Unit 5 — Modeling with Statistics
Description
This unit develops students' statistical reasoning and data literacy. Students construct and interpret scatter plots, describing visual patterns including clustering, outliers, and linear versus nonlinear associations. They informally fit lines of best fit to data suggesting linear association and assess model fit. Students use linear models to solve problems, interpreting slope and intercept in context. The unit extends to categorical data, where students construct and interpret two-way frequency tables and two-way relative frequency tables, describing possible associations between variables. Students represent single-variable data using dot plots, histograms, and box plots. They use appropriate statistics such as median, mean, interquartile range, and standard deviation to compare center and spread of two or more data sets, interpreting differences in context and accounting for outliers. Students fit functions to data using technology, solve prediction problems, plot residuals, and assess model fit. Throughout, students distinguish between correlation and causation and make data-informed conclusions.
Essential Questions
- How can we use visual representations and statistics to understand and compare data?
- What does it mean for two variables to be associated, and how is this different from causation?
- How do we select appropriate models and assess how well they fit data?
- How can categorical data reveal patterns and associations?
Learning Objectives
- Construct and interpret scatter plots for bivariate measurement data
- Describe patterns of association including clustering, outliers, and linear versus nonlinear association
- Informally fit a line of best fit and assess model fit by judging closeness of points to the line
- Use linear model equations to solve problems, interpreting slope and intercept in context
- Construct and interpret two-way frequency tables and two-way relative frequency tables
- Describe associations between categorical variables using relative frequencies
- Represent data using dot plots, histograms, and box plots
- Compare center and spread of two or more data sets using appropriate statistics
- Interpret differences in shape, center, and spread in context
- Explain effects of outliers when summarizing data
- Fit functions to data using technology and solve prediction problems
- Plot residuals and informally assess fit of linear and nonlinear functions
- Distinguish between correlation and causation
Supplemental Resources
- Printed data sets for constructing scatter plots and histograms
- Graphic organizers for organizing statistical measures
- Grid paper for creating visual data representations
- Rulers for drawing lines of best fit
- Index cards for describing associations and interpreting statistics
Statistics and Probability
Students engage in collaborative discussions about mathematical concepts, construct arguments to support mathematical claims using evidence, analyze and interpret information presented in diverse formats, and write informative explanations of mathematical processes and procedures.
Students apply mathematical reasoning to analyze scientific data, use quantitative relationships to describe phenomena, construct explanations based on evidence, and model real-world relationships in biological and physical systems.
Formative Assessments
- CPM checkups on scatter plot interpretation and data representation
- Quizzes on comparing statistics and describing associations
- Observations of students analyzing residuals and assessing model fit
- Pair-and-share on distinguishing between correlation and causation
- Exit tickets on interpreting statistics and models in context
Summative Assessment
Unit 4 test on scatter plots, data representations, statistics, categorical data, and function fitting; performance assessment analyzing real-world data sets and making evidence-based conclusions
Benchmark Assessment
Benchmark covering standards (S.ID.A, S.ID.B, 8.SP.A, F.IF.B)
Alternative Assessment
Students may demonstrate understanding through verbal descriptions of scatter plot patterns and associations, with teacher or peer scribing of written responses as needed. Visual aids such as annotated scatter plot examples, pre-labeled axes, and sentence frames describing clustering, outliers, and linear associations may be provided to support analysis and communication of findings.
IEP (Individualized Education Program)
Students may benefit from graphic organizers that pre-structure scatter plots, frequency tables, and data displays, reducing the organizational demand while maintaining focus on interpretation. Providing a reference sheet with definitions of key statistical terms (such as mean, median, interquartile range, standard deviation, and correlation) supports access to vocabulary-heavy content throughout the unit. Directions for multi-step tasks — such as constructing and interpreting two-way tables or fitting a line of best fit — should be broken into numbered steps with visual models of completed examples. Allowing oral responses or the use of a calculator without penalty supports students who may struggle with computation fluency while still demonstrating statistical reasoning.
Section 504
Extended time on quizzes and the unit test is especially important given the volume of data interpretation and written explanation required in this unit. Preferential seating and a low-distraction environment support sustained focus during tasks involving graph reading and multi-step statistical comparisons. Providing printed copies of any data displays or tables shown on the board ensures students can annotate and reference materials at their own pace.
ELL / MLL
This unit's dense statistical vocabulary — including terms like association, residual, correlation, causation, and relative frequency — should be pre-taught with visual anchors such as labeled example graphs and illustrated word walls before students encounter the terms in context. Simplified, sequenced directions for constructing and interpreting data displays help students focus on mathematical reasoning rather than language processing. Where possible, connect real-world data contexts to students' cultural or community backgrounds to make the content more meaningful, and encourage students to discuss patterns and conclusions with a partner before writing independently.
At Risk (RTI)
Entry points into this unit can be strengthened by connecting new representations — scatter plots, box plots, two-way tables — to data displays and summary statistics students have encountered in prior grades, building on existing familiarity before introducing more complex interpretation. Reducing the number of data sets or variables students work with at one time allows for deeper engagement with one concept before moving to the next. Structured practice with sentence frames for describing associations, comparing distributions, and explaining the difference between correlation and causation supports students in communicating their reasoning with confidence.
Gifted & Talented
Students who demonstrate early mastery of core statistical concepts can extend their thinking by investigating real-world data sets with nonlinear associations, critically evaluating the appropriateness of different function types beyond linear models. Exploring the distinction between correlation and causation in depth — including examining flawed statistical claims from media or research contexts — encourages higher-order analysis and argumentation. Students may also be challenged to design their own data collection questions, analyze the resulting bivariate or categorical data using technology, and present evidence-based conclusions that account for confounding variables and limitations of their model.