ok grade 7 math item specs

OKLAHOMA SCHOOL TESTING PROGRAM OKLAHOMA CORE CURRICULUM TESTS

ITEM SPECIFICATIONS

Mathematics Grade 7

Sandy Garrett State Superintendent of Public Instruction Oklahoma State Department of Education Oklahoma City, Oklahoma Revised

May 2008

Grade 7 Mathematics Item Specifications 1

Purpose

The purpose of this test is to measure Oklahoma seventh-grade students’ level of proficiency in mathematics. On the Grade 7 Mathematics Test, students are required to respond to a variety of items linked to the seventh-grade mathematics content standards identified in the Priority Academic Student Skills (PASS). Each Mathematics Test form tests each identified content standard and objective listed below. The following standards and objectives are intended to summarize the knowledge as identified in PASS.

PASS Content Standards and Objectives Algebraic Reasoning • Properties (1.1) • Linear Equations (1.2)

Number Sense • Integers (2.1) • Ratio/Proportion/Percent (2.2) • Exponents (2.3) Geometry • Geometric Figures (3.1) • Angles (3.2) • Coordinate System (3.3)

Measurement • Area and Perimeter (4.1) • Customary/Metric Measurements (4.2)

Data Analysis and Probability • Outcomes/Simple Probability (5.1) • Probability with Or, And, or Not (5.2) • Combinations/Permutations (5.3)


General Considerations

It is necessary to create test items that are reliable, fair, and targeted to the PASS standards listed on the following pages. There are some general considerations and procedures for effective item development. These considerations include, but are not limited to, the following:

1. Each test form contains items assessing all content standards and objectives listed in the Test Blueprint for seventh-grade mathematics.

2. Test items that assess each standard are not limited to one particular type of response format.

3. Test questions attempt to focus on content that is authentic and that seventh-grade students can relate to and understand.

4. Test items are worded precisely and clearly.

5. All items are reviewed to eliminate language that shows bias or is otherwise likely to disadvantage a particular group of students. That is, items do not display unfair representations of gender, race, disability, culture, or religion; nor do items contain elements that are offensive to any such groups.

6. All answer choices in multiple-choice items (the key and all distractors) are similar in length and syntax. Students should not be able to rule out a wrong answer or identify a correct response solely because it looks or sounds different from the other answer choices. Distractors are created so that students reason their way to the correct answer rather than simply identify incorrect responses because of a distractor’s obviously inappropriate nature. Distractors should always be plausible (but incorrect) in the context of the item stem. Correct responses are approximately equally distributed among As, Bs, Cs, and Ds.

Universal Test Design Considerations

Universal design, as applied to assessments, is a concept that allows the widest possible range of students to participate in assessments and may even reduce the need for accommodations and alternative assessments by expanding access to the tests themselves. In the Oklahoma Core Curriculum Tests, modifications have been made to some items that simplify and clarify instructions, and provide maximum readability, comprehensibility, and legibility. This includes such things as reduction of language load in content areas other than Reading, increased font size, fewer items per page, and boxed items to assist visual focus. Reading tests will have vocabulary at grade level. In all other tests, the vocabulary level will be below the grade being tested except for content words. Grades 3 and 4 will be one grade level below, and grades 5, 6, 7, and 8 will be two grade levels below. These modifications are evident in the sample items included in this document.


Multiple-Choice Item Rules

• All items clearly indicate what is expected in a response and direct students to focus on their response.

• Each multiple-choice item has a stem (question, statement, or incomplete statement and/or graphic component) and four answer (or completion) options, only one of which is correct.

• Multiple-choice item stems present a complete problem so that students know what to do before looking at the answer choices; students should not need to read all answer choices before knowing what is expected.

In summary, mathematics-test items assess whether students understand mathematical concepts and procedures, communicate their understandings effectively in mathematical terms, approach problems, and develop viable solutions.


OVERVIEW OF ITEM SPECIFICATIONS For each PASS standard, item specifications are organized under the following headings: • PASS Standard and PASS Objective • Item Specifications

a. Emphasis b. Stimulus Attributes c. Format d. Content Limits e. Primary Process Standards f. Distractor Domain g. Sample Test Items

The headings “PASS Standard” and “PASS Objective” state the standard and objective being measured as found in the seventh-grade mathematics section of the Priority Academic Student Skills document.

The heading “Item Specifications” highlights important points about the items’ emphasis, stimulus attributes, format, content limits, primary process standards, distractor domain, and sample test items. Although it is sometimes possible to score single items for more than one concept, all items in these tests are written to address a single content standard as the primary concept.

Note about the Item Specifications and Sample Test Items:

With the exception of content limits, the item specifications give suggestions of what might be included and do not give an exhaustive list of what can be included. The sample test items are not intended to be definitive in nature or construction—the stimuli and the test items that follow them may differ from one test form to another, as may their presentations.


PRIORITY ACADEMIC STUDENT SKILLS

MATHEMATICS CONTENT STANDARDS

Grade 7

Asterisks (*) have been used to identify standards and objectives that must be assessed by the local school district. All other skills may be assessed by the Oklahoma School Testing Program (OSTP).

Standard 1: Algebraic Reasoning—The student will use number properties to simplify and solve simple linear equations.

1. Identify and apply the commutative, associative, distributive, inverse, and identity properties (e.g., n + 0 = n, 2(x + 3) = 2x + 6).

2. Use a variety of methods to model and solve one-step linear equations (e.g., use properties of equality, graph ordered pairs with paper and pencil, use graphing calculators).

Standard 2: Number Sense—The student will use numbers and number relationships to acquire basic facts and determine the reasonableness of results.

1. Integers

a. Compare and order positive and negative integers and describe their use in real-life situations (e.g., temperature, sea level, stock market fluctuations, football yardage).

b. Use the basic operations on integers to solve problems.

2. Ratio, Proportion, and Percents

*a. Demonstrate the concept of ratio and proportion with models (e.g., similar geometric shapes, scale models).

b. Set up equivalent ratios, estimate and solve problems using ratio, proportions, and percents including percents greater than 100 and less than 1 (e.g., determine missing sides of similar figures, heart rate per minute, cost per pound, pay to hours worked overtime).

c. Solve percent application problems (e.g., discounts, tax, finding the missing value of percent/part/whole).


3. Exponents

*a. Analyze and develop generalizations of exponential patterns, including zero as an exponent, using manipulatives and calculators (e.g., model getting paid a penny the first day, 2 cents the second day, 4 cents the third day…).

b. Build and recognize models of multiples to investigate squares and square roots (e.g., build rectangular arrays for numbers 1 to 100 and note which can be represented as squares).

c. Estimate the square root of a number (e.g., between two consecutive integers).

Standard 3: Geometry—The student will apply the properties and relationships of plane geometry in a variety of contexts.

1. Classifying Geometric Figures

a. Classify triangles according to their sides and angles.

b. Classify quadrilaterals according to their sides and angles (e.g., determine whether all squares are rectangles).

2. Identify and compare bisectors, interior, exterior, and vertical angles (e.g., using graph paper, software, protractors to measure angles between parallel lines with a transversal).

3. Rectangular Coordinate System

a. Locate points on a plane in all four quadrants.

b. Identify geometric transformation of figures (rotations, translations, and reflections).

Standard 4: Measurement—The student will use measurement to solve problems in a variety of contexts.

1. Area and Perimeter

a. Develop area and perimeter concepts (e.g., use grids to estimate the area of irregular shapes).

b. Apply formulas to solve problems involving perimeter (circumference) and area of polygons and circles.

2. Customary and Metric Measurements

a. Select and use appropriate tools for measurements in practical applications and make reasonable estimates of measurements in a particular situation using the appropriate unit.

b. Use estimates to relate customary and metric measurements to each other.


Standard 5: Data Analysis and Probability—The student will use probability to formulate and justify predictions from a set of data.

1. Use data from a sample to predict possible outcomes and compute simple probabilities as fractions, decimals, or percents (e.g., the data from lists, tree diagrams, frequency distribution tables, area models).

2. Determine the probability of an event involving “or”, “and”, or “not” (e.g., on a spinner with 1 blue, 2 red, and 2 yellow sections, what is the probability of getting a red or a yellow?).

3. Find all possible combinations and permutations involving a limited number of variables.


MATHEMATICS PROCESS STANDARDS

Grade 7

Process Standard 1: Problem Solving

1. Develop and test strategies to solve practical, everyday problems which may have single or multiple answers.

2. Use technology to generate and analyze data to solve problems.

3. Formulate problems from situations within and outside of mathematics and generalize solutions and strategies to new problem situations.

4. Evaluate results to determine their reasonableness.

5. Apply a variety of strategies (e.g., restate the problem, look for a pattern, diagrams, solve a simpler problem, work backwards, trial and error) to solve problems, with emphasis on multistep and nonroutine problems.

6. Use oral, written, concrete, pictorial, graphical, and/or algebraic methods to model mathematical situations.

Process Standard 2: Communication

1. Discuss, interpret, translate (from one to another) and evaluate mathematical ideas (e.g., oral, written, pictorial, concrete, graphical, algebraic).

2. Reflect on and justify reasoning in mathematical problem solving (e.g., convince, demonstrate, formulate).

3. Select and use appropriate terminology when discussing mathematical concepts and ideas.

Process Standard 3: Reasoning

1. Identify and extend patterns and use experiences and observations to make suppositions.

2. Use counter examples to disprove suppositions (e.g., all squares are rectangles, but are all rectangles squares?).

3. Develop and evaluate mathematical arguments (e.g., agree or disagree with the reasoning of other classmates and explain why).

4. Select and use various types of reasoning (e.g., recursive [loops], inductive [specific to general], deductive [general to specific], spatial, and proportional).


Process Standard 4: Connections

1. Apply mathematical strategies to solve problems that arise from other disciplines and the real world.

2. Connect one area or idea of mathematics to another (e.g., relate equivalent number representations to each other, relate experiences with geometric shapes to understanding ratio and proportion).

Process Standard 5: Representation

1. Use a variety of representations to organize and record data (e.g., use concrete, pictorial, and symbolic representations).

2. Use representations to promote the communication of mathematical ideas (e.g., number lines, rectangular coordinate systems, scales to illustrate the balance of equations).

3. Develop a variety of mathematical representations that can be used flexibly and appropriately (e.g., base-10 blocks to represent fractions and decimals, appropriate graphs to represent data).

4. Use a variety of representations to model and solve physical, social, and mathematical problems (e.g., geometric objects, pictures, charts, tables, graphs).


PASS Standard: Standard 1: Algebraic Reasoning—The student will use number properties to simplify and

solve simple linear equations.

PASS Objective: 1. Identify and apply the commutative, associative, distributive, inverse, and identity

properties (e.g., n + 0 = n; 2(x + 3) = 2x + 6).

Item Specifications: Emphasis: Demonstrate a working knowledge of the properties of the number system.

Stimulus Attributes: Test items may include illustrations of the following: number lines, counting manipulatives, balances, two- and three-dimensional geometric figures, data sets, charts, tables, and other diagrams.

Format: • Identify examples and use of the basic properties of numbers and operations • Use the basic properties of numbers and operations to solve mathematical problems and

problems in real-world contexts • Use variables for unknowns • Coefficients may be positive or negative

Content Limits: • Limit properties to commutative, associative, distributive, inverse, and identity • Limit coefficients of variables to integers and fractions • Limit fractional coefficients to halves, thirds, fourths, fifths, sixths, eighths, tenths, and

twelfths

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 2: Communication Process Standard 3: Reasoning

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Order of operations errors


PASS 1.1 Sample Items:

Primary Process Standard: 7M2.1 Depth of Knowledge: 1 Correct Answer: A

Which equation demonstrates the identity property of multiplication?

A 3

4− x • 1 =

3

4− x

B 1

2(x + 4) =

1

2x +

1

2(4)

C 2

3n • 0 = 0

D –1

5 • (3n • 2) = (–

1

5 • 3n) • 2

Primary Process Standard: 7M2.3 Depth of Knowledge: 1 Correct Answer: C

Which equation demonstrates the distributive property?

A x • 3 = 3 • x

B 4(n • 6) = 4n • 6

C 3(x + 4) = 3x + 12

D n • n1

= 1


4( 3)x+

Which of these is equivalent to the expression shown above? A 4 3x+

B 4 4x+

C 4 7x+

D 4 12x+

Primary Process Standard: 7M3.3 Depth of Knowledge: 1 Correct Answer: B

Which equation demonstrates the commutative property of multiplication?

A x • x1

= 1

B 6x • 3 = 3 • 6x

C 3(4m • 5) = 12m • 15

D 12 • (n • 2) = (12 • n) • 2

Primary Process Standard: 7M3.4 Depth of Knowledge: 2 Correct Answer: D



Which properties are demonstrated in these steps?

(5 0) 4 5 4 Step 1

4 5 Step 2

x x

x

+ + = += +

A Step 1: Inverse

Step 2: Commutative

B Step 1: Identity Step 2: Associative

C Step 1: Identity Step 2: Commutative

D Step 1: Inverse Step 2: Associative


PASS Standard: Standard 1: Algebraic Reasoning—The student will use number properties to simplify and

solve simple linear equations. PASS Objective:

2. Use a variety of methods to model and solve one-step linear equations (e.g., use properties of equality, graph ordered pairs with paper and pencil, use graphing calculators).

Item Specifications: Emphasis: Demonstrate the ability to solve simple linear equations in mathematical and real-world contexts.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, number lines, calculator displays, tables, graphs, charts, and data sets.

Format: • Identify, write, and solve 1-step linear equations involving mathematical and real-world

contexts • Model and translate among algebraic, graphic, and pictorial representations of simple linear

equations • Coefficients may be positive or negative

Content Limits: • Limit linear equations to 1-step equations • Limit coefficients of variables to integers and fractions • Limit fractional coefficients to halves, thirds, fourths, fifths, sixths, eighths, tenths, and

twelfths • Limit graphing to recognition of the graph that matches a linear equation given at least

2 points on the graph or recognition of the linear equation that matches a graph given at least 2 points on the graph

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 5: Representation

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Order of operations errors


What is the solution to this equation?

5x = 35

A x = 40

B x = 30

C x = 7

D x = 3




Which point is found on the line represented by the equation y + 6 = x?

A (–5, 1)

B (2, – 4)

C (3, 9)

D (6, 6)



Which equation is equivalent to y – 3 = x? A y = – 3x

B y = 3

x

C y = 3 – x

D y = x + 3


Vicki sold 48 picture frames at a craft fair and had 36 left. Which equation could be used to find n, the number of picture frames Vicki originally had?

A n + 36 = – 48

B n – 36 = 48

C n + 48 = 36

D n – 48 = –36


John had a jar that contained x dimes. He put another 58 dimes in the jar and now has a total of 84 dimes. Which equation could be used to find x, the number of dimes John had in the jar originally?

A x + 58 = 84

B x – 58 = 84

C 84 – x = 58

D 84 + x = 58



PASS Standard: Standard 2: Number Sense—The student will use numbers and number relationships to

acquire basic facts and determine the reasonableness of results. PASS Objective:

1. Integers

a. Compare and order positive and negative integers and describe their use in real-life situations (e.g., temperature, sea level, stock market fluctuations, football yardage).

b. Use the basic operations on integers to solve problems.

Item Specifications: Emphasis: Demonstrate a working knowledge of positive and negative integers to solve problems in mathematical and real-world contexts.

Stimulus Attributes: Test items may include: illustrations of coordinate graphs, number lines, balances, two- and three-dimensional geometric figures; rulers, thermometers, beakers, and other measuring instruments; calculator displays, tables, graphs, charts, maps, scale drawings, frequency charts; line, bar, and picture graphs; Venn diagrams; stem-and-leaf plots, box-and-whisker plots, scatter plots; histograms, circle graphs, data sets, spinners, and other diagrams.

Format: • Compare, order, and translate among representations of positive and negative integers in

mathematical, geometric, and real-life contexts • Select, apply, and justify the use of the basic operations on positive and negative integers to

solve problems in mathematical, geometric, and real-world contexts

Content Limits: Limit operations to addition, subtraction, multiplication, and division.

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 3: Reasoning Process Standard 4: Connections Process Standard 5: Representation

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties


PASS 2.1a Sample Items:


Which of these lists of integers is in order from greatest to least? A 8, 5, 3, 0− − −

B 7, 5, 2, 1− −

C 8, 5, 7, 4− −

D 3, 0, 1, 6− −



The table shows the mean temperatures for each of five days during one week last winter.

Mean Temperatures

Day Temperature (°F)

Monday 7

Tuesday −2

Wednesday −1

Thursday 4

Friday 0

Which lists the weekdays in order from the day with the lowest mean temperature to the day with the highest mean temperature?

A Friday, Wednesday, Tuesday, Thursday, Monday

B Tuesday, Wednesday, Friday, Thursday, Monday

C Friday, Tuesday, Wednesday, Thursday, Monday

D Tuesday, Friday, Wednesday, Thursday, Monday


Theresa had $1,000 in her checking account and a balance of $800 to pay on a loan. Theresa used money from her checking account to make a payment that decreased her loan to half of the balance. What is her new checking account balance? A $200

B $400

C $500

D $600

PASS 2.1b Sample Items:


Chad works at a flower shop located on the 80th floor of a building. He went down 60 floors to deliver flowers, back up 15 floors, and finally down 2 floors to make a third delivery. Which floor was Chad on when he made the third delivery?

A 33rd

B 35th

C 37th

D 47th




The table lists all of the deposits and withdrawals Harold made to his bank account during the month of March.

If there was $450 in Harold’s bank account on March 1, what was his bank account balance at the end of March?

A $315

B $475

C $585

D $745



acquire basic facts and determine the reasonableness of results.

PASS Objective: 2. Ratio, Proportion, and Percents

b. Set up equivalent ratios, estimate and solve problems using ratio, proportions, and percents including percents greater than 100 and less than 1 (e.g., determine missing sides of similar figures, heart rate per minute, cost per pound, pay to hours worked overtime).

c. Solve percent application problems (e.g., discounts, tax, finding the missing value of percent/part/whole).

Item Specifications: Emphasis: Demonstrate the ability to use ratio and proportion to estimate and solve mathematical and real-world problems, including percent application problems.

Stimulus Attributes: Test items may include: illustrations of coordinate graphs, number lines, balances, two- and three-dimensional geometric figures; rulers, thermometers, beakers, and other measuring instruments; calculator displays, tables, graphs, charts, maps, scale drawings, frequency charts; line, bar, and picture graphs; Venn diagrams; stem-and-leaf plots, box-and-whisker plots, scatter plots; histograms, circle graphs, data sets, spinners, and other diagrams.

Format: • Select and apply ratios and proportions to solve problems in mathematical, geometric, and

real-world contexts • Select and apply ratios and proportions among other methods to solve percent application

problems in mathematical, geometric, and real-world contexts

Content Limits: • Limit number of variables in a proportion to one • Limit real-world contexts to age-appropriate situations

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 4: Connections

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies




There are 42 students in Kim’s band class. Of those students, 31 are girls. Which proportion can be used to find x, the percent of students in the class that are boys?

A 3142

= 100

x

B 3111

= 100x

C 1131

= 100x

D 4211

= 100x


The ratio of time Tim spends on math homework to science homework is 5 to 4. If he spends 40 minutes on math homework, how many minutes does he spend on science homework?

A 20 minutes

B 32 minutes

C 60 minutes

D 90 minutes


Steven earns $12 an hour plus a 15% commission from every sale that he makes. During a two-week period, Steven worked 80 hours and made a total of $1,300 in sales. What was the total amount of Steven’s paycheck for the two-week period? A $1,155

B $1,495

C $2,260

D $2,340

PASS 2.2c Sample Items: Primary Process Standard: 7M4.1 Depth of Knowledge: 3 Correct Answer: C

Ronnie’s Furniture Store had a sale on Saturday. Every item was reduced by 15%. Mike purchased these items.

Original Prices

Which amount is closest to the total cost of Mike’s purchases after the 15% discount and including the 6% sales tax?

A $410

B $510

C $540

D $640


• one couch for $199.99 • two tables for $149.99 each • one lamp for $99.99




PASS Objective: 3. Exponents

b. Build and recognize models of multiples to investigate squares and square roots (e.g., build rectangular arrays for numbers 1 to 100 and note which can be represented as squares).

Item Specifications: Emphasis: Demonstrate an understanding of perfect squares and square roots through the use of models.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, number lines, 10-by-10 grids, counting manipulatives, two-dimensional geometric figures, calculator displays, tables, graphs, charts, maps, scale drawings, data sets, and other diagrams.

Format: • Use numbers to explore and identify square roots and perfect squares in mathematical,

geometric, and real-world contexts • Use graphic representations including arrays and models of multiples to explore and identify

square roots and perfect squares in mathematical, geometric, and real-world contexts

Content Limits: • Limit graphic representations to common two-dimensional geometric figures • Limit arrays to two-dimensional arrays


Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies • Incorrect interpretation of data display


Which of these models can be used to represent the area of a square with a side length of 4 ?

A

B

C

D



Which model represents 32 ?

A

B

C

D





Which model is shaded to represent 144 ? A

C

B

D

Josh has 56 identical square tiles. Which change would best allow Josh to combine all of the square tiles he has to create a single square?

A adding 6 tiles to the 56 he has

B adding 7 tiles to the 56 he has

C subtracting 6 tiles from the 56 he has

D subtracting 7 tiles from the 56 he has




PASS Objective: 3. Exponents

c. Estimate the square root of a number (e.g., between two consecutive integers).

Item Specifications: Emphasis: Demonstrate an understanding of the relationship between integers and approximate square roots.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, number lines, 10-by-10 grids, two-dimensional geometric figures, calculator displays, tables, graphs, charts, maps, scale drawings, data sets, and other diagrams.

Format: • Use numbers to estimate square roots in mathematical, geometric, and real-world contexts • Use graphic representations including arrays and models of multiples to estimate square roots

in mathematical, geometric, and real-world contexts

Content Limits: • Limit graphic representations to common two-dimensional geometric figures • Limit arrays to two-dimensional arrays

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 3: Reasoning

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies • Rounding errors


PASS 2.3c Sample Items:


The square root of 154 is between which two integers?

A 11 and 12

B 12 and 13

C 14 and 15

D 15 and 16


Which whole number is closest to the value of 126 ?

A 10

B 11

C 12

D 13



Which point is closest to the value of 905 on the number line?

A point A

B point B

C point C

D point D


PASS Standard: Standard 3: Geometry—The student will apply the properties and relationships of plane

geometry in a variety of contexts.

PASS Objective: 1. Classifying Geometric Figures

a. Classify triangles according to their sides and angles.

b. Classify quadrilaterals according to their sides and angles (e.g., determine whether all squares are rectangles).

Item Specifications: Emphasis: Demonstrate the ability to classify triangles and quadrilaterals based on sides and angles.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, two-dimensional geometric figures, protractors, geoboards, other geometric manipulatives, tables, graphs, charts, maps, data sets, and other diagrams.

Format: • Classify triangles according to their attributes • Classify quadrilaterals according to their attributes

Content Limits: Limit quadrilaterals to rectangles, squares, parallelograms, rhombuses, and trapezoids.

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 2: Communication Process Standard 3: Reasoning Process Standard 5: Representation

Distractor Domain: • Common errors • Incorrect procedures • Incorrect use of rules or properties




Leticia drew a triangle with exactly two sides of equal length. What type of triangle did Leticia draw?

A scalene

B isosceles

C equilateral

D equiangular


Which kind of triangle has angles with these three measures?

45°, 45°, and 90°

A equilateral

B obtuse

C right

D acute


The figure shows a rectangle divided into two congruent triangles.

Which term best describes these triangles?

A equilateral

B isosceles

C scalene

D obtuse

Which type of triangle is always similar to all other triangles of the same type?

A acute

B right

C scalene

D equilateral




Which term best describes this quadrilateral?

A trapezoid

B rectangle

C rhombus

D square



Penny drew a quadrilateral with these characteristics.

What type of quadrilateral did Penny draw?

A rhombus

B rectangle

C square

D trapezoid


• all sides are of equal length • the opposite sides are parallel• two angles are acute




PASS Objective: 2. Identify and compare bisectors, interior, exterior, and vertical angles (e.g., using

graph paper, software, protractors to measure angles between parallel lines with a transversal).

Item Specifications: Emphasis: Demonstrate a working knowledge of angle types and their measures in geometric figures and polygons.


Format: • Identify and compare angles and angle relationships based on their positions in geometric

figures, including the assessment of complementary and supplementary angles • Find the measures of angles based on their positions and relationships in geometric figures

Content Limits: Limit geometric figures to two dimensions

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 3: Reasoning Process Standard 5: Representation

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties




The drawing shows parallel lines l and m intersected by transversal t.

Which statement about angles 2 and 4 is true?

A They are interior angles.

B They are vertical angles.

C They are corresponding angles.

D They are complementary angles.

t

l

m

1 2 4 3

5 6 8 7



The drawing shows parallel lines l and m intersected by transversal t.

Which statement best describes angles 1 and 5?

A They are interior angles.

B They are vertical angles.

C They are complementary angles.

D They are corresponding angles.

t

l

m

1 2 4 3

5 6 8 7



In this drawing, two rays begin at point R on line QV.

Which statement about ∠ QRS and ∠ VRS is true?

A They are vertical angles.

B They are obtuse angles.

C They are supplementary angles.

D They are complementary angles.


Two lines intersect at a 35° angle, as shown.

What is the value of x?

A 35

B 55

C 145

D 165





PASS Objective: 3. Rectangular Coordinate System

a. Locate points on a plane in all four quadrants.

b. Identify geometric transformation of figures (rotations, translations, and reflections).

Item Specifications: Emphasis: Demonstrate a working knowledge of the location of points on a coordinate plane; demonstrate the ability to identify geometric transformations.


Format: • Identify the quadrant in which a given point is found on a coordinate plane • Identify the coordinates of an identified point on a coordinate plane or map • Identify the point located at identified coordinates on a coordinate plane or map • Distinguish among transformations of figures on a coordinate plane and in real-world

contexts

Content Limits: • Limit geometric figures to two dimensions • Limit transformations to reflections, rotations, and translations


Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Incorrect interpretation of data display • Confusion among geometric transformations





Point K is located at (–3, 8) on a coordinate plane. In which quadrant is point K located?

A quadrant IV

B quadrant III

C quadrant II

D quadrant I

Which point best represents the ordered pair (–3, 6) on this coordinate grid?

A point A

B point B

C point C

D point D


PASS 3.3b Sample Items: Primary Process Standard: 7M5.4 Depth of Knowledge: 1 Correct Answer: C

Which best describes the one-step transformation in position from Figure 1 to Figure 2?

A reflection

B translation

C rotation

D dilation



Which best shows the position of the parallelogram QRST after it is reflected across the y-axis to form parallelogram Q R S T′ ′ ′ ′?

A

C

B

D


PASS Standard: Standard 4: Measurement—The student will use measurement to solve problems in a variety

of contexts.

PASS Objective: 1. Area and Perimeter

a. Develop area and perimeter concepts (e.g., use grids to estimate the area of irregular shapes).

b. Apply formulas to solve problems involving perimeter (circumference) and area of polygons and circles.

Item Specifications: Emphasis: Demonstrate the ability to estimate and solve area and perimeter problems for geometric figures and polygons.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, two-dimensional geometric figures, rulers, calculator displays, tables, graphs, charts, combined forms, maps, scale drawings, frequency charts, circles, data sets, formulas, and other diagrams.

Format: • Explore the concepts of area and perimeter in mathematical, geometric, and real-world

contexts • Estimate the area and perimeter of circles and polygons in a variety of contexts • Apply the formula used to find the area and perimeter of circles and polygons in a variety of

contexts

Content Limits: • Two-dimensional geometric shapes may be regular, irregular, or combined forms

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 3: Reasoning Process Standard 4: Connections Process Standard 5: Representation

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules, properties, or formulas • Use of incorrect formula • Confusion between area and perimeter


PASS 4.1a Sample Items: Primary Process Standard: 7M5.4 Depth of Knowledge: 2 Correct Answer: C

The shaded figure on the grid is a quadrilateral.

Which is closest to the area, in square units, of the quadrilateral?

A 39 sq units

B 4221

sq units

C 44 sq units

D 4521

sq units



The figure shown is made up of line segments that meet at right angles.

What is the perimeter of the figure in meters (m)?

A 24 m

B 26 m

C 28 m

D 30 m



Which measure is closest to the area of thisshaded figure in square feet (sq ft)?

A 32 sq ft

B 41 sq ft

C 56 sq ft

D 68 sq ft


PASS 4.1b Sample Items: Primary Process Standard: 7M1.6 Depth of Knowledge: 2 Correct Answer: A


Tomas used a string with a piece of chalk tied to one end to draw a circle on the sidewalk. He held one end of the string on the sidewalk and then drew the circle using the chalk tied to the other end. The area of the circle was about 113 square inches. Which is closest to the length of the string?

A 6 in.

B 12 in.

C 18 in.

D 36 in.

The length of a parallelogram is 18 inches. If the perimeter of the parallelogram is 60 inches, what is the width, in inches (in.)?

A 12 in.

B 21 in.

C 24 in.

D 42 in.

2circleA rπ=


PASS Standard: Standard 4: Measurement—The student will use measurement to solve problems in a variety

of contexts.

PASS Objective: 2. Customary and Metric Measurements

a. Select and use appropriate tools for measurements in practical applications and make reasonable estimates of measurements in a particular situation using the appropriate unit.

b. Use estimates to relate customary and metric measurements to each other.

Item Specifications: Emphasis: Demonstrate the ability to make appropriate measurements and to integrate knowledge of the metric and customary systems using estimation strategies.

Stimulus Attributes: Test items may include illustrations of the following: coordinate graphs, two- and three-dimensional geometric figures, rulers, calculator displays, tables, graphs, charts, rectangular solids, prisms, cones, cylinders, pyramids, combined forms, maps, scale drawings, frequency charts, circles, data sets, formulas, and other diagrams.

Format: • Identify the appropriate measurement tool in a real-world context • Make and estimate measurements in mathematical, geometric, and real-world contexts • Translate metric measurements and quantities into customary units and customary

measurements and quantities into metric units

Content Limits: Limit assessment to linear measure, weight, mass, time, temperature, perimeter, area, capacity, and volume.

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 2: Communication

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies • Rounding errors • Errors in converting units


PASS 4.2a Sample Items: Primary Process Standard: 7M1.4 Depth of Knowledge: 1 Correct Answer: B

Which is the most reasonable length for a new pencil?

A 19 millimeters

B 19 centimeters

C 19 meters

D 19 kilometers


Which measurement represents a reasonable amount of water needed to completely fill a standard bathroom sink?

A 2 cups

B 2 pints

C 2 ounces

D 2 gallons


PASS 4.2b Sample Items: Primary Process Standard: 7M1.1 Depth of Knowledge: 3 Correct Answer: C

Mary bought a 3-liter bottle of lemon-lime soda. Which is closest to the number of ounces (oz) of soda in the bottle when it is half full?

4 liters 128 ounces≈

A 24 oz

B 32 oz

C 48 oz

D 96 oz


Lee Ann is the tallest girl on the 10th-grade basketball team. Her height is 1.8 meters. Which is closest to Lee Ann’s height in inches (in.)?

1 meter 39 inches≈ A 50 in.

B 60 in.

C 70 in.

D 80 in.


PASS Standard:

Standard 5: Data Analysis and Probability—The student will use probability to formulate and justify predictions from a set of data.

PASS Objective: 1. Use data from a sample to predict possible outcomes and compute simple

probabilities as fractions, decimals, or percents (e.g., the data from lists, tree diagrams, frequency distribution tables, area models).

Item Specifications: Emphasis: Demonstrate the ability to use data from a variety of sources to predict outcomes and probabilities.

Stimulus Attributes: Test items may include: illustrations of coordinate graphs, number lines, tables, graphs, and charts; such as frequency charts, line, bar, and picture graphs; Venn diagrams; stem-and-leaf plots, box-and-whisker plots, and scatter plots; histograms, circle graphs, data sets, spinners, and other diagrams.

Format: • Analyze data from a variety of sources to predict outcomes (may use the Fundamental

Counting Principle) in mathematical and real-world contexts • Analyze data from a variety of sources to compute the probability of an event occurring or

not occurring • Translate among decimal, fraction, and percent expressions of simple probabilities

Content Limits: • Limit to simple probability experiments • Limit sample to no more than 20 pieces of data • Limit real-world contexts to age-appropriate situations

Primary Process Standards: Process Standard 1: Problem Solving Process Standard 2: Communication Process Standard 3: Reasoning

Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies • Incorrect interpretation of data display


PASS 5.1 Sample Items: Primary Process Standard: 7M3.1 Depth of Knowledge: 1 Correct Answer: C

A spinner is divided into 4 sections of different sizes and colors. The table shows the results of spinning the pointer 100 times.

Results of 100 Spins

Based on these results, what is the probability that the pointer will stop on blue on the next spin?

A 101

B 103

C 52

D 53

Color of Section

Number ofTimes

green 20 red 30 blue 40 yellow 10



A survey was conducted to determine the favorite colors of 120 seventh-grade students. The circle graph shows the results of the survey.

Survey of Favorite Colors

A student will be selected at random from the 120 students surveyed. Based on the graph, what is the probability that the student’s favorite color will be blue?

A 51

B 14

C 103

D 136

orange 10%

blue 30%

yellow 25%

red 20%

other colors 15%



Which of these fair spinners has the highest probability of the arrow landing on an even number?

A

C

B

D



A local sandwich shop offers the choices shown for their lunch special. Jamie wants to order 1 sandwich.

Sandwich Choices

Meat Sandwich Spread Bread

ham turkey chicken

mustard mayonnaise ketchup

wheat white

How many possible sandwiches can Jamie make using 1 type of meat, 1 sandwich spread, and 1 type of bread?

A 3

B 6

C 12

D 18


PASS Standard: Standard 5: Data Analysis and Probability—The student will use probability to formulate and

justify predictions from a set of data. PASS Objective:

2. Determine the probability of an event involving “or”, “and”, or “not” (e.g., on a spinner with 1 blue, 2 red, and 2 yellow sections, what is the probability of getting a red or a yellow?).

Item Specifications: Emphasis: Demonstrate the ability to predict probabilities in specified mathematical and real-world contexts.

Stimulus Attributes: Test items may include: illustrations of coordinate graphs, number lines, tables, graphs, and charts, such as frequency charts, line, bar, and picture graphs; Venn diagrams; stem-and-leaf plots, box-and-whisker plots, and scatter plots; histograms, circle graphs, data sets, spinners, and other diagrams.

Format: • Predict the probability of the outcome of a specified event or experiment in a mathematical

or real-world context based on “or,” “and,” or “not” statements • Express probabilities in various forms, including decimal, fraction, and percent

Content Limits: • Limit sample to no more than 20 pieces of data • Limit real-world contexts to age-appropriate situations


Distractor Domain: • Common errors • Incorrect procedures • Computational errors • Incorrect use of rules or properties • Use of incorrect equivalencies


PASS 5.2 Sample Test Items: Primary Process Standard: 7M5.3 Depth of Knowledge: 2 Correct Answer: C

When Norma bought lunch at a restaurant, she was given a scratch-off game card with this statement:

1 out of 8 cards is a winner!

What is the probability that Norma did not receive a winning game card?

A 8%

B 12.5%

C 87.5%

D 92%



The prize wheel at the school fair is divided into 6 sections of equal size. The sections are numbered 1 through 6.

If the arrow is spun once, what is the probability that it will stop on a section labeled with an even number divisible by 3 or a section labeled with an odd number?

A 61

B 21

C 32

D 65



The graph shows the results of a survey given to a group of students.

If one student is picked at random, what is the probability that the student has a family with 6 or 7 members?

A 261

B 263

C 264

D 267



As part of a probability experiment, Susannah rolled two fair number cubes, one after the other. Each cube had its faces numbered 1 through 6. What is the probability that the first cube landed on 5 and the second cube landed on 6?

A 1

6

B 1

12

C 1

18

D 1

36



Pam is playing a game with two spinners. One spinner has 3 sections of equal size, each labeled with a number 1 through 3. The other spinner has 5 sections of equal size, each labeled with a letter J through N. She drew this tree diagram to show the possible outcomes.

What is the probability of the arrow on either spinner landing on a 2 or a K on the next spin?

A 1

5

C 7

15

B 1

3

D 8

15



There are 20 students in Mr. Zapata’s class. The Venn diagram shows the pets that some of the students have.

If Mr. Zapata chooses a student at random, what is the probability that the student has a dog or a cat?

A 3

20

B 9

20

C 3

4

D 5

6


PASS Standard: Standard 5: Data Analysis and Probability—The student will use probability to formulate

and justify predictions from a set of data. PASS Objective:

3. Find all possible combinations and permutations involving a limited number of variables.

Item Specifications: Emphasis: Demonstrate the ability to find all possible combinations and permutations given a limited number of variables.

Stimulus Attributes: Test items may include illustrations of the following: data sets, tables, charts, other diagrams, or illustrations.

Format: Given a limited number of variables, the student will determine all possible combinations and permutations.

Content Limits: • Limit combinations and permutations to up to 10 objects taken up to 10 at a time • Limit real-world contexts to age-appropriate situations


Distractor Domain: • Computational errors • Misunderstanding of concepts


PASS 5.3 Sample Test Items: Primary Process Standard: 7M3.4 Depth of Knowledge: 2 Correct Answer: C

If digits cannot be repeated, how many different 2-digit numbers can be made from the digits in this set?

{1, 2, 3}

A 3 numbers

B 4 numbers

C 6 numbers

D 9 numbers


Redland Middle School has 6 students who are finalists in the spelling contest. In how many different orders could 3 of these students finish in 1st, 2nd, and 3rd place?

A 15 orders

B 18 orders

C 120 orders

D 216 orders



A school club has 5 members. From these 5 members, a 2-person team must be chosen to represent the club at a school carnival. How many different 2-person teams can be made from the 5 club members?

A 10 teams

B 15 teams

C 20 teams

D 25 teams


Amy has 9 different compact discs. She can place 3 compact discs in her CD player. How many different groups of 3 compact discs could Amy place in her CD player? A 12 groups

B 27 groups

C 81 groups

D 84 groups



Emilio is coloring a map of the United States. He can choose a group of 5 colors from a total of 9 different colors. Which expression represents the number of different groups that Emilio can choose?

A 9 8 7 6 5

(9 5)!−i i i i

B 9 8 7 6 5

5!

i i i i

C 9!

(9 5)!−

D 9!

5!

ok grade 7 math item specs

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