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Overview

Site: Gladwin
Course: Michigan Algebra I Sept. 2012
Book: Overview
Printed by: Guest user
Date: Thursday, November 21, 2024, 9:29 AM

Description

Overview

Table of contents

Introduction

In this unit, students will explore two-variable data by collecting, organizing, and displaying data in order to identify patterns, and determine which type of model best fits the data. Students will also explore recursive, piecewise, and step functions. It is anticipated that this unit will take from four to six weeks in a traditional hourly schedule to complete.


Students Will Be Able To

After successful completion of this unit, students will be able to:
  • Organize and display data appropriately.
  • Identify patterns in data, clusters, and outliers.
  • Identify and find a recursive or an explicit model.
  • Find an explicit model for the data and test the model for accuracy of fit.
  • Find the least squares regression line and use the equation of the line to make appropriate predictions.
  • Recognize and define functions that behave differently over different intervals of the domain.

Mastered HSCEs

The following Michigan High School Content Expectations will be mastered in this unit:

L1.2.2 Interpret representations that reflect absolute value relationships (e.g. I x – a I b, or a b) in such contexts as error tolerance.

L1.2.4 Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media.

A2.1.4 Recognize that functions may be defined by different expressions over different intervals of their domains. Such functions are piecewise defined.

A2.1.5 Recognize that functions may be defined recursively. Compute values of and graph simple recursively defined functions.

A2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representation; recognize that different families of functions have different asymptotic behavior at infinity and describe these behaviors.

A2.4.1 Identify the family of function best suited for modeling a given real-world situation.

S2.1.1 Construct a scatter plot for a bivariate data set with appropriate labels and scales.

S2.1.2 Given a scatter plot, identify patterns, clusters, and outliers, recognize no correlation, weak correlation, and strong correlation.

S2.1.3 Estimate and interpret Pearson’s correlation coefficient for a scatter plot of a bivariate data set; recognize that correlation measures the strength of linear association.

S2.1.4 Differentiate between correlation and causation. Know that a strong correlation does not imply a cause-and-effect relationship. Recognize the role of lurking variables in correlation.

S2.2.1 For bivariate data that appear to form a linear pattern, find the least squares regression by estimating visually and by calculating the equation of the regression line. Interpret the slope of the equation for a regression line.

S2.2.2 Use the equation of the least squares regression to make appropriate predictions.

Source

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project