Heather Stephan WESTERN MIDDLE, ELON, NC
7th Grade Math : Unit #2 - Proportional Reasoning : Lesson #10

# Problem Solving Connections - Can you apply what you know about proportional reasoning?

Objective: Students will be able to apply aspects of proportional reasoning including unit rates, graphs, tables, and equations to work a real world problem.
Standards: 7.RP 7.RP.A.1 7.RP.A.2 7.RP.A.2a 7.RP.A.2b 7.RP.A.2c 7.RP.A.2d MP1 MP2 MP3 MP4 MP5 MP6 MP7 MP8
Subject(s): Math
60 minutes
1 Launch - 10 minutes

OpenerAs students enter the room, they will immediately pick up and begin working on the opener – Instructional Strategy - Process for openers.  This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3

Learning Target:  After completion of the opener, I will address the day’s learning targets to the students.  In today’s lesson, the intended target is, “I can apply what I know about unit rates and proportional relationships to solve a real world problem.” Students will jot the learning target down in their agendas (our version of a student planner, there is a place to write the learning target for every day).

Thoughts from Me! In this lesson, students will be looking for patterns and repeated reasoning, and drawing conclusions (mathematical practices 7 and 8).  Using real world problems, students will create graphs (mathematical practice 4) and given a graph, students will be able to determine an equation and whether or not the relationship is proportional (mathematical practice 2). It will be important that students pay close attention to precision (mathematical practice 6), and use tools (calculator, graph, table) as needed (mathematical practice 5).

resources
Problem Solving Connections Opener.docx
https://betterlesson.com/lesson/resource/1966946/opener
2 Explore - 45 minutes
Activity Reflection
Data Analysis

For some very odd reason, the biggest misconception I encountered was students deciding to calculate the unit rate and then multiply it by ten?!  I sat with one group, and when I asked why they multiplied by ten, they said because 4 miles per hour didn't sound fast - well, then it hit me, they were trying to make the unit rate into miles per hour - but really it was given to them in miles per minute! I was concerned going into the lesson that I was going to have to walk them through it, but I was pleasantly surprised.  I partnered the kids homogeneously and they were able to dive right in.

I have stuck with the kids not being able to use calculators, and it has been really helpful I think in tweaking their skills with rational numbers.  Instead of freaking out that the table consisted of fractions, they just got to work :)

3 Summary - 5 minutes

Instructional Strategy - Table DiscussionTo summarize this lesson, I will have students have a table discussion on the question:  What are all the ways you can identify the constant of proportionality?