Jason Colombino COLLINS MIDDLE, SALEM, MA
Algebra I : Unit #8 - Our City Statistics: Who We Are and Where We are Going : Lesson #9

What does it mean? Interpreting linear models

Objective: SWBAT interpret the rate of change (slope) and intercept for various contexts modeled by linear functions.
Standards: HSS-ID.C.7 MP1 MP2 MP3 MP4
Subject(s): Math
90 minutes
1 Entry Ticket - 15 minutes

Student will complete the Entry Ticket: Interpreting Rate of Change and Intercepts of Linear Models where they have to compute and interpret the slope and intercepts to a graph of a linear model. This entry ticket is designed to activate student’s prior knowledge on calculating and interpreting slope and intercept for linear functions and equations.  

Academic Vocabulary:

Slope

Rate of Change

Intercept

Interpret

Linear Model

*Note: place academic vocabulary on word wall as a strategy to assist students in learning academic vocabulary. 

 

2 Explicit Instruction and Active Note-taking - 30 minutes

After the entry ticket, I will present the PowePoint Slides: Interpreting Rate of Change and Intercepts for Linear Models. This lecture addresses computing and interpreting the rate of change (slope) and intercepts for different scenarios that can be modeled using linear functions.

 

3 Collaborative Work and/or Exit Ticket: Interpreting Linear Models - 15 minutes

To wrap up work on interpreting the rate of change and intercept for linear models students work on the Exit Ticket: Interpreting Linear Models assignment to show their understanding of the day's main learning objectives. 

This activity can be utilized by the teacher in a number of ways. Students can work on the Exit Ticket as a collaborative activity where they work in groups. Alternatively, the Exit Ticket can be used as a formative assessment where students complete the assignment independently.

4 Our City Statistics Project Interpreting the Data - 30 minutes

To conclude today's lesson I have students work in groups on their collaborative project: Our City Statistics Project Overview

For more details on the expectations and steps for the project see the Project: Our City Statistics Assignment Sheet.

 Link

 

Interpreting Scatterplots in Context for Deeper Understanding
Real World Applications

Link

When students have to interpret data that is connected to a real world context, they are encouraged to grapple more with the relevance and application of the math. In addition, having student work and reasoning as to what the scatterplots and other forms of data students produced in this project gave me a priceless window into how my students are thinking about the concept.

Collaboration for Inquiry and Application
Real World Applications

In this lesson I have the groups of students work together on interpreting the scatterplot they have designed for their project. To do this, students can respond to the items under interpreting the data on the project assignment sheet. More specifically, groups can collaborate on interpreting the slope and the intercept of the line of best fit in the context of their data and research question.

It is important to note many times the intercept won't be a reasonable solution. For example, one group compared house prices (x) and crime rate (y) over time. An intercept would mathematically predict the crime rate when house prices are equal to zero. I would look for students to be able to realize this point is not reasonable as house prices are not liklely to go to zero anytime in the near future!

I like the real world application aspect of this project. Providing students with choice of topics for this assignment not only makes the assignment relevant to students but also engages students and I have found they tend to ask better questions and are invested in the process.