Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [6.DR]

OREGON MATH STANDARDS (2021): [6.DR]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 6.DR.A.1

ODE and Oregon Math Project Logo

Cluster: 6.DR.A - Formulate Statistical Investigative Questions

STANDARD: 6.DR.A.1

 Standards Statement (2021):

Formulate and recognize statistical investigative questions as those that anticipate changes in descriptive data related to the question and account for it in the answers.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.DR.A.1

7.DR.A.1

5.NF.B.7

6.SP.A.1

6.DR Crosswalk

 Standards Guidance:

Clarifications 

  • Students can generate questions about things they notice and wonder from a real-life situation.
  • Students should be able to generate their own statistical questions.

Terminology

  • A statistical question is one that requires data that vary.
  • A statistical investigative question is one that allows for exploration through statistical inquiry and reasoning.

Teaching Strategies

  • Students should be able to use the statistical process to formulate questions. The statistical process involves asking a statistical investigative question, collecting the data, analyzing the data, and interpreting the results.

Progressions

  • Statistical investigations begin with a question, and students now see that answers to such questions always involve variability in the data collected to answer them. (Please reference page 4 in the Progression document).

Examples

  • “How old are the students in my school?” is a statistical question because it anticipates variability in students’ ages.
  • “How old am I?” is a question used to collect data to answer the investigative question.
  • Student Achievement Partners:

 

2021 Oregon Math Guidance: 6.DR.B.2

 ODE and Oregon Math Project Logo

Cluster: 6.DR.B - Collect and Consider Data

STANDARD: 6.DR.B.2

 Standards Statement (2021):

Collect and record data with technology to identify and describe the characteristics of numerical data sets using quantitative measures of center and variability.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.DR.A.1

7.DR.B.2

 N/A

6.SP.A.2, 6.SP.B.4

6.DR Crosswalk

 Standards Guidance:

Clarifications 

  • 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.A.2)
  • Students should understand the concept of outliers.
  • Students should be able to describe the nature of the statistical attribute under investigation, including how it was measured and its units of measurement.

Boundaries

  • A set of data collected to answer a statistical question has a distribution, which can be described by
    • Measures of center - mean, median, mode
    • Measures of variation (spread) - range, interquartile range, and/or mean absolute deviation
    • Descriptions of overall shape - symmetrical vs non- symmetrical
  • The focus of mean absolute deviation (MAD) is visualizing deviations from the mean as a measure of variability as opposed to a focus on calculating MAD.
    • In sixth grade, students should explore the conceptual idea of MAD – not the formula.
    • Students should be able to apply their understanding of absolute value (rather than use operations on negative integers) in the context of MAD.

Progressions

  • Students extend their knowledge of symmetric shapes, to describe data displayed in dot plots and histograms in terms of symmetry. They identify clusters, peaks, and gaps, recognizing common shapes and patterns in these displays of data distributions (MP7). (Please reference page 4 in the Progression document).

Examples

  • Arthur and Aaron are on the same 6th  grade basketball team. Both players have scored an average of ten points over the past ten games. Here are the students’ number of points scored during each of the last ten games.
    • Arthur: 9, 10, 10, 11, 11, 9, 10, 10, 10, 10
    • Aaron: 16, 18, 4, 3, 5, 13, 18, 3, 13, 7
    • Which student is more consistent?
    • Possible Student Response/Solution:  Arthur is more consistent because his MAD is smaller than Aaron’s MAD; Arthur has less variability than Aaron.

2021 Oregon Math Guidance: 6.DR.C.3

 ODE and Oregon Math Project Logo

Cluster: 6.DR.C - Analyze, summarize, and describe data

STANDARD: 6.DR.C.3

 Standards Statement (2021):

Analyze data representations and describe measures of center and variability of quantitative data using appropriate displays.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.DR.B.2

7.DR.C.3

 N/A

6.SP.A.3

6.DR Crosswalk

 Standards Guidance:

Clarification

  • Recognize that a measure of center for a numerical data set is a single number that summarizes all of the values in the data set, while a measure of variation is a single number that describes how the values in the data set vary from one another. (6.SP.A.3)
  • Display numerical data in plots on a number line, including dot plots and histograms. (6.SP.A.4)
  • Students have experience with displaying categorical data using bar graphs from elementary grades. In sixth grade, students are extending their understanding of analyzing categorical data displayed on histograms.

Boundaries

  • Sixth grade students should be able to create dot plots and box plots to analyze the results of a statistical investigation.
  • Sixth grade students should focus on describing and interpreting data displayed.
  • Students should be able to identify that each quartile presented in a box plot represents 25% of the data set.

Teaching Strategies

  • Students should be able to analyze the shape of a data distribution and determine the impact single data points have on the data set represented visually.
  • Describe the impact that inserting or deleting a data point has on the mean, median, and mode of a data set.
  • As a result of an investigation, students should summarize categorical and quantitative (numerical) data sets in relation to the context.
  • Students should be able to describe the nature of the statistical attribute under investigation, including how it was measured and its units of measurement.

Progressions

  • To be useful, center and spread must have well-defined numerical descriptions that are commonly understood by those using the results of a statistical investigation. (Please reference page 4 in the Progression document).

Examples

  • Categorical Example:

  • What could be the weight of the smallest dog? The largest?
  • Quantitative (numerical) Example:
    • Here are the birth weights, in ounces, of all the puppies born at a kennel in the past month.

  • What do you notice and wonder about the distribution of the puppy weights?

 

 

2021 Oregon Math Guidance: 6.DR.D.4

 ODE and Oregon Math Project Logo

Cluster: 6.DR.D - Interpret data and answer investigative questions

STANDARD: 6.DR.D.4

 Standards Statement (2021):

Interpret quantitative measures of center to describe differences between groups from data collected to answer investigative questions.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.DR.B.2

7.DR.D.4

 N/A

6.SP.B.5

6.DR Crosswalk

 Standards Guidance:

Clarifications 

  • Identify, describe, and interpret the characteristics of numerical data sets using quantitative measures of center and variability. 
  • Additional descriptions include number of observations, measurement attributes, and shape of distribution. (6.SP.A.5)

Terminology

  • In sixth grade, students should explore the conceptual idea of MAD – not the formula.
  • Students should be able to apply their understanding of absolute value (rather than use operations on negative integers) in the context of MAD.

Boundaries

  • Students should be able to determine the number of observations from a context or diagram.
  • Students should be able to describe the distribution of a quantitative (numerical) variable collected to answer a statistical investigative question, including its center (median, mean), variability (interquartile range (IQR), mean absolute deviation (MAD), and range), and overall shape (symmetrical vs non-symmetrical).
  • Students should be able to describe the nature of the statistical attribute under investigation, including how it was measured and its units of measurement.

Teaching Strategies

  • Identification and description of data characteristics related to their context includes:
    • Reporting the number of observations.
    • Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
    • 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.
  • Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
  • Students should explore conceptually the measures of center (mean, median) and variability (interquartile range and range) for a set of numerical data gathered from contextual, mathematical situations and use these measures to describe the shape of the data presented in various forms.