ohio’s state tests · involving angle measure, circles, area, surface area, and volume. use facts...

Ohio’s State Tests

ITEM RELEASE

SPRING 2019

GRADE 7MATHEMATICS

i (2019)

Table of Contents Content Summary and Answer Key ............................................................................... iii Depth of Knowledge (DOK) ........................................................................................... x Question 2: Question and Scoring Guidelines .............................................................. 1 Question 2: Sample Response ........................................................................................ 3 Question 4: Question and Scoring Guidelines .............................................................. 4 Question 4: Sample Response ........................................................................................ 6 Question 8: Question and Scoring Guidelines .............................................................. 7 Question 8: Sample Response ...................................................................................... 10 Question 9: Question and Scoring Guidelines ............................................................ 11 Question 9: Sample Responses ..................................................................................... 14 Question 11: Question and Scoring Guidelines .......................................................... 19 Question 11: Sample Response .................................................................................... 21 Question 13: Question and Scoring Guidelines .......................................................... 22 Question 13: Sample Responses ................................................................................... 25 Question 14: Question and Scoring Guidelines .......................................................... 30 Question 14: Sample Response .................................................................................... 32 Question 17: Question and Scoring Guidelines .......................................................... 33 Question 17: Sample Responses ................................................................................... 36 Question 18: Question and Scoring Guidelines .......................................................... 41 Question 18: Sample Response .................................................................................... 44 Question 20: Question and Scoring Guidelines .......................................................... 45 Question 20: Sample Response .................................................................................... 47 Question 21: Question and Scoring Guidelines .......................................................... 48 Question 21: Sample Responses ................................................................................... 51 Question 22: Question and Scoring Guidelines .......................................................... 56 Question 22: Sample Responses ................................................................................... 59 Question 24: Question and Scoring Guidelines .......................................................... 64 Question 24: Sample Response .................................................................................... 66

ii (2019)

Question 25: Question and Scoring Guidelines .......................................................... 67 Question 25: Sample Response .................................................................................... 69 Question 29: Question and Scoring Guidelines .......................................................... 70 Question 29: Sample Response .................................................................................... 73 Question 36: Question and Scoring Guidelines .......................................................... 74 Question 36: Sample Responses ................................................................................... 77 Question 37: Question and Scoring Guidelines .......................................................... 81 Question 37: Sample Response .................................................................................... 84 Question 38: Question and Scoring Guidelines .......................................................... 85 Question 38: Sample Response .................................................................................... 88 Question 41: Question and Scoring Guidelines .......................................................... 89 Question 41: Sample Responses ................................................................................... 92 Question 42: Question and Scoring Guidelines .......................................................... 97 Question 42: Sample Responses ................................................................................. 100

iii (2019)

Grade 7 Math Spring 2019 Item Release

Content Summary and Answer Key Question

No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points

2 Multiple Choice Item

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (7.NS.2) d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Level 1 B 1 point


Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume.

Work with circles. (7.G.4) b. Know and use the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems.

Level 1 B 1 point


Summarize and describe distributions representing one population and draw informal comparisons between two populations.

Describe and analyze distributions. (7.SP.3) b. Informally assess the degree of visual overlap of two numerical data distributions with roughly equal variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot (line plot), the separation between the two distributions of heights is noticeable.

Level 3 B 1 point

* The question number matches the item number in the Item Level Report in the Online Reporting System. The items are numbered sequentially in the practice site.

iv (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points

9 Grid Item

Draw, construct, and describe geometrical figures and describe the relationships between them.

Draw (freehand, with ruler and protractor, and with technology) geometric figures with given conditions. (7.G.2)

Level 2 --- 1 point


Use sampling to draw conclusions about a population.

Understand that statistics can be used to gain information about a population by examining a sample of the population. (7.SP.1) b. Understand that conclusions and generalizations about a population are valid only if the sample is representative of that population. Develop an informal understanding of bias.

Level 1 C 1 point

13 Equation Item

Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5)

Level 2 --- 1 point


Analyze proportional relationships and use them to solve real-world and mathematical problems.

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. (7.RP.1)

Level 2 C 1 point


v (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points

17 Grid Item


Recognize and represent proportional relationships between quantities. (7.RP.2) d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Level 3 --- 1 point



Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Level 3 C 1 point



Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. (7.G.3)

Level 2 B 1 point


vi (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points

21 Equation item

Investigate chance processes and develop, use, and evaluate probability models.

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (7.SP.5)

Level 3 --- 1 point

22 Equation Item


Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. (7.NS.3)

Level 2 --- 1 point



Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Level 1 D 1 point


vii (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points



Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals. (7.G.1) a. Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale.

Level 1 A 1 point


Use properties of operations to generate equivalent expressions.

In a problem context, understand that rewriting an expression in an equivalent form can reveal and explain properties of the quantities represented by the expression and can reveal how those quantities are related. For example, a discount of 15% (represented by p – 0.15p) is equivalent to (1 – 0.15)p, which is equivalent to 0.85p or finding 85% of the original price. (7.EE.2)

Level 2 B 1 point

36 Equation Item


Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7.RP.3)

Level 2 --- 1 point


viii (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points



Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. (7.SP.6)

Level 2 D 1 point


Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. (7.EE.3)

Level 1 D 1 point


ix (2019)



No.* Item Type

Content Cluster

Content Standard

Depth of Knowledge

Answer Key Points

41 Equation Item


Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (7.SP.7) a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Level 2 --- 1 point

42 Equation Item


Recognize and represent proportional relationships between quantities. (7.RP.2) c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Level 2 --- 2 points


x (2019)

Depth of Knowledge (DOK) DOK refers to the complexity of thinking required to complete a task in a given item. Items with a DOK 1 designation focus on the recall of information, such as definitions and terms, and simple procedures. Items with a DOK 2 designation require students to make decisions, solve routine problems, perform calculations, or recognize patterns. Items with a DOK 3 designation feature higher-order cognitive tasks. These DOK 3 tasks include but are not limited to: critiquing a statement and forming a conclusion; explaining, justifying, or proving a statement; or approaching abstract, complex, open-ended, and non-routine problems. Each grade’s blueprint contains information about the number of points of opportunity students will encounter at each DOK level.

Table 1: Math Descriptors – Applying Depth of Knowledge Levels for Mathematics (Webb, 2002) & NAEP 2002 Mathematics Levels of Complexity

(M. Petit, Center for Assessment 2003, K. Hess, Center for Assessment, updated 2006)

Level 1 Recall

Level 2 Skills/Concepts

Level 3 Strategic Thinking

Level 4 Extended Thinking

a. Recall, observe, or recognize a fact, definition, term, or property

b. Apply/compute a well-known algorithm (e.g., sum, quotient)

c. Apply a formula d. Determine the area

or perimeter of rectangles or triangles given a drawing and labels

e. Identify a plane or three-dimensional figure

f. Measure g. Perform a specified

or routine procedure (e.g., apply rules for rounding)

h. Evaluate an expression

i. Solve a one-step word problem

j. Retrieve information from a table or graph

a. Classify plane and three-dimensional figures

b. Interpret information from a simple graph

c. Use models to represent mathematical concepts

d. Solve a routine problem requiring multiple steps/ decision points, or the application of multiple concepts

e. Compare and/or contrast figures or statements

f. Construct 2-dimensional patterns for 3-dimensional models, such as cylinders and cones

g. Provide justifications for steps in a solution process

h. Extend a pattern

a. Interpret information from a complex graph

b. Explain thinking when more than one response is possible

c. Make and/or justify conjectures

d. Use evidence to develop logical arguments for a concept

e. Use concepts to solve non-routine problems

f. Perform a procedure with multiple steps and multiple decision points

g. Generalize a pattern h. Describe, compare,

and contrast solution methods

i. Formulate a mathematical model for a complex situation

j. Provide mathematical justifications

a. Relate mathematical concepts to other content areas

b. Relate mathematical concepts to real- world applications in new situations

c. Apply a mathematical model to illuminate a problem, situation

d. Conduct a project that specifies a problem, identifies solution paths, solves the problem, and reports results

e. Design a mathematical model to inform and solve a practical or abstract situation

f. Develop generalizations of the results obtained and the strategies used and apply them to new problem situations

Table 1 continued on next page.

xi (2019)

Level 1 Recall

Level 2 Skills/Concepts

Level 3 Strategic Thinking

Level 4 Extended Thinking

k. Recall, identify, or make conversions between and among representations or numbers (fractions, decimals, and percents), or within and between customary and metric measures

l. Locate numbers on a number line, or points on a coordinate grid

m. Solve linear equations

n. Represent math relationships in words, pictures, or symbols

o. Read, write, and compare decimals in scientific notation

i. Retrieve information from a table, graph, or figure and use it to solve a problem requiring multiple steps

j. Translate between tables, graphs, words and symbolic notation

k. Make direct translations between problem situations and symbolic notation

l. Select a procedure according to criteria and perform it

m. Specify and explain relationships between facts, terms, properties, or operations

n. Compare, classify, organize, estimate, or order data

k. Solve a multiple- step problem and provide support with a mathematical explanation that justifies the answer

l. Solve 2-step linear equations/ inequalities in one variable over the rational numbers, interpret solution(s) in the original context, and verify reasonableness of results

m. Translate between a problem situation and symbolic notation that is not a direct translation

n. Formulate an original problem, given a situation

o. Analyze the similarities and differences between procedures

p. Draw conclusion from observations or data, citing evidence

g. Apply one approach among many to solve problems

h. Apply understanding in a novel way, providing an argument/ justification for the application

NOTE: Level 4 involves such things as complex restructuring of data or establishing and evaluating criteria to solve problems.

Updated 2006 © Marge Petit & Karin K. Hess, National Center for Assessment, Dover, NH Permission to reproduce is given when authorship is fully cited [email protected]

1 (2019)

Grade 7 Math

Spring 2019 Item Release

Question 2

Question and Scoring Guidelines

2 (2019)

Question 2

25765

Points Possible: 1 Content Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Content Standard: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (7.NS.2) d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Depth of Knowledge: Level 1 b. Apply/compute a well-known algorithm (e.g., sum, quotient) Calculator Designation: No Calculator

3 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may correctly divide 8 by 11 but incorrectly terminate the decimal. Rationale for Option B: Key – The student correctly divides 8 by 11, noticing that 0.72 is a repeating decimal. Rationale for Option C: This is incorrect. The student may correctly divide 8 by 11 but incorrectly round the repeating decimal. Rationale for Option D: This is incorrect. The student may divide 11 by 8.

Sample Response: 1 point

4 (2019)

Grade 7 Math


Question 4


5 (2019)

Question 4

32631

Points Possible: 1 Content Cluster: Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume. Content Standard: Work with circles. (7.G.4) b. Know and use the formulas for the area and circumference of a circle and use them to solve real-world and mathematical problems. Depth of Knowledge: Level 1 a. Recall, observe, or recognize a fact, definition, term, or property

Calculator Designation: Calculator Neutral

6 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may confuse the formula for the circumference of the circle with the formula for the area of a circle. Rationale for Option B: Key – The student remembers that the area formula for a circle is πr2 and identifies the option that correctly uses this formula with the given radius. Rationale for Option C: This is incorrect. The student may incorrectly think that the formula for the area of a circle A with radius r is A = π2r instead of A = πr2. Rationale for Option D: This is incorrect. The student may confuse the radius and diameter and think that he or she needs to divide the given measure by 2 in order to use the formula for the area of a circle.


7 (2019)

Grade 7 Math


Question 8


8 (2019)

Question 8

29490

9 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may calculate and find that the mean of type B is higher, but there exist Type A oranges that weigh the same and more than Type B. Rationale for Option B: Key – The student understands that because the mean in Type B is higher and the variance is less, it is likely that a Type B orange will weigh more than a Type A orange.

Rationale for Option C: This is incorrect. The student may not understand how to interpret this data and think that there is no way to determine which orange is going to weigh more. Rationale for Option D: This is incorrect. The student may incorrectly think variance has to do with the height of the graph (number of oranges at each weight) and thus choose that there is more variance in the weight of Type B oranges.

Points Possible: 1 Content Cluster: Summarize and describe distributions representing one population and draw informal comparisons between two populations.

Content Standard: Describe and analyze distributions. (7.SP.3) b. Informally assess the degree of visual overlap of two numerical data distributions with roughly equal variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot (line plot), the separation between the two distributions of heights is noticeable. Depth of Knowledge: Level 3 a. Interpret information from a complex graph c. Make and/or justify conjectures e. Use concepts to solve a non-routine problem Calculator Designation: Calculator Neutral

10 (2019)


11 (2019)

Grade 7 Math


Question 9


12 (2019)

Question 9

29284

Points Possible: 1 Content Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. Content Standard: Draw (freehand, with ruler and protractor, and with technology) geometric figures with given conditions. (7.G.2) Depth of Knowledge: Level 2 a. Classify plane and three-dimensional figures d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts l. Select a procedure according to criteria and perform it Calculator Designation: Calculator Neutral

13 (2019)

Scoring Guidelines Exemplar Response

Other Correct Responses

• any isosceles triangle where the third side is shorter than the other two sides

For this item, a full-credit response includes:

• a correct triangle (1 point).

14 (2019)

Grade 7 Math


Question 9

Sample Responses

15 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly draws an isosceles triangle with 2 equal sides and the third side shorter than the other 2 sides.

16 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly draws an isosceles triangle with 2 equal sides and the third side shorter than the other 2 sides.

17 (2019)

Sample Response: 0 points

Notes on Scoring This response earns no credit (0 points). The student correctly draws an isosceles triangle but forgets that the third side is supposed to be shorter than the other two sides.

18 (2019)


Notes on Scoring This response earns no credit (0 points). The student draws a triangle that has two sides longer than the third, but it is a scalene triangle. No sides are equal.

19 (2019)

Grade 7 Math


Question 11


20 (2019)

Question 11

32561

Points Possible: 1 Content Cluster: Use sampling to draw conclusions about a population. Content Standard: Understand that statistics can be used to gain information about a population by examining a sample of the population. (7.SP.1) b. Understand that conclusions and generalizations about a population are valid only if the sample is representative of that population. Develop an informal understanding of bias. Depth of Knowledge: Level 1 a. Recall, observe, or recognize a fact, definition, term, or property Calculator Designation: Calculator Neutral

21 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may select a sample that is a reasonable size but does not consider that this sample is not representative of the population. Rationale for Option B: This is incorrect. The student may not realize that only the population of interest should be sampled. Rationale for Option C: Key – The student correctly identifies a valid sample since it is most likely to be representative of the population. Rationale for Option D: This is incorrect. The student may select a sample that is a reasonable size but would not be representative of the population and would most likely lead to biased results.


22 (2019)

Grade 7 Math


Question 13


23 (2019)

Question 13

29411

24 (2019)


• 180 – x


• any equivalent expression


• a correct expression (1 point).

Points Possible: 1 Content Cluster: Solve real-life and mathematical problems involving angle measure, circles, area, surface area, and volume. Content Standard: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5) Depth of Knowledge: Level 2 c. Use models to represent mathematical concepts d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts i. Retrieve information from a table, graph, or figure and use it to solve a problem requiring multiple steps k. Make direct translations between problem situations and symbolic notation Calculator Designation: No Calculator

25 (2019)

Grade 7 Math


Question 13

Sample Responses

26 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly creates an expression that represents the measure of angle DCE in terms of x. The straight line is always 180 degrees and by subtracting the measure of angle x from 180, you get the measure of angle DCE.

27 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly creates an expression that represents the measure of angle DCE in terms of x. The straight line is always 180 degrees and by subtracting the measure of angle x from 180, you get the measure of angle DCE.

28 (2019)


Notes on Scoring This response earns no credit (0 points). The student may mistake angle DCE for angle ACE and therefore identify angles BCD and ACE as congruent vertical angles.

29 (2019)


Notes on Scoring This response earns no credit (0 points). The student may mistakenly think that linear pairs add up to 90 degrees instead of 180 degrees.

30 (2019)

Grade 7 Math


Question 14


31 (2019)

Question 14

32727 054

Points Possible: 1 Content Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Content Standard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. (7.RP.1) Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts e. Compare and/or contrast figures or statements k. Make direct translations between problem situations and symbolic notation Calculator Designation: Calculator Neutral

32 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may only consider the number of apples in each bag instead of the relationship between the number of apples and the cost. Rationale for Option B: This is incorrect. The student may incorrectly take the reciprocal of the rates and calculate the number of apples per dollar instead of the cost per apple. Rationale for Option C: Key – The student correctly identifies that the unit cost for green apples is greater than the unit cost for red apples because 10.8 ÷ 12 is a little less than $1 per apple and 6.9 ÷ 6 is a little more than $1 per apple. Rationale for Option D: This is incorrect. The student may write a proportion of green apples over red apples (6.9/10.8 = 6/12) and think that since the left side is greater than the right side, this means that green apples cost more than red apples.


33 (2019)

Grade 7 Math


Question 17


34 (2019)

Question 17

27167

Points Possible: 1 Content Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Content Standard: Recognize and represent proportional relationships between quantities. (7.RP.2) d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Depth of Knowledge: Level 3 e. Use concepts to solve a non-routine problem f. Perform a procedure with multiple steps and multiple decision points m. Translate between a problem situation and symbolic notation that is not a direct translation Calculator Designation: Calculator Neutral

35 (2019)



• any line that graphs the equation y = 60x


• a correct graph (1 point).

36 (2019)

Grade 7 Math


Question 17

Sample Responses

37 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly creates a graph that shows the relationship between the square footage of the walls and the number of paint cans needed.

38 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly creates a graph that shows the relationship between the square footage of the walls and the number of paint cans needed.

39 (2019)


Notes on Scoring This response earns no credit (0 points). The student plots a point to represent the 2 cans of paint needed for 120 square feet but does not graph a line that shows the relationship between any number of square feet and how many paint cans would be needed to cover the area.

40 (2019)


Notes on Scoring This response earns no credit (0 points). The student graphs a line that shows the relationship between the square feet and number of paint cans needed but may not notice that the x-axis goes up by 1

2 for each gridline.

41 (2019)

Grade 7 Math


Question 18


42 (2019)

Question 18

33445

43 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may interpret the double negative in front of q as an upward motion on a vertical number line and therefore an upward motion on the weight. Rationale for Option B: This is incorrect. The student may think that because the spring is pulled down to a length of p centimeters, the original length is negative. Rationale for Option C: Key – The student correctly identifies that subtracting q centimeters from the length is equivalent to adding –q. Rationale for Option D: This is incorrect. The student correctly identifies that subtracting q centimeters from the length is equivalent to adding –q but may think that, because the spring is pulled down to a length of p centimeters, the original length is negative.

Points Possible: 1 Content Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Content Standard: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. Depth of Knowledge: Level 3 e. Use concepts to solve a non-routine problem i. Formulate a mathematical model for a complex situation m. Translate between a problem situation and symbolic notation that is not a direct translation Calculator Designation: Calculator Neutral

44 (2019)


45 (2019)

Grade 7 Math


Question 20


46 (2019)

Question 20

26384

Points Possible: 1 Content Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. Content Standard: Describe the two-dimensional figures (cross sections) that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. (7.G.3) Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts e. Compare and/or contrast figures or statements Calculator Designation: Calculator Neutral

47 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may identify that the cross section will be the same shape as the base but incorrectly think the area will be larger. Rationale for Option B: Key – The student identifies that a cross section parallel to the base will be the same shape as the base and have a smaller area. Rationale for Option C: This is incorrect. The student may consider a cross section perpendicular to the base and think the cross section therefore will have a larger area. Rationale for Option D: This is incorrect. The student may consider a cross section perpendicular to the base and think the cross section therefore will have a smaller area.


48 (2019)

Grade 7 Math


Question 21


49 (2019)

Question 21

26594

50 (2019)


• A. 0.75

B. 0.25


• any two values with the following characteristics: o Value in A is greater than value in B. o Values in A and B must both be greater than 0 and less than 1. o The sum of the values in A and B is exactly 1.


• two correct probabilities (1 point).

Points Possible: 1 Content Cluster: Investigate chance processes and develop, use, and evaluate probability models. Content Standard: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (7.SP.5) Depth of Knowledge: Level 3 e. Use concepts to solve a non-routine problem Calculator Designation: Calculator Neutral

51 (2019)

Grade 7 Math


Question 21

Sample Responses

52 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly enters a possible probability that a student plays sports in Part A and enters a correct probability in Part B based on their answer in Part A. Value A is greater than Value B, and the two values add up to exactly 1.

53 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly enters a possible probability that a student plays sports in Part A and enters a correct probability in Part B based on their answer in Part A. Value A is greater than Value B, and the two values add up to exactly 1.

54 (2019)


Notes on Scoring This response earns no credit (0 points). The student correctly enters a possible probability that a student plays sports in Part A and enters a probability in Part B that is less than the value in Part A. Although Value A is greater than Value B, the student does not take into consideration that the two values need to add up to exactly 1.

55 (2019)


Notes on Scoring This response earns no credit (0 points). The student may realize that 60% for Value A and 40% for Value B would meet the given criteria but does not rewrite these in an acceptable form. All probabilities should be expressed as a number between 0 and 1, with 0 being impossible and 1 being certain.

56 (2019)

Grade 7 Math


Question 22


57 (2019)

Question 22

28744

Points Possible: 1 Content Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Content Standard: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions. (7.NS.3) Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts Calculator Designation: No Calculator

58 (2019)


• -4


• any placement where point P is located at (x, y) and point Q is located at (x+2, y+3)


• a correct value (1 point).

59 (2019)

Grade 7 Math


Question 22

Sample Responses

60 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly evaluates the expression. The student may calculate within the parentheses first and get (–9+3) equal to –6, and then take two thirds of –6, which is −4.

61 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly evaluates the expression. The student may calculate within the parentheses first and get (–9+3) equal to –6, then multiply this result by 2 to get –12, and finally write this result over 3 to get a correct value written in fraction form.

62 (2019)


Notes on Scoring This response earns no credit (0 points). The student may forget to take the negative sign into consideration when responding and gets 4 instead of –4.

63 (2019)


Notes on Scoring This response earns no credit (0 points). The student may mistakenly calculate – (9+3) to get –12 instead of –6, and then multiply by 2

3 to get −24

3, which is –8.

64 (2019)

Grade 7 Math


Question 24


65 (2019)

Question 24

32526

Points Possible: 1 Content Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Content Standard: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. Depth of Knowledge: Level 1 a. Recall, observe, or recognize a fact, definition, term, or property l. Locate numbers on a numberline, or points on a coordinate grid Calculator Designation: No Calculator

66 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may subtract 6 from –6. Rationale for Option B: This is incorrect. The student may not take the negative sign into consideration, adding 6 and 6. Rationale for Option C: This is incorrect. The student may confuse today's change in temperature with today's actual temperature. Rationale for Option D: Key – The student correctly identifies today's temperature as 0 degrees Fahrenheit.


67 (2019)

Grade 7 Math


Question 25


68 (2019)

Question 25

32658

Points Possible: 1 Content Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. Content Standard: Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals. (7.G.1) a. Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale. Depth of Knowledge: Level 1 a. Recall, observe, or recognize a fact, definition, term, or property i. Solve a one-step word problem Calculator Designation: Calculator Neutral

69 (2019)

Scoring Guidelines Rationale for Option A: Key – The student correctly divides the length of the garden by 2 to find the number of inches in the model. Rationale for Option B: This is incorrect. The student may incorrectly use the scale and subtract 2 from the number of feet rather than dividing by 2. Rationale for Option C: This is incorrect. The student may think that the side length, in inches, of the scale model is equal to the side length, in feet, of the garden because they are similar shapes. Rationale for Option D: This is incorrect. The student may incorrectly use the scale and multiply the number of feet by 2 to find the side length rather than dividing by 2.


70 (2019)

Grade 7 Math


Question 29


71 (2019)

Question 29

32729

72 (2019)

Scoring Guidelines

Rationale for Option A: This is incorrect. The student identifies an expression that reveals the number of chairs on each side of the original two-square rectangular table. Rationale for Option B: Key – The student identifies an expression that reveals the number of chairs on each side of a three-square rectangular table. Rationale for Option C: This is incorrect. The student may confuse the number of chairs for each square table. Rationale for Option D: The student may identify an expression that reveals the number of chairs along two adjacent sides of the three-square rectangular table.

Points Possible: 1 Content Cluster: Use properties of operations to generate equivalent expressions. Content Standard: In a problem context, understand that rewriting an expression in an equivalent form can reveal and explain properties of the quantities represented by the expression and can reveal how those quantities are related. For example, a discount of 15% (represented by p – 0.15p) is equivalent to (1 – 0.15)p, which is equivalent to 0.85p or finding 85% of the original price. (7.EE.2) Depth of Knowledge: Level 2 h. Extend a pattern i. Retrieve information from a table, graph, or figure and use it to solve a problem requiring multiple steps j. Translate between tables, graphs, words and symbolic notation k. Make direct translations between problem situations and symbolic notation Calculator Designation: Calculator

73 (2019)


74 (2019)

Grade 7 Math


Question 36


75 (2019)

Question 36

24728

20512

Points Possible: 1 Content Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Content Standard: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. (7.RP.3) Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts Calculator Designation: Calculator

76 (2019)


• $4.00


• N/A

For this item, a full-credit response includes

• the correct value (1 point).

77 (2019)

Grade 7 Math


Question 36

Sample Responses

78 (2019)


Notes on Scoring This response earns full credit (1 point). The student correctly calculates how much interest was in Pete’s account after one year. The student may first calculate the amount Teagan started with by dividing 2.20 by 0.0275 to get $80; thereafter, because the two started with the same amount, multiplying 80 by 0.05 to get $4.

79 (2019)


Notes on Scoring This response earns no credit (0 points). The student may reason that 5% is around twice as much as 2.75%, so they decide to double $2.20.

80 (2019)


Notes on Scoring This response earns no credit (0 points). The student may think that since both Pete and Teagan started with the same amount of money, they would earn the same amount of interest.

81 (2019)

Grade 7 Math


Question 37


82 (2019)

Question 37

32891

83 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may read the table and respond with how many times the digit 4 was produced in the initial 500 runs of the generator. Rationale for Option B: This is incorrect. The student may think that the number generator was random, therefore dividing 4000 by 5 possible outcomes, and chooses the number closest to 800. Rationale for Option C: This is incorrect. The student may think that the number generator only generates 4 unique numbers, therefore dividing 4000 by 4 possible outcomes, and chooses the number closest to 1000. Rationale for Option D: Key – The student correctly identifies that the probability of the number 4 being produced on the weighted number generator is about 30% based on the table of data (152 out of 500), and chooses the number closest to 1,200.

Points Possible: 1 Content Cluster: Investigate chance processes and develop, use, and evaluate probability models. Content Standard: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. (7.SP.6) Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts i. Retrieve information from a table, graph or figure and use it to solve a problem requiring multiple steps Calculator Designation: Calculator

84 (2019)


85 (2019)

Grade 7 Math


Question 38


86 (2019)

Question 38

31768

87 (2019)

Points Possible: 1 Content Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Content Standard: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. (7.EE.3) Depth of Knowledge: Level 1 m. Solve linear equations Calculator Designation: Calculator Neutral

88 (2019)

Scoring Guidelines Rationale for Option A: This is incorrect. The student may notice that dividing 16 by 4 will make the left side of the equation 4 but does not remember that both sides of the equation have to be divided by 4 to maintain equivalency. Rationale for Option B: This is incorrect. The student may confuse adding 12 to both sides with subtracting 12 from both sides. Rationale for Option C: This is incorrect. The student may notice that division by 4 will make the left side equal to 4 but does not notice that the right side of the equation is not divided by 4 which is necessary to maintain equivalency. Rationale for Option D: Key – The student notices that the 12 was eliminated from the right side. Therefore, by subtracting 12 from each side of the equation, maintains equivalency.


89 (2019)

Grade 7 Math


Question 41


90 (2019)

Question 41

32858

91 (2019)

20512


• 410


• any equivalent value


• a correct probability (1 point).

Points Possible: 1 Content Cluster: Investigate chance processes and develop, use, and evaluate probability models. Content Standard: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (7.SP.7) a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts Calculator Designation: Calculator Neutral

92 (2019)

Grade 7 Math


Question 41

Sample Responses

93 (2019)


Notes on Scoring This response earns full credit (1 point). The student identifies the correct probability that Matt will select one of the letters in the word JUMP. The student may first identify that all four letters in the word JUMP are in the set of letters and then identify that there are ten letters in the set.

94 (2019)


Notes on Scoring This response earns full credit (1 point). The student identifies the correct probability that Matt will select one of the letters in the word JUMP. The student may first identify that all four letters in the word JUMP are in the set of letters and then identify that there are ten letters in the set. Finally, the student correctly responds with an equivalent fraction to 4

10.

95 (2019)


Notes on Scoring This response earns no credit (0 points). The student may think the task is asking for the probability of only 1 letter instead of one of the four letters.

96 (2019)


Notes on Scoring This response earns no credit (0 points). The student may only focus on the word JUMP and calculate the probability for picking one of the letters in the word JUMP from only those four letters.

97 (2019)

Grade 7 Math


Question 42


98 (2019)

Question 42

28778

99 (2019)

20512


• A. c = 1.25s

B. 20


• an equivalent equation • an equivalent value • student may also enter s = 20 in second response box


• a correct equation (1 point) AND

• the correct number of songs (1 point).

Points Possible: 2 Content Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. Content Standard: Recognize and represent proportional relationships between quantities. (7.RP.2) c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Depth of Knowledge: Level 2 d. Solve a routine problem requiring multiple steps/decision points, or the application of multiple concepts k. Make direct translations between problem situations and symbolic notation Calculator Designation: Calculator

100 (2019)

Grade 7 Math


Question 42

Sample Responses

101 (2019)


Notes on Scoring This response earns full credit (2 points). Part A: The student may divide $10 by 8 songs to get that each song costs $1.25. The student uses this number correctly when creating an equation to represent the relationship. Part B: The student uses the correct equation and calculates that 20 songs can be purchased for $25.

102 (2019)


Notes on Scoring This response earns full credit (2 points). Part A: The student may set up $10 divided by 8 as a fraction to figure out how much one song costs. Then the student may calculate an equivalent fraction to 10

8 and get 5

4 dollars per song. The

student uses this to create a correct equation that represents the relationship. Part B: The student correctly calculates that 20 songs can be purchased for $25.00.

103 (2019)


Notes on Scoring This response earns partial credit (1 point). Part A: The student may incorrectly divide 8 songs by $10 by setting it up as a fraction, 8

10 , dividing numerator and denominator by 2 to get

45. The student uses this number when creating an incorrect

equation to represent the relationship. Part B: The student may start from the beginning of the problem, using a calculator to divide $10 by 8 songs to get $1.25 per song. Thereafter dividing 25 by 1.25, the student correctly calculates that 20 songs can be purchased for $25.

104 (2019)


Notes on Scoring This response earns partial credit (1 point). Part A: The student may use a calculator to divide $10 by 8 songs to get $1.25 per song and create a correct equation to represent the relationship. Part B: The student may substitute 25 for s instead of for c in the equation and then round down.

105 (2019)


Notes on Scoring This response earns no credit (0 points). Part A: The student confuses the variables and only writes an expression instead of an equation. Part B: The student uses their incorrect expression, correctly substitutes 25 for c, resulting in 31.25 as the cost for one song and rounds to a whole number.

ohio’s state tests · involving angle measure, circles, area, surface area, and volume. use facts...

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