Statistics (Inferences from Data)

8 Components
Initial Task
Animals
Big Ideas
Big Idea 1 Big Idea 2 Big idea 3
Formative Assessment Lesson
A Case of Muddying the Waters
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources ALG II Unit 6 Find aligned Regents questions with Quiz Banker
A2 U6: Statistics (Inferences from Data)
Unit Outline
Initial Task
Animals
Big Ideas
Big Idea 1 Big Idea 2 Big idea 3
Formative Assessment Lesson
A Case of Muddying the Waters
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources ALG II Unit 6 Find aligned Regents questions with Quiz Banker
None
A2 U6:

Statistics (Inferences from Data)

How do we compare different data sets?
4 weeks
See Standards
Common Core: Major Standards:
S-ID.C.7

Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.C.8

Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.C.9

Interpret linear models​. Distinguish between correlation and causation.

S-IC.B.3

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S-IC.B.4

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.B.5

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

S-IC.B.6

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.

Common Core: Supporting Standards:
S-ID.B.5

Summarize, represent, and interpret data on two categorical and quantitative variables.  Summarize categorical data for two categories in two‐way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

S-ID.B.6

Summarize, represent, and interpret data on two categorical and quantitative variables.  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.B.6a

Summarize, represent, and interpret data on two categorical and quantitative variables. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  Clarification: includes the use of the regression capabilities of the calculator

S-IC.A.1

Understand and evaluate random processes underlying statistical experiments.  Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.A.2

Understand and evaluate random processes underlying statistical experiments.  Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Common Core: Additional Standards:
S-ID.A.1

Summarize, represent, and interpret data on a single count or measurement variable. Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.A.2

Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S-ID.A.3

Summarize, represent, and interpret data on a single count or measurement variable. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S-ID.A.4

Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

The purpose of this unit is for students to learn about how statistics are used and potentially misused. Students will need opportunities to actually carry out sampling processes for themselves and learn about how statistics are used to support conclusions.  In this unit, students will explore the process of making inferences about populations. This unit relies heavily on vocabulary and conceptual understandings. Simulation is also a critical part of developing inferences. Students should spend time learning about the various data collection instruments by constructing and carrying them out for themselves. Comparisons between collected data and simulations will lend a real-life feel to this unit.

This unit contains three main ideas: interpreting data using measures of center and spread, modeling data using familiar functions, and making the connection between probability and statistics. Students make comparisons between graphs, lists, and tables of multiple data sets by describing the shape, center, spread, and extreme values. Students should develop a conceptual understanding of correlation and causation and recognize that correlation does not imply causation. Students should be able to use technology to find regression functions.

Essential Questions:

  • How do we compare different data sets?
  • How do we determine if different quantities are correlated to each other?
  • How do we use what we know about probability to analyze data?
Printable Unit Plan

Unit Outline

8 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 3 itemsHide 3 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 0 itemsHide 0 items

End of Unit Assessments See 3 itemsHide 3 items