# Temperature Slopes and Meaning-Making

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## Objective

Students reflect on the their heated water graphs, drawing meaning from the slope of the graphs and relating temperature change to the physical characteristics of their lab trials.

#### Big Idea

Physical systems can be modeled by mathematical and graphical relationships.

## Warm-up

20 minutes

To start class, I ask students to reflect on their responses to the prompts at the end of the first class (their "exit ticket," see sketching thermo graphs resource).  Using a think-pair-share process, students move from private reflection to larger group discussion, which tends to promote more participation and confidence.

My goals, in this part of the lesson, are two-fold.  First, I want students to recognize that the slopes of the lines they sketch represent the rate of change of the water temperature. Second, I want them to consider how various physical properties will affect that rate.

At first, we consider the responses to the exit ticket questions.  Different scenarios lead to different rates of change, naturally prompting the discussion of the important physical properties.  At the board, I collect student thoughts of potential traits that could affect a material's resistance to changing temperature.

## Explanation

20 minutes

Having intuited the traits that impact temperature change, I provide students with a 1-page notes summary (see Energy-Temperature Notes, Part One resource) that highlights the "energy-temperature" and "power-slope" relationships.

After giving students a few minutes to read the summary, I present a short lecture to amplify on those notes, drawing attention to units involved and making a connection between the two equations.  The goals, at this moment, are to clarify the relationships and to provide students with the background necessary to solve simple thermal energy problems.

After showing one example problem (see "prelude to guided practice" and solution resources), we are ready to move to some guided practice.

## Guided Practice

25 minutes

One way to formatively assess student understanding is to provide time and resources for guided practice.  As students work collaboratively on a set of questions (Energy-Temperature questions resource), I circulate around the room to check for understanding.

This is an excellent time for me to get to know student strengths and weaknesses.  Also, by allowing collaboration, I can start to build a community of learners where helping one another is a norm.

## Homework Framing

15 minutes

I want to set up the first homework assignment of the year with a few minutes of framing. My goal is to provide students with a sense of clarity and confidence.

On the board, I show a generic linear relationship (see resource entitled "y=mx+b").  I ask students to identify the slope and intercept.  Using the exact same graph, though now marked as "temperature" and "time" on the axes (see temp vs time resource), I ask what the "initial temperature" and the "rate of change of the temperature" are.  The point is to have students transfer their math background (all of these students have completed Algebra and Geometry) into the realm of Physics.

As a follow-up exercise, I ask student volunteers come to the board to draw in temperature graphs with impromptu properties (various slope and initial temperature combinations).  This activity will help the transfer become complete.  The number and exact nature of these questions varies from class to class as I sense the specific needs of each group.  For example, if the students are struggling with the concept of the initial temperature, I may ask a student to demonstrate three temperature graphs which share the same RATE OF CHANGE OF TEMPERATURE but have different INITIAL TEMPERATURES.

Then I hand out the assignment (see resource entitled "thermodynamics graphical hw") and show students that the work they'll be doing is aligned with this thinking . . .  and will also contain some questions similar to the work done earlier in class.  If time allows, they may start.