

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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: 6.C.8.2

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

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1. Complete the table to display the data in the graph X Y

2. Bonnie says that the next point in this linear graph is (6, 7.5). Is she correct? Explain your reasoning. 3. Write the equation for this line in terms of x based on your table. Explain how you arrived at this answer. 4. Which of the following represents the change in y as x increases by 1.5?

A. Y increases by 1.5 C. Y stays the same B. Y decreases by 1.5 D. Y multiplies by 1.5

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

1. 2. Bonnie is correct because both x and y are increasing by 1.5

X Y 1.5 3 3 4.5

4.5 6

3. 𝑦 = 𝑥 + 1.5 The value of y is always the x value plus 1.5

4. A

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MATH: 6-8

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