grade 6 mathematics item specification c1 ti claim...

Grade 6 Mathematics Item Specification C1 TI

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Claim 1: Concepts and Procedures Students can explain and apply mathematical concepts and carry out mathematical

procedures with precision and fluency. Content Domain: Statistics and Probability Target I [a]: Develop an understanding of statistics variability. (DOK 2)

Tasks for this target will ask students to identify and pose questions that lead to variable responses; identify a reasonable center and/or spread for a given context. Some flawed reasoning tasks will be used as part of evidence for Claim 3 (e.g., explaining why a given measure of center is unreasonable for a dataset or context – without performing any

calculations). Standards:

6.SP.A, 6.SP.1, 6.SP.2, 6.SP.3

6.SP.A Develop understanding of statistical variability.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’

ages. 6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3 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.

Related Below-Grade and Above-Grade

Standard for Purposes of Planning for Vertical Scaling:

5.MD.B, 5.MD.2

7.SP.B, 7.SP.3

Related Grade 5 Standards 5.MD.B Represent and interpret data. 5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8 ). Use operations on fractions for

this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Related Grade 7 Standards 7.SP.B Draw informal comparative inferences about two populations.

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar 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, the separation between the two distributions of heights is noticeable.

DOK Level: 2

Achievement Level Descriptors:

RANGE Achievement Level

Descriptor (Range ALD)

Target I: Develop

Level 1 Students should be able to identify questions that lead to variable responses posed in familiar contexts and recognize that such questions are statistical questions.

Level 2 Students should be able to recognize that questions that lead to variable responses are statistical questions and vice versa,


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understanding of statistical variability.

and they should relate the concept of varying responses to the notion of a range of possible responses. They should develop an

understanding that the responses to a statistical question will have a representative center and a given set of numerical data. They should be able to identify a reasonable measure of central tendency with respect to a familiar context.

Level 3 Students should be able to pose statistical questions and understand that the responses to a statistical question have a distribution described by its center, spread, and overall shape. They should also understand that a measure of center summarizes all of

its values with a single number, while a measure of variation describes how its values vary with a single number. They should be able to identify a reasonable center and spread with respect to a context.

Level 4 Students should be able to justify the reasonableness of their identified center and spread with respect to an unfamiliar context. They should be able to create or complete a data set with

given measures (e.g., mean, median, mode, interquartile range). Evidence Required: 1. The student recognizes a statistical question as one that

anticipates variability.

2. The student identifies statements that describe the center and/or spread, and/or overall shape of a set of data.

3. The student recognizes 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.

Allowable Response Types:

Multiple Choice, single correct response; Matching Tables

Allowable Stimulus Materials:

Dot/line plots, lists of numbers, tables, graphs, or other visual graphics to display a set of numbers

Construct-Relevant Vocabulary:

variation (variability), interquartile range, range, mean absolute deviation, center, spread, mean, median, outliers, shape (pertaining to statistics such as gap, cluster, peak, skew, bell curve, and

uniform distribution) Allowable Tools: Calculator

Target-Specific Attributes:

Non-Targeted Constructs:

Accessibility Concerns:

Visual graphics may be difficult or not accessible for students who are blind or visually impaired. Reviewing tactile graphs may be time

consuming but not prohibitive. The simplest graphics should be used to minimize this issue. Students with visual perceptual disabilities may have difficulty differentiating shapes and angles. Students who are visually impaired or blind may need enlarged or brailled text. Students with reading disabilities may struggle with the reading load

of word problems. All vocabulary should be at or below grade level to minimize this issue. Students with reading disabilities may need to read the text out loud, or have access to trackers or maskers to follow along. Students with visual processing impairments may benefit from using a tracker or masker when reading. Drag and Drop

response types may not be accessible for students who are visually


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impaired. Consider replacing these response types with multiple choice items for Braille versions. The accommodations listed here

are suggestions and could be altered depending on what accommodations will be allowable.

Development Notes: Tasks for this target will ask students to identify and pose questions that lead to variable responses; identify a reasonable center and/or spread for a given context. Some flawed reasoning tasks will be used as part of evidence for Claim 3 (e.g., explaining why a given measure of center is unreasonable for a dataset or context – without performing any calculations).


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Task Model 1

Response Types: Multiple Choice, single correct response; Matching Tables

DOK Level 2 6.SP.1 Recognize a statistical question

as one that anticipates variability in the data related to the question and accounts for it in the

answers. For example, “How old am I?” is not a statistical question, but “How old are the

students in my school?” is a statistical question because one anticipates variability

in students’ ages. Evidence Required: 1. The student recognizes a

statistical question as one that anticipates variability.

Tools: Calculator

Prompt Features: The student is prompted to identify whether questions are statistical in nature based on whether they anticipate

variability in the answer data. Stimulus Guidelines: Context should be familiar to students 11 to 13 years old. TM1a

Stimulus: The student is presented with questions based on a statistical scenario. Example Stem: Julie is writing a report about rainbows and needs to gather data from her classmates.

Which is a statistical question Julie could ask her classmates?

A. What are the colors of the rainbow?

B. When was the first rainbow seen? C. Is there really a pot of gold at the end of a rainbow? D. How many rainbows have you seen this month?

Rubric: (1 point) Student selects the statistical question (e.g., D)

Response Type: Multiple Choice, single correct response TM1b Stimulus: The student is presented with three statistical and non-statistical questions.

Example Stem: A statistical question anticipates variability in the data related to it. Determine whether each question can be classified as a statistical question. Select Yes or No for each question.

Question Yes No

How many hours a week do people exercise?

How many hours are there in a day?

How many rainbows have students seen this month?

Rubric: (1 point) Student identifies all three questions correctly (e.g., Y, N, Y). At least one question should be statistical.

Response Type: Matching Tables


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Task Model 2

Response Type: Matching Tables DOK Level 2 6.SP.2

Understand that a set of data collected to answer a statistical question has a distribution

which can be described by its center, spread, and overall shape.

Evidence Required: 2. The student identifies statements that describe the

center and/or spread, and/or overall shape of a set of data.

Tools: Calculator

Prompt Features: The student is prompted to identify statements that describe the center, spread, or overall shape of a set of data

related to a statistical question. Stimulus Guidelines:

Context should be familiar to students 11 to 13 years old. Numbers in data set should be whole numbers. Data can be presented in the form of a:

o list o dot plot o table o graph including histogram o box plot.

Item difficulty can be adjusted via these methods: o Students describe the spread of a data given a list or

table of values. o Students describe the spread of a data set given dot

plot or graph.

o Students describe the shape of a dot plot or graph. o Students describe the center of a data set given a list

or table of values. o Students describe the center of a data set given a dot

plot or graph.

TM2 Stimulus: The student is presented with a set of data. Example Stem 1: Ted surveyed his neighbors to see how much

money they spent on gasoline each week. The results are shown in the dot plot.

Determine whether each statement about the spread of the data is true. Select True or False for each statement.

Statement True False

The range of data values changes when data values 75 and 85 are removed.

The median of the data values is used to calculate the range of the data.

The range of the data values describes how the values

vary from the greatest value to the least value.

Rubric: (1 point) Student correctly identifies all three statements as true or false (e.g., T, F, T).


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Task Model 2






Tools: Calculator

Example Stem 2: Ted surveyed his neighbors to see how much money they spent on gasoline each week. The results are shown in

the dot plot.

Determine whether each statement about the shape of the data is true. Select True or False for each statement.


There is a gap in the data values between 35 and 75.

The data is skewed left.

The only outlier for the data

set is 85.

Rubric: (1 point) Student correctly identifies all three statements as true or false (e.g., T, F, F). False statements will include confusing terms such as skewed right, skewed left, bell curve, uniform distribution, cluster, gap, peak, and outlier.

Example Stem 3: Ted surveyed his neighbors to see how much money they spent on gasoline each week. The results are shown in the dot plot.

Determine whether each statement about the center of the data is

true. Select True or False for each statement.


The median of the data values

is used to determine the range of the data.

The mean of the data values is greater than the median of the data values because of the outliers.

The median of the data values is an outlier of the data set.

Rubric: (1 point) Student correctly identifies all three statements as true or false (e.g., F, T, F).


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Task Model 2






Tools: Calculator

Example Stem 4: Ted surveyed his classmates to collect data about

the number of books read during the summer. The results are shown in the box plot.

Determine whether each statement about Ted’s survey data is true.

Select True or False for each statement.


The median of the data values is 9.

The interquartile range of the data values is the difference

between 11 and 8.

The shape of the data is skewed right.

Rubric: (1 point) Student correctly identifies all three statements as true or false (e.g., T, F, T). False statements will confuse the function of a measure of center, variation, and shape.

Response Type: Matching Tables


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Task Model 3


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. Evidence Required: 3. The student

recognizes 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.

Tools: Calculator

Prompt Features: The student is prompted to identify statements about measures of center and/or variation for a given data set.

Stimulus Guidelines: Context should be familiar to students 11 to 13 years old. TM3 Stimulus: The student is presented with statements regarding

measures of center and/or variation about a data set. Example Stem: Mike surveyed his classmates to collect data about the number of minutes they each spent doing homework last night. The data values range from 30 to 90.

Determine whether each statement about Mike’s survey data is true. Select True or False for each statement.


The mean of the data values is greater than 30.

The range of the data values is between 30 and 90.

The median of the data values must be 60.

Rubric: (1 point) Student correctly identifies all three statements as

true or false (e.g., T,T,F). Response Type: Matching Tables

grade 6 mathematics item specification c1 ti claim...

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