High School, Claim 2

12 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Task Expectations:

x Mathematical information is presented in a table or graph or extracted from a context.

x The student is asked to solve well-posed problems in pure mathematics and arising in everyday life, society, and the workplace.

Example Item1: Primary Target 2A (Content Domain N-Q), Secondary Target 1C (CCSS N-Q.1), Tertiary Target 2D Hannah makes 6 cups of cake batter. She pours and levels all the batter into a rectangular cake pan with a length of 11 inches, a width of 7 inches, and a depth of 2 inches.

One cubic inch is approximately equal to 0.069 cup. What is the depth of the batter in the pan when it is completely poured in? Round your answer to the nearest inch. Rubric: (1 point) The student correctly determines the depth (e.g., 1 )

Response Type: Equation/Numeric

High School, Claim 2

13 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Example Item2: Primary Target 2A (Content Domain A-CED), Secondary Target 1G (CCSS A-CED.1), Tertiary Target 2D The $1000 prize for a lottery is to be divided evenly among the winners. Initially there are x winners. However, one more winner comes forward, causing each winner to receive $50 less. Part A Enter an equation that represents the situation and can be used to solve for x, the initial number of winners. Enter your equation in the first response box. Part B Enter the number of initial winners in the second response box.

Rubric: (2 points) The student creates a correct equation and determines the number of initial winners (e.g.,

). (1 point) The student is able to correctly answer Part A or Part B, but not both.

Response Type: Equation/Numeric (2 response boxes)

High School, Claim 2

14 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Example Item 3: Primary Target 2A (Content Domain A-CED), Secondary Target 1G (CCSS A-CED.1), Tertiary Target 2B The figure below is made up of a square with height, h units, and a right triangle with height, h units, and base length, b units.

The area of this figure is 55 square units. Part A

Write an equation that represents the height, h, in terms of b. Enter the equation in the first response box. Part B

If the base of the triangle is 10 units, determine the value of h, in units. Enter your answer in the second response box.

Rubric: (2 points) The students correctly answers both parts (e.g., Part A is 21 18016 4

h b b � � and Part B

is 5). (1 point) The student correctly answers Part A or Part B, but not both. Response Type: Equation/Numeric (2 response boxes)

High School, Claim 2

15 Version 2.0

Spin the Wheel

1 ticket 35%

2 tickets 25%

3 tickets 20%

5 tickets 15%

10 tickets 5%

X Probability

2 0.1225 3 0.1750

4 5 0.1000

6 0.1450 7 0.0750 8 0.0600 10

11 0.0350 12 0.0250

13 15 0.0150

20 0.0025

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Example Item 4: Primary Target 2A (Content Domain S-CP), Secondary Target 1X (CCSS S-CP.4), Tertiary Target 2B (Source: Adapted from Illustrative Mathematics S-CP Return to Fred’s Fun Factory) At a local fair, the price of admission includes the Opportunity for a person to spin a wheel for free ride tickets.

x Each spin of the wheel is a random event. x The results from each spin of the wheel are independent

of the results of previous spins. x Each spin of the wheel awards tickets according to the

probabilities shown at the right. Let X be the number of tickets a person wins based on 2 spins. There are 13 possible values for X that a person can obtain in this case. Some values of X are more common than others. For example, winning only 2 tickets in two spins is a somewhat common occurrence with probability 0.1225. It means the person wins 1 ticket on the first spin and 1 ticket on the second spin (0.35 y 0.35). A list of the possible values of X and the corresponding probabilities for most values of X is shown at right. Three probability values still need to be calculated. Fill in the three missing probability values in the table. Rubric: (3 points) The student correctly determines the missing probabilities. Each answer probability scores 1 point, independently (e.g., 0.2025, 0.0225, 0.02). Response Type: Fill-in Table

High School, Claim 2

16 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Example Item 5:

Primary Target 2A (Content Domain F-BF), Secondary Target 1N (CCSS F-BF.2), Tertiary Target 2D

A restaurant serves a vegetarian and a chicken lunch special each day. Each vegetarian special is the same price. Each chicken special is the same price. However, the price of the vegetarian special is different from the price of the chicken special.

x On Thursday, the restaurant collected $467 selling 21 vegetarian specials and 40 chicken specials.

x On Friday, the restaurant collected $484 selling 28 vegetarian specials and 36 chicken specials.

Enter the cost, in dollars, of the vegetarian lunch special.

Rubric: (1 point) The student correctly determines the cost of the vegetarian special (e.g., 7).

Response Type: Equation/Numeric

High School, Claim 2

17 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

.

Example Item 6: Primary Target 2A (Content Domain F-BF), Secondary Target 1N (CCSS F-BF.2) (Source: Adapted from Illustrative Mathematics A-SSE Course of Antibiotics) Susan has an ear infection. Her doctor prescribes a course of antibiotics. Susan is told to take a 250-milligram dose of the antibiotic every 12 hours for the next 10 days.

x Susan does some research on the antibiotic and finds out that 4% of the drug is still in her body after 12 hours.

x Assume each dose is exactly 250 milligrams and taken at the prescribed 12-hour intervals.

Part A How much of the drug, in milligrams, is in Susan’s body immediately after taking the 2nd dose? Enter your answer in the first response box. Part B

How much of the drug, in milligrams, is in Susan’s body immediately after taking the 20th dose? Enter your answer in the second response box.

Rubric: (2 points) The student correctly determines the amount of antibiotic in her body for Part A and B (e.g., 260, 260.4167). Note: An acceptable range for Part B is 260.4-260.417. (1 point) The student is able to determine the amount for Part A or Part B, but not both. Response Type: Equation/Numeric

High School, Claim 2

18 Version 2.0

Task Model 1

DOK Levels

2, 3

Apply

mathematics

to solve well-

posed

problems in

pure

mathematics

and arising in

everyday life,

society, and

the workplace.

Target A

Example Item 7:

Primary Target 2A (Content Domain G-C), Secondary Target 1X (CCSS G-C.2), Tertiary Target 2D

A circle has its center at (6, 7) and passes through the point (1, 4). A second circle is tangent to the first circle at the point (1, 4) and has the same area.

Enter the ordered pair that corresponds to the center of the second circle.

( , )

Rubric: (1 point) The student correctly determines the indicated ordered pair [e.g., (-04, +01)]. Note: The student does not need to select the zeros (0) or the positive sign (+) in order to receive full credit. (-4, 1) is sufficient. Response Type: Hot Spot

High School, Claim 2

19 Version 2.0

Task Model 2

DOK Levels

1, 2

Select and use

appropriate

tools

strategically.

Target B

Task Expectations:

x Mathematical information is presented in a table or graph or extracted from a context. x The student is asked to solve a problem that requires strategic use of tools or formulas.

Example Item 1:

Primary Target 2B (Content Domain G-SRT), Secondary Target 1O (CCSS G-SRT.8), Tertiary Target 2D

Melissa and Carrie both drew right triangles. The length of the hypotenuse in each triangle

is √ units.

The perimeter of Melissa’s triangle is √ units. Part A: Use the Connect Line tool to draw Melissa’s triangle.

The perimeter of Carrie’s triangle is √ units. Part B: Use the Connect Line tool to draw Carrie’s triangle.

Interaction: The student uses the Connect Line tool to create each right triangle.

Rubric: (1 point) The student is able to construct both triangles that meet the requirements (e.g., see sample shown). Response Type: Graphing

High School, Claim 2

20 Version 2.0

Task Model 2

DOK Levels

1, 2

Select and use

appropriate

tools

strategically.

Target B

Example Item 2:

Primary Target 2B (Content Domain N-Q), Secondary Target 1M (CCSS F-IF.7),

Teritiary Target 1E (CCSS A-SSE.3) Select the calculator viewing window that would allow you to see the maximum value of the following quadratic function. ( ) . A. and B. and C. and D. and

Rubric: The student selects the appropriate viewing window (e.g., D). Response Types: Multiple Choice, single correct response

High School, Claim 2

21 Version 2.0

Task Model 3

DOK Level 2

Interpret

results in the

context of a

situation.

Target C

Task Expectations:

x Mathematical information is presented in a table or graph or extracted from a context. x The student is asked to solve a problem that may require the integration of concepts and skills from

multiple domains.

Example Item 1:

Primary Target 2C (Content Domain A-CED), Secondary Target 1G (CCSS A-CED.1), Tertiary Target 2A A rectangular garden measures 13 meters by 17 meters and has a cement walkway around its perimeter, as shown. The width of the walkway remains constant on all four sides. The garden and walkway have a combined area of 396 square meters.

Part A Enter an equation in the first response box that can be solved for the width, W, of the walkway. Part B Determine the width, in meters, of the walkway. Enter your answer in the second response box. Rubric: (2 points) The student solves both parts correctly. [e.g., (13+2x)(17+2x)=396; W=2.5]. (1 point) The student answers only one part correctly. Response Type: Equation/Numeric (2 response boxes)

High School, Claim 2

22 Version 2.0

Task Model 4

DOK Levels

2, 3

Identify

important

quantities in a

practical

situation and

map their

relationships

(e.g., using

diagrams,

two-way

tables, graphs,

flowcharts, or

formulas).

Target D

Task Expectations:

x Mathematical information is presented in a table or graph or extracted from a context. x The student is asked to solve a problem that may require the integration of concepts and skills from

multiple domains.

Example Item 1: Primary Target 2D (Content Domain S-CP), Secondary Target 1X (CCSS S-CP.4), Tertiary Target 2A

Jaime randomly surveyed some students at his school to find out their opinions on a possible increase to the length of the school day. The results of his survey are shown in the table below.

Lengthening School Day Survey

Grade In Favor Opposed Undecided

9 12 6 9 10 15 3 11 11 8 12 10 12 5 16 9

Part A: A newspaper reporter randomly selects a Grade 11 student from this survey to interview. What is the probability that the student selected is opposed to lengthening the school day? Enter your answer in the first response box. Part B: The newspaper reporter also wants to interview a student in favor of lengthening the school day. If a student in favor is randomly selected, what is the probability that this student is also from Grade 11? Enter your answer in the second response box.

Rubric: (2 points) The students answers both parts correctly (e.g., 0.4, 0.2). (1 point) The student answers only one part correctly. Response Type: Equation/Numeric (2 response boxes)

High School, Claim 2

23 Version 2.0

Task Model 4

DOK Levels

2, 3

Identify

important

quantities in a

practical

situation and

map their

relationships

(e.g., using

diagrams,

two-way

tables, graphs,

flowcharts, or

formulas).

Target D

Example Item 2:

Primary Target 2D (Content Domain F-IF), Secondary Target 1M (CCSS F-IF.11), Tertiary Target 2B (Content Domain F-IF)

The table shows several inputs and outputs for two functions, f and g, that are both continuous on the interval 0 to 8.

x f(x) g(x)

0 -5 120

1 -4 103

2 -1 86

3 4 69

4 11 52

5 20 35

6 31 18

7 44 1

8 59 16

There is exactly one solution for which f(x) = g(x).

Click the number line to show the consecutive integer interval of x in which the solution f(x) = g(x) must lie.

Rubric: (1 point) The student correctly identifies the correct interval (e.g., see below).

Response Type: Hot Spot

High School, Claim 2

24 Version 2.0

Task Model 4

DOK Levels

2, 3

Identify

important

quantities in a

practical

situation and

map their

relationships

(e.g., using

diagrams,

two-way

tables, graphs,

flowcharts, or

formulas).

Target D

Example Item 3:

Primary Target 2D (Content Domain G-SRT), Secondary Target 1O (CCSS G-SRT.6) (Source: Adapted from HS Practice Test 682) Consider triangle ABC, where angle C is a right angle. Drag each given measure of Angle A to the column that shows the correct relationship between sin A and cos A. Rubric: (1 point) The student correctly classifies all angles (e.g., see below).

Response Type: Drag and Drop

65˚ 85˚ 70˚

45˚

30˚ 10˚

Angle A

10˚ 65˚ 45˚ 30˚ 85˚ 70˚