﻿ Gr. HS Descriptive Statistics ~ Math Units of Study ~ Instruction ~ School Improvement in Maryland

# Gr. HS Unit: Descriptive Statistics

##### Unit Overview

Experience with descriptive statistics began as early as Grade 6. Students were expected to display numerical data and summarize it using measures of center and variability. By the end of middle school they were creating scatter plots and recognizing linear trends in data. This unit builds upon that prior experience, providing students with more formal means of assessing how well a model fits data. Students use regression techniques to describe approximately linear functional relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

Essential Questions:

• When is mathematics an appropriate tool to use in problem solving?
• When is it important to analyze data?
• What characteristics of problems determine how to model a situation and develop a problem solving strategy?
• What characteristics of a problem lead to determining if a problem should be represented by single count/measurement variables or two categorical/quantitative variables?
• What characteristics of a problem influence the choice of representation and analysis of the data?
• What characteristics of a problem determine the type of function that would serve as an appropriate model for the problem?
• How can mathematical representations be used to communicate information effectively?
• How can data be represented to best communicate important information about a problem?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

##### Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.

##### Available Model Lesson Plans

The lesson plan(s) have been written with specific standards in mind. Each model lesson plan is only a MODEL - one way the lesson could be developed. We have NOT included any references to the timing associated with delivering this model. Each teacher will need to make decisions related ot the timing of the lesson plan based on the learning needs of students in the class. The model lesson plans are designed to generate evidence of student understanding.

This chart indicates one or more lesson plans which have been developed for this unit. Lesson plans are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignment: S.ID.6, S.ID.7, S.ID.8, S.ID.9

This is a lengthy lesson plan which would take several days to complete if all of the activities are used. The various activities begin by developing linear regression model and using this model to develop the concept of the correlation coefficient and then ends with a discussion of correlation versus causation.

##### Available Model Lesson Seeds

The lesson seed(s) have been written with specific standards in mind. These suggested activity/activities are not intended to be prescriptive, exhaustive, or sequential; they simply demonstrate how specific content can be used to help students learn the skills described in the standards. Seeds are designed to give teachers ideas for developing their own activities in order to generate evidence of student understanding.

This chart indicates one or more lesson seeds which have been developed for this unit. Lesson seeds are being written and posted on the Curriculum Management System as they are completed. Please check back periodically for additional postings.

CCSC Alignnment: S.ID.1

Developmental
As students select the best word from a word bank which contains words connected to various data plots, they are demonstrating their prior knowledge and at the same time previewing the lesson.

CCSC Alignnment: S.ID.1, S.ID.3

Motivation
This introductory activity provides a kinesthetic way of having students become familiar with the attributes of a box plot.

CCSC Alignnment: S.ID.1, S.ID.2

Reinforcement
Students work in groups to make a plot for a set of collected data. They then decide if the plot that they created was the best one for the given data set.

CCSC Alignnment: S.ID.3

Investigation
Students will collect data, create a plot, compute measures of center and variability and share findings of an investigation.

CCSC Alignnment: S.ID.3

Practice
This activity provides two data sets for which students draw two box plots on the same axis. Students are then required to compare the data sets using the plots.

CCSC Alignnment: S.ID.3

Investigation
This activity provides a data set which has an outlier. Students investigate what happens to the summary statistics if the outlier is removed from the data set.

CCSC Alignnment: S.ID.7, S.ID.8

Investigation
Students will do an experiment to collect data. They will then find a line of best fit for the data and interpret the slope, y-intercept and correlation coefficient in terms of the context.

CCSC Alignnment: S.ID.9

Developmental Activity
Students will read an article and then compare and contrast correlation and causation.