ohio’s state tests...understand a rational number as a point on the number line. extend number...

Ohio’s State Tests

ITEM RELEASE

SPRING 2017

GRADE 6MATHEMATICS

i

Table of Contents

Questions 1 – 19: Content Summary and Answer Key ................................................ iii

Question 1: Question and Scoring Guidelines .............................................................. 1

Question 1: Sample Responses ....................................................................................... 5

Question 2: Question and Scoring Guidelines ............................................................ 11

Question 2: Sample Response ...................................................................................... 13

Question 3: Question and Scoring Guidelines ........................................................... 15

Question 3: Sample Responses ..................................................................................... 19













Question 10: Question and Scoring Guidelines .......................................................... 71

Question 10: Sample Response .................................................................................... 73


Question 11: Sample Responses ................................................................................... 79


Question 12: Sample Responses ................................................................................... 89


Question 13: Sample Response .................................................................................... 99

ii

Question 14: Question and Scoring Guidelines ........................................................ 101

Question 14: Sample Response .................................................................................. 103


Question 15: Sample Responses ................................................................................. 109









iii

Grade 6 Math

Spring 2017 Item Release

Content Summary and Answer Key

Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

1 Equation

Item

Apply and

extend

previous

understandings

of arithmetic to

algebraic

expressions.

Write and evaluate numerical

expressions involving whole-

number exponents. (6.EE.1)

--- 1 point

2 Multiple

Choice

Understand

ratio concepts

and use ratio

reasoning to

solve problems.

Understand the concept of a

ratio and use ratio language to

describe a ratio relationship

between two quantities. For

example, “The ratio of wings to

beaks in the bird house at the

zoo was 2:1, because for every 2

wings there was 1 beak.” “For

every vote candidate A

received, candidate C received

nearly three votes.” (6.RP.1)

D 1 point

3 Short

Response

Apply and

extend

previous

understandings

of numbers to

the system of

rational

numbers.

Understand ordering and

absolute value of rational

numbers. (6.NS.7)

b. Write, interpret, and explain

statements of order for rational

numbers in real-world contexts.

For example, write −3°C > −7°C

to express the fact that −3°C is

warmer than −7 °C.

--- 2 points

iv

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

4 Multiple

Choice

Develop

understanding

of statistical

variability.

Recognize that a measure of

center for a numerical data set

summarizes all of its values with a

single number, while a measure

of variation describes how its

values vary with a single number.

(6.SP.3)

A 1 point

5 Multiple

Choice

Apply and

extend

previous

understandings

of arithmetic to

algebraic

expressions.

Write, read, and evaluate

expressions in which letters stand

for numbers. (6.EE.2)

a. Write expressions that record

operations with numbers and

with letters standing for numbers.

For example, express the

calculation “Subtract y from 5”

as 5 − y.

B 1 point

6 Equation

Item

Compute

fluently with

multi-digit

numbers and

find common

factors and

multiples.

Fluently add, subtract, multiply,

and divide multi-digit decimals

using the standard algorithm

for each operation. (6.NS.3)

--- 1 point

7 Multiple

Choice

Apply and

extend

previous

understandings

of numbers to

the system of

rational

numbers.

Understand a rational number as

a point on the number line.

Extend number line diagrams

and coordinate axes familiar

from previous grades to

represent points on the line and

in the plane with negative

number coordinates. (6.NS.6)

c. Find and position integers and

other rational numbers on a

horizontal or vertical number line

diagram; find and position pairs

of integers and other rational

numbers on a coordinate plane.

A 1 point

v

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

8 Equation

Item

Apply and

extend

previous

understandings

of

multiplication

and division to

divide fractions

by fractions.

Interpret and compute quotients

of fractions, and solve word

problems involving division of

fractions by fractions, e.g., by

using visual fraction models and

equations to represent the

problem. For example, create a

story context for (2

3) ÷ (

3

4) and use

a visual fraction model to show

the quotient; use the relationship

between multiplication and

division to explain that (2

3) ÷ (

3

4) =

6

9

because 3

4of

6

9is

2

3. (In general,

(𝑎

𝑏) ÷ (

𝑐

𝑑) =

𝑎𝑑

𝑏𝑐.) How much

chocolate will each person get if

3 people share 1

2 pound of

chocolate equally? How many 3

4cup servings are in

2

3 of a cup of

yogurt? How wide is a

rectangular strip of land with

length 3

4 mi and area

1

2 square

mi? (6.NS.1)

--- 1 point

9

Graphic

Response

Item

Apply and

extend

previous

understandings

of numbers to

the system of

rational

numbers.

Solve real-world and

mathematical problems by

graphing points in all four

quadrants of the coordinate

plane. Include use of

coordinates and absolute value

to find distances between points

with the same first coordinate or

the same second coordinate.

(6.NS.8)

--- 1 point

vi

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

10

Multi-

Select

Item

Reason about

and solve one-

variable

equations and

inequalities.

Understand solving an equation

or inequality as a process of

answering a question: which

values from a specified set, if

any, make the equation or

inequality true? Use substitution

to determine whether a given

number in a specified set makes

an equation or inequality true.

(6.EE.5)

A, C, E 1 point

11 Equation

Item

Understand

ratio concepts

and use ratio

reasoning to

solve problems.

Use ratio and rate reasoning to

solve real-world and

mathematical problems, e.g., by

reasoning about tables of

equivalent ratios, tape diagrams,

double number line diagrams, or

equations. (6.RP.3b)

b. Solve unit rate problems

including those involving unit

pricing and constant speed. For

example, if it took 7 hours to

mow 4 lawns, then at that rate,

how many lawns could be

mowed in 35 hours? At what rate

were lawns being mowed?

--- 1 point

vii

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

12 Table Item

Represent and

analyze

quantitative

relationships

between

dependent

and

independent

variables.

Use variables to represent two

quantities in a real-world

problem that change in

relationship to one another; write

an equation to express one

quantity, thought of as the

dependent variable, in terms of

the other quantity, thought of as

the independent variable.

Analyze the relationship

between the dependent and

independent variables using

graphs and tables, and relate

these to the equation. For

example, in a problem involving

motion at constant speed, list

and graph ordered pairs of

distances and times, and write

the equation d = 65t to represent

the relationship between

distance and time. (6.EE.9)

--- 2 points

13 Multiple

Choice

Solve real-

world and

mathematical

problems

involving area,

surface area,

and volume.

Draw polygons in the coordinate

plane given coordinates for the

vertices; use coordinates to find

the length of a side joining points

with the same first coordinate or

the same second coordinate.

Apply these techniques in the

context of solving real-world and

mathematical problems. (6.G.3)

A 1 point

viii

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

14 Multiple

Choice

Understand

ratio concepts

and use ratio

reasoning to

solve problems.







equations. (6.RP.3c)

c. Find a percent of a quantity as

a rate per 100, e.g., 30% of a

quantity means 30

100 times the

quantity; solve problems

involving finding the whole, given

a part and the percent.

D 1 point

15 Equation

Item

Summarize and

describe

distributions.

Summarize numerical data sets

in relation to their context, such as by: (6.SP.5)

c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

--- 1 point

ix

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

16 Multiple

Choice

Understand

ratio concepts

and use ratio

reasoning to

solve problems.

Understand the concept of a

unit rate a/b associated with a

ratio a:b with b ≠ 0, and use rate

language in the context of a

ratio relationship. For example,

“This recipe has a ratio of 3 cups

of flour to 4 cups of sugar, so

there is 3

4 cup of flour for each

cup of sugar.” “We paid $75 for

15 hamburgers, which is a rate of

$5 per hamburger.” (6.RP.2)

A 1 point

17 Table Item

Understand

ratio concepts

and use ratio

reasoning to

solve problems.







equations. (6.RP.3)

a. Make tables of equivalent

ratios relating quantities with

whole-number measurements;

find missing values in the tables;

and plot the pairs of values on

the coordinate plane. Use tables

to compare ratios.

--- 1 point

x

Grade 6 Math



Question

No.

Item

Type

Content

Cluster

Content

Standard Answer

Key Points

18 Equation

Item

Reason about

and solve one-

variable

equations and

inequalities.

Write an inequality of the form

x > c or x < c to represent a

constraint or condition in a real-

world or mathematical problem.

Recognize that inequalities of the

form x > c or x < c have infinitely

many solutions; represent

solutions of such inequalities on

number line diagrams. (6.EE.8)

--- 1 point

19 Multiple

Choice

Apply and

extend

previous

understandings

of arithmetic to

algebraic

expressions.

Apply the properties of

operations to generate

equivalent expressions. For

example, apply the distributive

property to the expression

3(2 + x) to produce the

equivalent expression 6 + 3x;

apply the distributive property to

the expression 24x + 18y to

produce the equivalent

expression 6(4x + 3y); apply

properties of operations to

y + y + y to produce the

equivalent expression 3y. (6.EE.3)

B 1 point

1

Grade 6

Math


Question 1

Question and Scoring Guidelines

2

Question 1

16661

20512

Points Possible: 1

Content Cluster: Apply and extend previous understandings of

arithmetic to algebraic expressions.

Content Standard: Write and evaluate numerical expressions

involving whole-number exponents. (6.EE.1)

Calculator Designation: No calculator

3

Scoring Guidelines

Exemplar Response

14

Other Correct Responses

Any equivalent value.

For this item, a full-credit response includes:

The correct value (1 point).

5

Grade 6

Math


Question 1

Sample Responses

6

Sample Response: 1 point

Notes on Scoring

This response earns full credit (1 point) because the student

calculates the correct value of the expression.

7


Notes on Scoring



8

Sample Response: 0 points

Notes on Scoring

This response earns no credit (0 points) because the student

does not calculate the correct value of the expression. The

student may incorrectly perform the subtraction first and then

apply the exponent, arriving at this large value.

9


Notes on Scoring


does not calculate the correct value of the expression. The

student may subtract “3 times 4” from 95 to get this incorrect

response.

11

Grade 6

Math


Question 2


12

Question 2

16662

Points Possible: 1

Content Cluster: Understand ratio concepts and use ratio reasoning

to solve problems.

Content Standard: Understand the concept of a ratio and use ratio

language to describe a ratio relationship between two quantities.

For example, “The ratio of wings to beaks in the bird house at the zoo

was 2:1, because for every 2 wings there was 1 beak.” “For every

vote candidate A received, candidate C received nearly three

votes.” (6.RP.1)

Calculator Designation: Calculator neutral

13

Scoring Guidelines

Rationale for Option A: This is incorrect. The student may compare the number

of daisies to the number of sunflowers only to come to this answer.

Rationale for Option B: This is incorrect. The student may compare the number

of daisies to the number of tulips only to come to this answer.

Rationale for Option C: This is incorrect. The student may compare the number

of daisies to the total number of flowers that are not daises to come to this

answer.

Rationale for Option D: Key – The student correctly compares the number of

daisies to the total number of flowers.


15

Grade 6

Math


Question 3


16

Question 3

16663

Points Possible: 2


numbers to the system of rational numbers.

Content Standard: Understand ordering and absolute value of

rational numbers. (6.NS.7)

b. Write, interpret, and explain statements of order for rational

numbers in real-world contexts. For example, write −3°C > −7°C to

express the fact that −3°C is warmer than −7 °C.


17

Scoring Guidelines

Score Point Description

2 points The response includes the following:

The correct month of January (1 point);

AND

An explanation (1 point) that includes either:

o –10.4 > –11.6 or –10.4 is greater than –11.6

OR

–11.6 < –10.4 or –11.6 is less than –10.4

OR

–11.6 is to the left of/below –10.4 on a

number line

OR

–10.4 is to the right of/above –11.6 on a

number line. (1 point)

1 point The response includes the following:

The correct month of January (1 point);

OR

A correct explanation as indicated above

(1 point).

0 points The response does not meet the criteria required to

earn one point. The response indicates inadequate or

no understanding of the task and/or the idea or

concept needed to answer the item. It may only

repeat information given in the test item. The response

may provide an incorrect solution/response and the

provided supportive information may be irrelevant to

the item, or possibly, no other information is shown. The

student may have written on a different topic or

written, “I don't know.”

19

Grade 6

Math


Question 3

Sample Responses

20


Notes on Scoring

This response earns full credit (2 points) because the student

identifies the correct month and gives a correct explanation

of why a temperature in the –11° range is a lower

temperature than one in the –10° range.

21


Notes on Scoring


identifies the correct month and gives a correct

mathematical inequality showing that January is on average

colder than December.

22


Notes on Scoring

This response earns partial credit (1 point) because the

student identifies the correct month but does not explain why

–11.6° is a lower temperature than –10.4°

23


Notes on Scoring


student identifies the correct month but does not explain why

–11.6° is a lower temperature than –10.4°

24


Notes on Scoring


student responds with the correct month but does not explain

why –11.6° is a lower temperature than –10.4°

25


Notes on Scoring


does not identify the correct month and does not provide an

explanation for why one average low temperature is lower

than another.

26


Notes on Scoring


does not identify the correct month. Instead, the response

identifies the month with the warmest average low

temperature.

27


Notes on Scoring


does not identify the correct month and gives no explanation

for the average low temperature chosen.

29

Grade 6

Math


Question 4


30

Question 4

16664

Points Possible: 1

Content Cluster: Develop understanding of statistical

variability.

Content Standard: Recognize that a measure of center for a

numerical data set summarizes all of its values with a single number,

while a measure of variation describes how its values vary with a

single number. (6.SP.3)


31

Scoring Guidelines

Rationale for Option A: Key – The student determines that the average

number of sightings over the 5-year period describes the mean for this data

set.

Rationale for Option B: This is incorrect. The student may think that the

difference between the number of sightings each year will describe the mean

for this data set.

Rationale for Option C: This is incorrect. The student may think that the total

number of sightings over the 5-year period will describe the mean for this data

set.

Rationale for Option D: This is incorrect. The student may think that the mean

number of sightings each year is not an average but the actual number

recorded.


33

Grade 6

Math


Question 5


34

Question 5

16665

Points Possible: 1



Content Standard: Write, read, and evaluate expressions in which

letters stand for numbers. (6.EE.2)

a. Write expressions that record operations with numbers and with

letters standing for numbers. For example, express the calculation

“Subtract y from 5” as 5 − y.


35

Scoring Guidelines

Rationale for Option A: This is incorrect. The student may think that "one-half

of” is the same as "times 2".

Rationale for Option B: Key – The student identifies the correct expression.

Rationale for Option C: This is incorrect. The student may think that "one-half of"

means to subtract one-half (one-half off).

Rationale for Option D: This is incorrect. The student may confuse multiplication

with addition.


37

Grade 6

Math


Question 6


38

Question 6

16666

20512

Points Possible: 1

Content Cluster: Compute fluently with multi-digit numbers and find

common factors and multiples.

Content Standard: Fluently add, subtract, multiply, and divide multi-

digit decimals using the standard algorithm for each operation.

(6.NS.3)


39

Scoring Guidelines

Exemplar Response

12.8


Any equivalent value


A correct value (1 point).

41

Grade 6

Math


Question 6

Sample Responses

42


Notes on Scoring


correctly calculates the value of the expression.

43


Notes on Scoring


correctly calculates the value of the expression.

44


Notes on Scoring


provides an incorrect value of the expression. The student

may incorrectly eliminate the decimal point and calculate

48 times 2, and then add 3.2 to get 99.2.

45


Notes on Scoring


provides an incorrect value of the expression. The student

may correctly multiply 4.8 by 2 to get 9.6, and then incorrectly

add 32, forgetting about the decimal point between the 3

and the 2.

47

Grade 6

Math


Question 7


48

Question 7

16667

Points Possible: 1



Content Standard: Understand a rational number as a point on the

number line. Extend number line diagrams and coordinate axes

familiar from previous grades to represent points on the line and in

the plane with negative number coordinates. (6.NS.6)

c. Find and position integers and other rational numbers on a

horizontal or vertical number line diagram; find and position pairs of

integers and other rational numbers on a coordinate plane.


49

Scoring Guidelines

Rationale for Option A: Key – The student identifies a distance of 8 as the

largest distance.

Rationale for Option B: This is incorrect. The student may think that all negative

numbers are farthest from 0.

Rationale for Option C: This is incorrect. The student may think that the

question is asking for the closest number on the number line.

Rationale for Option D: This is incorrect. The student may think that since -9 has

the greatest absolute value, it must be the farthest from -2.


51

Grade 6

Math


Question 8


52

Question 8

16668

20512 Points Possible: 1

Content Cluster: Apply and extend previous understandings of multiplication

and division to divide fractions by fractions.

Content Standard: Interpret and compute quotients of fractions, and solve

word problems involving division of fractions by fractions, e.g., by using visual

fraction models and equations to represent the problem. For example, create

a story context for (2

3) ÷ (

3

4) and use a visual fraction model to show the

quotient; use the relationship between multiplication and division to explain

that (2

3) ÷ (

3

4) =

6

9 because

3

4 of

6

9 is

2

3. (In general, (

𝑎

𝑏) ÷ (

𝑐

𝑑) =

𝑎𝑑

𝑏𝑐.) How much

chocolate will each person get if 3 people share 1

2 pound of chocolate

equally? How many 3

4cup servings are in

2

3 of a cup of yogurt? How wide is a

rectangular strip of land with length 3

4mi and area

1

2 square mi? (6.NS.1)


53

Scoring Guidelines

Exemplar Response

5

6


Any equivalent value



55

Grade 6

Math


Question 8

Sample Responses

56


Notes on Scoring



57


Notes on Scoring



58


Notes on Scoring


calculates an incorrect value of the expression. To get 40

3, the

student may multiply the two given numbers instead of

dividing them.

59


Notes on Scoring


calculates an incorrect value of the expression. To get 12

10, the

student may incorrectly invert the first number and then

multiply by the second number.

61

Grade 6

Math


Question 9


62

Question 9

16669




Content Standard: Solve real-world and mathematical problems by

graphing points in all four quadrants of the coordinate plane.

Include use of coordinates and absolute value to find distances

between points with the same first coordinate or the same second

coordinate. (6.NS.8)


63

Scoring Guidelines

Exemplar Response


Any placement where point A is located at (x, y) and point B is located at

(–x, y)


A correct location of point A and point B (1 point).

65

Grade 6

Math


Question 9

Sample Responses

66


Notes on Scoring


correctly places points A and B at possible locations on the

coordinate grid.

67


Notes on Scoring


correctly places points A and B at possible locations on the

coordinate grid. This placement requires the values of both x

and y for point A to be negative.

68


Notes on Scoring


does not place points A and B correctly at possible points on

the coordinate grid. The values of both x and y for point A are

negative therefore point B would be in quadrant IV.

69


Notes on Scoring

This response earns no credit (0 points) because the student does

not place points A and B correctly at possible points on the

coordinate grid. With point A in quadrant I, point B would be in

quadrant II instead of quadrant III.

71

Grade 6

Math


Question 10


72

Question 10

16670

20512

Points Possible: 1

Content Cluster: Reason about and solve one-variable equations

and inequalities.

Content Standard: Understand solving an equation or inequality as a

process of answering a question: which values from a specified set, if

any, make the equation or inequality true? Use substitution to

determine whether a given number in a specified set makes an

equation or inequality true. (6.EE.5)


73

Scoring Guidelines

Rationale for First Option: Key – The student correctly identifies that substituting

n=3 into the inequality leads to a correct statement.

Rationale for Second Option: This is incorrect. The student may realize that

substituting n=3 in the left side of the inequality makes both sides of the

inequality equal, but missed that this would not make the inequality true.

Rationale for Third Option: Key – The student correctly identifies that

substituting n=3 into the inequality leads to a correct statement.

Rationale for Fourth Option: This is incorrect. The student may think that 9 is

greater than 9.5.

Rationale for Fifth Option: Key – The student correctly identifies that substituting

n=3 into the inequality leads to a correct statement.

Rationale for Sixth Option: This is incorrect. The student may realize that

substituting n=3 in the left side of the inequality makes both sides of the

inequality equal, but missed that this would not make the inequality true.


75

Grade 6

Math


Question 11


76

Question 11

16671



to solve problems.

Content Standard: Use ratio and rate reasoning to solve real-world

and mathematical problems, e.g., by reasoning about tables of

equivalent ratios, tape diagrams, double number line diagrams, or

equations. (6.RP.3b)

b. Solve unit rate problems including those involving unit pricing and

constant speed. For example, if it took 7 hours to mow 4 lawns, then

at that rate, how many lawns could be mowed in 35 hours? At what

rate were lawns being mowed?

Calculator Designation: Calculator

77

Scoring Guidelines

Exemplar Response

105





79

Grade 6

Math


Question 11

Sample Responses

80


Notes on Scoring


correctly calculates the number of pages.

81


Notes on Scoring


correctly calculates the number of pages.

82


Notes on Scoring


does not correctly calculate the number of pages. The

student may divide 75 pages by 5 minutes to find how many

pages are printed per minute, but then forget to multiply by 7

to get the correct answer to the question.

83


Notes on Scoring


does not correctly calculate the number of pages. The

student may simply multiply 75 by 7 to get this incorrect

response.

85

Grade 6

Math


Question 12


86

Question 12

16672

20512

Points Possible: 2

Content Cluster: Represent and analyze quantitative relationships

between dependent and independent variables.

Content Standard: Use variables to represent two quantities in a real-

world problem that change in relationship to one another; write an

equation to express one quantity, thought of as the dependent

variable, in terms of the other quantity, thought of as the

independent variable. Analyze the relationship between the

dependent and independent variables using graphs and tables,

and relate these to the equation. For example, in a problem

involving motion at constant speed, list and graph ordered pairs of

distances and times, and write the equation d = 65t to represent the

relationship between distance and time. (6.EE.9)


87

Scoring Guidelines

Exemplar Response




One correct column (1 point);

AND

The second correct column (1 point).

89

Grade 6

Math


Question 12

Sample Responses

90


Notes on Scoring


correctly completes both columns.

91


Notes on Scoring


correctly completes both columns.

92


Notes on Scoring


student correctly completes only the first column. The student

may multiply 40 from the first column by 20 to get the

incorrect response of 800, and do the same with the 60 in the

first column to get the incorrect response of 1200.

93


Notes on Scoring


student correctly completes only the first column.

94


Notes on Scoring


does not complete either column correctly. In the first

column, the student adds one dollar for each additional

room. In the second column, the student adds $12.00 instead

of $12.50 when calculating the charge for 3 rooms.

95


Notes on Scoring


does not complete either column correctly.

97

Grade 6

Math


Question 13


98

Question 13

16673

Points Possible: 1

Content Cluster: Solve real-world and mathematical problems

involving area, surface area, and volume.

Content Standard: Draw polygons in the coordinate plane given

coordinates for the vertices; use coordinates to find the length of a

side joining points with the same first coordinate or the same second

coordinate. Apply these techniques in the context of solving real-

world and mathematical problems. (6.G.3)


99

Scoring Guidelines

Rationale for Option A: Key – The student identifies that the figure is a

rectangle.

Rationale for Option B: This is incorrect. The student may identify that the figure

has four sides, but miscalculates the length of one of the sides.

Rationale for Option C: This is incorrect. The student may miscalculate the

length of one of the sides of the figure and assume the opposite side will have

the same length.

Rationale for Option D: This is incorrect. The student may miscalculate the

length of one of the sides of the figure and assume the opposite side will have

the same length.


101

Grade 6

Math


Question 14


102

Question 14

16674

Points Possible: 1


to solve problems.




equations. (6.RP.3c)

c. Find a percent of a quantity as a rate per 100, e.g., 30% of a

quantity means 30

100 times the quantity; solve problems involving

finding the whole, given a part and the percent.


103

Scoring Guidelines

Rationale for Option A: This is incorrect. The student may calculate the

percentage of the 1050 people who can vote but did not vote in the election.

Rationale for Option B: This is incorrect. The student may calculate the

percentage of the 840 people who voted who chose to vote for Mr. Jones.

Rationale for Option C: This is incorrect. The student may calculate the

percentage of the 840 people who voted who chose to vote for Ms. Smith.

Rationale for Option D: Key – The student correctly calculates the percentage

of the 1050 people who can vote who actually did vote in the election.


105

Grade 6

Math


Question 15


106

Question 15

16675


Content Cluster: Summarize and describe distributions.

Content Standard: Summarize numerical data sets in relation to

their context. (6.SP.5)

c. Giving quantitative measures of center (median and/or mean)and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.


107

Scoring Guidelines

Exemplar Response

6

Exemplar Response




109

Grade 6

Math


Question 15

Sample Responses

110


Notes on Scoring


correctly identifies the missing value.

The range for the data is 5 and the lowest data point is 1;

therefore, the missing data point needs to be 5 away from 1,

and a negative number does not make sense in this scenario.

111


Notes on Scoring


correctly identifies the missing value.




112


Notes on Scoring


does not correctly identify the missing value.




The data point the student identifies gives the data a range of 4.

113


Notes on Scoring


does not correctly identify the missing value.

The student may add the values that the points in the dot plot

represent, 1 + 1 + 1 + 2 + 2 + 3 = 10.

115

Grade 6

Math


Question 16


116

Question 16

16676

Points Possible: 1


to solve problems.

Content Standard: Understand the concept of a unit rate a/b

associated with a ratio a:b with b ≠ 0, and use rate language in the

context of a ratio relationship. For example, “This recipe has a ratio

of 3 cups of flour to 4 cups of sugar, so there is 3

4 cup of flour for each

cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of

$5 per hamburger.” (6.RP.2)


117

Scoring Guidelines

Rationale for Option A: Key – The student correctly calculates the cost per

minute.

Rationale for Option B: This is incorrect. The student may divide incorrectly

while calculating the unit rate.

Rationale for Option C: This is incorrect. The student may calculate the unit

rate per hour.

Rationale for Option D: This is incorrect. The student may calculate the

reciprocal of the unit rate.


119

Grade 6

Math


Question 17


120

Question 17

16677

20512

Points Possible: 1


to solve problems.




equations. (6.RP.3)

a. Make tables of equivalent ratios relating quantities with whole-

number measurements; find missing values in the tables; and plot the

pairs of values on the coordinate plane. Use tables to compare

ratios.


121

Scoring Guidelines

Exemplar Response




A correct table (1 point).

123

Grade 6

Math


Question 17

Sample Responses

124


Notes on Scoring


correctly completes the table using ratio reasoning.

125


Notes on Scoring


correctly completes the table using ratio reasoning.

126


Notes on Scoring


does not correctly complete the table using ratio reasoning.

The student may think that you add 3 to the pounds of

cement to get the pounds of sand.

127


Notes on Scoring


does not correctly complete the table using ratio reasoning.

The student may multiply each given number by 3 to find the

missing number in the row, making a mistake on row 3 where

12 should be divided by 3 instead.

129

Grade 6

Math


Question 18


130

Question 18

16678


Content Cluster: Reason about and solve one-variable equations and

inequalities.

Content Standard: Write an inequality of the form x > c or x < c to represent a

constraint or condition in a real-world or mathematical problem. Recognize

that inequalities of the form x > c or x < c have infinitely many solutions;

represent solutions of such inequalities on number line diagrams. (6.EE.8)


131

Scoring Guidelines

Exemplar Response

𝑡 > −7

Exemplar Response

Any equivalent inequality


A correct inequality (1 point).

133

Grade 6

Math


Question 18

Sample Responses

134


Notes on Scoring


correctly creates an inequality that shows all temperatures

warmer than the average annual low temperature in zone 6.

135


Notes on Scoring


correctly creates an inequality that shows all temperatures

warmer than the average annual low temperature in zone 6.

136


Notes on Scoring


does not correctly create an inequality that shows all

temperatures warmer than the average annual low

temperature in zone 6. Instead, the response shows


temperature in zone 7.

137


Notes on Scoring


does not correctly create an inequality that shows all


temperature in zone 6. Instead, the response is an equation

and shows a positive 7.

139

Grade 6

Math


Question 19


140

Question 19

16679

Points Possible: 1



Content Standard: Apply the properties of operations to generate

equivalent expressions. For example, apply the distributive property

to the expression 3(2 + x) to produce the equivalent expression

6 + 3x; apply the distributive property to the expression 24x + 18y to

produce the equivalent expression 6(4x + 3y); apply properties of

operations to y + y + y to produce the equivalent expression 3y.

(6.EE.3)


141

Scoring Guidelines

Rationale for Option A: This is incorrect. The student may multiply 1

3 by the first

term inside the parentheses but not the second term when distributing.

Rationale for Option B: Key – The student correctly distributes the fraction and

combines like terms.

Rationale for Option C: This is incorrect. The student may distribute 1

3 to every

term.

Rationale for Option D: This is incorrect. The student may combine the given

terms without distributing the fraction.


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