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): [8.DR]

OREGON MATH STANDARDS (2021): [8.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: 8.DR.A.1

ODE and Oregon Math Project Logo

Cluster: 8.DR.A - Formulate Statistical Investigative Questions.

STANDARD: 8.DR.A.1

 Standards Statement (2021):

Formulate statistical investigative questions to articulate research topics and uncover patterns of association seen in bivariate categorical data.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.DR.A.1

HS.DR.A.1, HS.DR.A.2, HS.DR.A.3, HS.DR.A.4

 N/A

8.SP.A.4

8.DR.A Crosswalk

 Standards Guidance:

Clarifications

  • Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
  • Students can generate questions about things they notice and wonder from a real-life situation.

Terminology

  • A statistical investigative question is one that requires data that will vary.

Teaching Strategies

  • Students should be able to use statistical reasoning to anticipate patterns of association as they formulate questions, such as and anticipated positive or negative association between the categorial variables of interest.
  • Provide opportunities to engage in an analysis of sources of bias within assumptions as students formulate questions.

Progressions

  • Building on experience with decimals and percent, and the ideas of association between measurement variables, students now take a more careful look at possible association between categorical variables. “Is there a difference between sixth graders and eighth graders with regard to their preference for rock, rap, or country music?”
  • Data from a random sample of sixth graders and another random sample of eighth graders are summarized by frequency counts in each cell in a two-way table of preferred music type by grade. The proportions of favored music type for the sixth graders are then compared to the proportions for eighth graders. If the two proportions for each music type are about the same, there is little or no association between the grade and music preference because both grades have about the same preferences. If the two proportions differ, there is some evidence of association because grade level seems to make a difference in music preferences. The nature of the association should then be described in more detail. (Please reference pages 11 & 12 in the Progression document).

Examples

2021 Oregon Math Guidance: 8.DR.B.2

 ODE and Oregon Math Project Logo

Cluster: 8.DR.B - Collect and Consider Data.

STANDARD: 8.DR.B.2

 Standards Statement (2021):

Collect or consider data using surveys and measurements to capture patterns of association, and critically analyze data collection methods.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.DR.B.2

HS.DR.B.5, HS.DR.B.6, HS.DR.B.7

 N/A

8.SP.A.2

8.DR.B Crosswalk

 Standards Guidance:

Clarification

  • Know that straight lines are widely used to model relationships between two quantitative variables.

Terminology

  • The line of best fit shows the linear relationship between two variables in a data set.
  • It is important to indicate ‘predicted’ to indicate this is a probabilistic interpretation in context, and not deterministic.

Teaching Strategies

  • Students should be able to use statistical reasoning to consider patterns of association, such as clustering, outliers, positive or negative association, linear association, and nonlinear association through the analysis of data presented in multiple ways.
  • Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. 
  • Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
  • Students should discover the line of best fit as the one that comes closest to most of the data points.
  • Provide opportunities to engage in an analysis of sources of bias within collection methods used by students.

Progressions

  • For a data showing a linear pattern, students sketch a line through the “center” of the cloud of points that captures the essential nature of the trend, at first by use of an informal fitting procedure, perhaps as informal as laying a stick of spaghetti on the plot. How well the line “fits” the cloud of points is judged by how closely the points are packed around the line, considering that one or more outliers might have tremendous influence on the positioning of the line. (Please reference page 11 in the Progression document).

Examples

2021 Oregon Math Guidance: 8.DR.C.3

 ODE and Oregon Math Project Logo

Cluster: 8.DR.C - Analyze, summarize, and describe data.

STANDARD: 8.DR.C.3

 Standards Statement (2021):

Analyze patterns of association between two quantitative or categorical variables and reason about distributions to compare groups.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.DR.C.3

HS.DR.C.8, HS.DR.C.9, HS.DR.C.10

 N/A

8.SP.A.1

8.DR.C Crosswalk

 Standards Guidance:

Clarification

  • Construct and interpret scatter plots for bivariate data to investigate patterns of association between two quantities.
  • Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
  • Students should be given opportunities to analyze the data distribution displayed graphically to answer the statistical investigative question generated from a real-life situation.

Terminology

  • Bivariate data are data for two variables (usually two types of related data), such as height and weight. 

Teaching Strategies

  • Students should be able to use statistical reasoning to describe patterns of association, such as clustering, outliers, positive or negative association, linear association, and nonlinear association through the analysis of data presented in multiple ways.
  • Create a scatter plot for bivariate data and, if appropriate, informally fit a straight line and use the line to predict values. Informally assess the model fit by judging the closeness of the data points to the line.

Progressions

  • Working with paired measurement variables that might be associated linearly or in a more subtle fashion, students construct a scatter plot, describing the pattern in terms of clusters, gaps, and unusual data points (much as in the univariate situation). Then, they look for an overall positive or negative trend in the cloud of points, a linear or nonlinear (curved) pattern, and strong or weak association between the two variables, using these terms in describing the nature of the observed association between the variables. (Please reference page 11 in the Progression document).

Examples

2021 Oregon Math Guidance: 8.DR.D.4

 ODE and Oregon Math Project Logo

Cluster: 8.DR.D - Interpret data and answer investigative questions.

STANDARD: 8.DR.D.4

 Standards Statement (2021):

Interpret scatter plots for bivariate quantitative data to investigate patterns of association between two quantities to answer investigative questions.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.DR.D.4

HS.DR.D.11, HS.DR.D.12, HS.DR.D.13

8.AFN.B.4, HS.AEE.B.4

8.SP.A.3

8.DR.D Crosswalk

 Standards Guidance:

Clarification

  • Interpret the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Terminology

  • A linear model shows the relationship between two variables in a data set, such as lines of best fit.
  • Bivariate data are data for two variables (usually two types of related data), such as height and weight. 
  • It is important to indicate ‘predicted’ to indicate this is a probabilistic interpretation in context, and not deterministic.

Teaching Strategies

  • Students should interpret contextual linear problems involving situations using bivariate quantitative data.

Progressions

  • After a line is fit through the data, the slope of the line is approximated and interpreted as a rate of change, in the context of the problem. The slope has important practical interpretations for most statistical investigations of this type (MP2). (Please reference page 11 in the Progression document).

Examples

  • In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
  • Illustrative Mathematics:
  • Student Achievement Partners: