mathematics grade 4. extended response item (scaffolded) 4.nf.4c; 4.nf.4b; 4.nf.4a; 4.nf.3a sylvia...

Mathematics

Grade 4

Extended Response Item (Scaffolded)

4.NF.4c; 4.NF.4b; 4.NF.4a; 4.NF.3aSylvia knows there are 5 people attending her party, including herself. She wants to be sure she makes enough punch for everyone. She estimates that each person will drink ¾ cup of punch.

Part AWrite an expression that represents how many cups of punch Sylvia will need to make.Part BFind the value of the expression in Part A. How many cups of punch will Sylvia need to make? Show your work.Part CDraw a fraction model to represent your answer from Part B. Explain your answer.Part DSylvia has cups of punch. Based on your answer in Part C, will this be enough punch for her party? Explain your answer or show your work.

Be sure to complete ALL parts of the task.Write your answer and show your work on the paper provided.

Do NOT type your answer in the text box below.

2

Exemplar Response

3

Part A 34

5

Part B

3 154 4

5 because 5 is the same as 51

and then multiply the numerators:

5 3 15 and then multiply the denominators: 1 4 4; so the answer is 34

3

or 154

.

Part C

Each large square is 1 cup, so there are 3

4 of a cup shaded in each square and

there are 5 squares, so if you count the shaded squares, you get 15, so there are 154

cups.

Part D

Yes, Sylvia will have enough punch because 12

4 is greater than 34

3 .

Or

Yes, because 1 3 2 3 6 3 32 4 4 4 4 4 4

4 3 4 3 3 3 .

RubricScore Designation Description

4 Thoroughly Demonstrated

The student correctly completes all elements of the item by solving word problems involving multiplication of a fraction by a whole number and using equations and fraction models to represent the problem (4.NF.4a, b, c) and by understanding addition and subtraction as joining and separating parts referring to the same whole (4.NF.3a).

3 Clearly Demonstrated

The student shows clear understanding of the skills listed above and correctly answers all parts, but one explanation or work shown is weak or insufficient.

2 Basically Demonstrated

The student shows basic understanding of the skills listed above by correctly answering three parts with at least two sufficient explanations or work shown.

1 Minimally Demonstrated

The student shows minimal understanding of the skills listed by correctly answering two parts with or without sufficient explanation or work shown.

0 Incorrect or irrelevant

The response is incorrect or irrelevant to the skill or concept being measured.

4

Student ResponseScore 2

5

Part C is correct; however, there is an insufficient explanation. Therefore, a higher score point cannot be given.

Part A is incorrect.

The student demonstrates a basic understanding of the mathematical concepts being measured by correctly answering and showing the work for Part B (5 x ¾ = 3 ¾) and Part D (Yes, because 4 ½ is more than 3 ¾).

Final Scoring: 2Part A: IncorrectPart B: Correct w/work shownPart C: Correct w/no explanationPart D: Correct w/work shown


6

Student correctly answers Parts C and D, but without sufficient explanation.

Part A is incorrect because the student provides an equation rather than an expression. Therefore, a higher score point cannot be given.

The student demonstrates a minimal understanding of the mathematical concepts being measured by correctly answering and showing the work for Part B (3/4 x 5 = 15/4).

Final Scoring: Score 1Part A: incorrectPart B: CorrectPart C: Correct w/no explanationPart D: Correct w/no explanation

Mathematics

Grade 6

Tanya played a computer game in which the score was calculated using the equation where s is the score, t is the number of points Tanya earned, and c is the number of points her computer opponent earned. Tanya recorded her scores for one week on the number line shown in the diagram.

The winner is determined by the highest score.Part AOn Tuesday, Tanya’s computer opponent scored 33 points. How many points did Tanya score? Explain your answer or show your work.Part BOn which day were the scores of Tanya and the computer the closest, but not the same? Who won that day? Explain your answer.Part CExplain what Friday’s score means about the number of points Tanya and the computer earned. Justify your answer using words and a mathematical statement.Part DOn which day(s) did Tanya win? Using t and c, write a mathematical statement to support your answer.

Extended Response Item6.NS.7; 6.EE.2; 6.EE.7

8

Exemplar ResponsePart ATanya scored 25 points.Substitute the values into the equation and solve.Part BTheir scores were closest on Saturday, and the computer won. The difference on Saturday is 6 points. Since t – c is negative, c is greater than t. This means the computer’s score was higher.OrTo compare scores, use the absolute value of the difference, which is The absolute value of all of the scores is the smallest on Saturday. Since is negative, c is greater than t. This means the computer’s score was higher.Part COn Friday Tanya and the computer earned the same number of points (or, they tied). This is true because if then Part DTanya won on Thursday, Monday, and Wednesday. Tanya will win whenever her score is greater than the computer’s, or whenever t > c.

9

RubricScore Designation Description

4 Thoroughly Demonstrated

The student successfully completes all elements of the item by demonstrating an understanding of ordering and absolute value of rational numbers (6.NS.7), in particular those related to number line comparisons (6.NS.7a, 6.NS.7c). The student demonstrates the ability to write, read, and evaluate expressions in which letters stand for numbers (6.EE.2), and to solve real-world and mathematical problems by solving equations (6.EE.7).


The student shows clear understanding of the skills listed above, but one of the explanations is weak or insufficientOrAll parts of the item are correctly done except for a minor computational errorOrThe student successfully completes three of the four parts of the item.


The student shows basic understanding of the skills listed above, but provides insufficient explanationsOrThe student successfully completes two of the four parts of the item.


The student shows minimal understanding of the skills listed above by completing only one of the four parts of the itemOrThe student had some correct answers, but provided no explanations.



10


11

Part A has the correct answer of 25, with support.

Part B has the correct answer, Saturday, with explanation.


12

Part C correctly explains the meaning of a zero on the graph with a correct justification but is missing a mathematical statement.

Part D has the correct answer, with correct support.


13

Part A has a correct answer, with work shown.

Part C correctly interprets the zero score on the graph as a tie, but lacks a sufficient justification.

Part B has the correct answer of Saturday, indicates the winner as the computer but does not provide a sufficient explanation.

Part D has the correct answer of Thursday, Monday, and Wednesday and gives mathematical statements for each day as support, but not a general statement.


14

Part A has a correct answer, but no explanation or work shown.

Part C correctly interprets the meaning of the zero score on the graph but the justification is insufficient.

Part B is incorrect.

Part D has the correct answer, but with no support.

Mathematics

Analytic Geometry

Extended Response ItemS.CP.7; S.CP.1

16

The total number of full-time and part-time employees at a store is 50. Each employee works either the morning shift or the afternoon shift. More information about the employees is given below.• 15 employees are part-time• 28 employees are males• 30 employees work the morning shift• 6 male employees work part-time• 12 male employees work the morning shiftThe names of each of the 50 employees are written on separate cards. The cards are shuffled and placed into a container.Part AIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is part-time or male? Show your work and explain your answer.Part BIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is male or works the afternoon shift? Show your work and explain your answer.Part CIf one card is selected at random from all 50 cards in the container, what is the probability that the employee is a female who does not work the morning shift? Show your work and explain your answer.

Be sure to complete ALL parts of the task.Write your answer and show your work on the paper provided.

Do NOT type your answer in the text box below.

Exemplar Response

17

Part A

The probability that the selected employee is part-time or male is 5037

or 74%.

To find this answer, use the general Addition Rule for the union of two events: P(part-time or male) = P(part-time) + P(male) – P(part-time and male)

P(part-time or male) 15 28 6 3750 50 50 50

Part B

The probability that the employee is male or works afternoons is 2516

or 64%.

To find this answer, use the general Addition Rule for the union of two events: P(male or afternoons) = P(males) + P(afternoons) – P(male and afternoons)

P(male or afternoons) = 2516

5032

5016

5020

5028

Part C

The probability that the employee is female who does not work mornings is 252

or 8%. To find this answer, we can reason from the given information that there are 22 female employees and 20 employees work afternoons. Since 12 males work mornings out of the 30 morning employees, 18 females work mornings. That leaves 4 females who work afternoons. Or, we can use the general Addition Rule for the union of two events and the complement: P(female who doesn’t work mornings) is equal to P(female and afternoons) P(female and afternoons)=P(not(male or mornings)) = 1 - P(male or mornings)

P(female who doesn’t work mornings) = 28 30 12 4 2

150 50 50 50 25

Rubric

18

Score Designation Description 4 Thoroughly

Demonstrated The student successfully completes all elements of the item by demonstrating knowledge and application of the Addition Rule for finding the probability of compound events, )()()()( BAPBPAPBAP , and can interpret the probability in terms of the model (S.CP.7) and describing events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events (S.CP.1).


The student shows clear understanding of the standards listed above, but one of the explanations or work shown is insufficient Or All parts of the item are correctly done except for a minor computational error Or The student successfully completes two of the three parts of the item and partially completes the other part.


The student shows basic understanding of the standards listed above, but two of the explanations or work shown is insufficient Or The student successfully completes one of the three parts of the item and partially completes the other parts.


The student shows minimal understanding of the standards listed above and completes only one of the three parts Or The student partially completes two of the three parts.




19

The student demonstrates a clear understanding of the mathematical concepts being measured by successfully completing two parts of the three parts of the item. In part A, the student successfully finds the correct probability of 37/50 and converts it to 74%. In part C the student successfully finds the correct probability of 4/50 and converts to 8%. In part B, the student partially completes the process, but does not find the final correct answer.


20

The student demonstrates a basic understanding of the mathematical concepts being measured by successfully completing one part of the item and partially completing the other two parts.

In part C, the student successfully finds the probability of 4/50 and successfully converts to the correct probability of .08

In parts A and B, the student partially completes the process, but does not find the correct final answers.


21

The student demonstrates a minimal understanding of the mathematical concepts being measured by partially completing all three parts.

In part A, the student correctly adds the part time employees and the male employees, but forgets to subtract out the part time employees that are male.

In part B, the student correctly adds the male workers to the afternoon workers, but forgets to subtract out the male workers that work afternoons.

In part C, the student correctly identifies the number of females, and the number of females who work mornings, but adds the two groups instead of subtracting.

mathematics grade 4. extended response item (scaffolded) 4.nf.4c; 4.nf.4b; 4.nf.4a; 4.nf.3a sylvia...

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parts c

student response score

correct wno explanation

correct wwork

insufficient explanation

d sylvia

cups of punch sylvia

basic understanding