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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.5-1

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

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Mikey is getting ready for his birthday party. He wants to give 2 toys to each of his 12 friends coming to his party. The toys come in packages of 5. Mikey tells his mom to buys 4 packages. Use numbers and words to explain why he is incorrect.

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

2 x 12 = 24 so Mikey needs 24 toys. 4 packages x 5 toys per package = 20 toys. He needs 4 more toys so he should have bought 5 packages.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.4-1

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

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Explain why the following is true.

12 = 3

6

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When I draw both diagrams, the same area is filled in.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.8

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

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Anna and Travis looked at the rectangles below. Anna stated that the area of rectangle A is less than the area of rectangle B because A is skinnier. Travis stated that both rectangles are the same. Who is right? Rectangle A 10 2

Rectangle B 4

5

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Travis is correct because both 2 x 10 = 20 and 4 x 5 = 20.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.D.2

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

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Amy is planting a garden that is 6 feet long and 12 feet wide. She planted ½ of the area with tomatoes, ¼ of the area with lettuce, and 1/8 of the area in carrots. How many square feet are left in the garden for radishes?

6 ft.

12 ft.

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

6 ft x 12 ft = 72 ft.2 (area) ½ x 72 = 36 ft2 (tomatoes) ¼ x 72 = 18 ft2 (lettuce) 1/8 x 72 = 9 fr2 (carrots) That leaves 1/8 x 72 = 9 ft2 (radishes)

They might also do 6 x 6 (half of 12) = 362 tomatoes 36/2 = 18 ft2

18/2 = 9 ft2 Item checked for: ☐ Bias & Sensitivity ☐ Style ☐ Answer Accuracy ☐ Evidence Statement ☐ Task Type ☐ Accept ☐ Accept with Edits ☐ Reject

MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.5-2

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

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Jill stated that ¾ is equivalent to 5/6 because she added 2 to the numerator and the denominator. Explain why she is incorrect.

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To find an equivalent fraction, you need to multiply and not add.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4C.4-3

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

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Choose the equation that correctly represents this diagram.

a. 5 x ¼ = 5/4 b. 5 x ¼ = 5 ¼ c. 5 + ¼ = 5 ¼ d. ¼ x ¼ x ¼ x ¼ x ¼ = 5/4

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A. 5 x ¼ = 5/4

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.D.1

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

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The Craft Camp is making bead bracelets today. Each bracelet tales 1/3 of a package of beads. Each package holds 60 beads. There will be 4 classes today with 8 students in each class. How many packages of beads will the Craft Camp need today?

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1/3 x 60 = 603

= 20 beads per student 8 x 4 = 32 kids 32 kids x 20 beads = 640 beads Think – I need 640 beads. Each package has 60. 60 x 10 = 600; 60 x 11 = 660, so I will need 11 packages.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.6-1

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

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The kindergarten teacher is making bags for her students. She is putting 1 box of crayons and 2 pencils in each bag. If she has 15 boxes of crayons and 24 pencils, how many bags can she make? What will be left over?

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They can make 12 bags with the remainder of 3 boxes of crayons left over.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.6-1

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

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Taylor has a bag of candy to share equally between him and 5 friends. The bag holds 128 pieces of candy. First, he gave 16 pieces to his little brother. Then he shared what was left over with his friends. How many pieces of candy will each person get?

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128 – 16 = 112 112/6 = 18 pieces with 4 left over

Wording and order of action is confusing. Is the little brother part of the friend group…which is could be interpreted as or is he the first step in the problem. If this is PBA, couldn’t they explain how they got their answer using words or numbers and explain.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.5-3

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

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Katherine and Eric both won 3 awards for poems they entered in the poetry contest. Katherine said she won awards for 2/3 of her poems while Eric only won awards for ½ of his poems. Eric disagreed because they both won the same amount of awards. Explain how Katherine’s statement can be true.

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Eric entered more poems than Katherine. Click here to enter text.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.6-3

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

Please write the complete item in the box below:

23 students in Mrs. Howell’s class were making treats with chocolate bars. Each student used 1/3 of a chocolate bar for their treat. If Mrs. Howell bought 10 chocolate bars, how many bars are left over? Use pictures and words to solve this problem.

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

2 1/3 bars are left over

Reword. Mrs. Howell’s class where making treats with chocolate bars. Each student used 1/3 of a chocolate bard for their treat. There are 23 students in Mrs. Howell’s class and she bought 10 chocolate bars. How much chocolate would be left over? Use pictures or words to solve this problem. Answers only suggest picture response.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.4-2

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

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Draw a diagram to prove that ¾ = ¼ + ¼ + ¼.

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+ + =

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.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:

Use an area model to show 124 ÷ 5. Correct Response:

5

5

124

10 50 10 50

4

20 → 4 left over

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See above.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.NF.4B-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:

3 x 56 =

a. 146

b. 86

c. 15

18

d. 8

18

e. 15

6

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

E. 156

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.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:

Josh was given the problem 3x ¼. He wrote the answer 314. His friend Sue said, “Your

answer is wrong; it should be ¾. Draw a picture that shows Sue is correct.

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

= ¾

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4. C. 3

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

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What is the rule being used in this In and Out box? In Out 6 60

60 600

600 6000

6000 60,000

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You are multiplying by 10. Click here to enter text.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4 NBT 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:

Drag and drop to complete the table. < 400 + 60 + 3 = Seventy-eight 8,104 800 + 10 + 4 3,071 = 293

a. 3000 +100 +70 + 1 b. 85 c. < d. > e. = f. 20 + 9 + 3 g. 463 h. 78 i. 200 + 90 + 3

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

85 < 400 + 60 + 3 78 = Seventy-eight 8,104 > 800 + 10 + 4 3,071 = 3000 +100 +70 + 1 293 = 200 + 90 + 3

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.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:

Choose which method is incorrect.

24 X 18

a. 24 X 18 32 (8 x 4) 160 ( 8 x 20) 40 (10 x 4) 200 ( 10 x 20) b. (8 x 24) + (10 x 24) =

c. (20 x 18) + (4 x 18) =

d. (20 x 10) + (4 x 8) =

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D. (20 x 10) + (4 x 8) = Click here to enter text.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: Click here to enter standard.

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 shirt costs $8.00. A backpack costs four times as much as the shirt. How much does the backpack cost? Drag the boxes to show the correct diagram for this problem.

$8

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

Kids need to drag the correct number of $8 and then drag the correct to represent the backpack.

$8 $8 $8 $8

Big rectangle the sizes of 2, 3, 5 times as big are distractors.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4 NBT 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:

Check the two numbers that would be correct for the missing number. 542 X 4 4 7 6 3 8 1 5

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6 1

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.7-4

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

Please write the complete item in the box below:

A recipe calls for 2/3 cup of sugar. Kristen wants to triple the recipe. Use arrows on the number line to show how much sugar she will need.

0 1 2 3 4 How much sugar is needed to triple the recipe?

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

0 X 1 X 2 3 4 X 2 cups

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.5-5

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

Please write the complete item in the box below:

Mariella plans to have eight friends at her party. She wants to serve each friend 5/8 pint of ice cream. She thinks she needs to buy 40/64 pints of ice cream to have enough for everyone. Is she correct? Explain. Possible Response:

8 of these turn to:

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

No, she needs to buy 40/8 or 5 whole pints of ice cream. 8 x 5/8 = 40/8

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.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:

Explain why this diagram is not correct. + = +

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It should be ½ + 2/4 = 2/4 + ½. Click here to enter text.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.7-1

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

Please write the complete item in the box below:

Sammy and Ashley are running the same race. Sammy has completed 2/3 of the race. Ashley has completed 8/12 of the race. Use the number lines to show how much each runner has completed.

Who has completed more of the race? Explain your answer.

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They have both completed the same amount. Both distances are at the same spot on the number line.

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MATH: 3-5

Sammy

Ashley

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4.C.7.2

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

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Use the number lines to show that 2/3 and 5/8 are both greater than ½.

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Click here to enter text.

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MATH: 3-5

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

Grade: ☐ 3 ☒ 4 ☐ 5 Mathematics Standard: 4C.7-3

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

Please write the complete item in the box below:

Use arrows to show 1 12

+ 2 14 on the number line.

What is the sum?

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Click here to enter text. Click here to enter text.

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MATH: 3-5