Tuesday, February 14, 2012 and Wednesday, February 15, 2012

What is a rate? Analyzing graphs to determine rate of change.

Maine State Learning Results:

Math:

Common Core

Use functions to model relationships between quantities. (8.F)

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table of from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. (8.F.4)

Describe qualitatively he functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (8.F.5)

Language Arts:

Follow multi-step instructions to complete an application or a complex task.

Evaluate the data contained in tables, charts, graphics, etc. for accuracy, credibility, and relevancy.

Explain and evaluate information from reading, listening, or viewing.

Ask appropriate clarifying questions.

Summarize and apply information presented.

Acknowledge and build upon the ideas of others.

Organize and present information logically.

Learning Objectives:

Students will use abstract thinking, reasoning and analytical skills to explain and justify the information presented in a graph.

Students identify effective ways to organize data that is shown graphically. Students are able to connect field study to in class learning, and can demonstrate by comparing

and contrasting field data that they collected. Students can locate patterns that are similar among different data sets and can explain results in

their own words.

Materials needed:

Persuade Your Peers Cards to give students.

Paper for students to take notes on to decide which Persuade Your Peer explanation is correct.

Homework paper

Need chalkboard/dry-erase board

Modifications:

To accommodate different learning styles and special needs, this lesson allows students to work in small groups, move around the room, and form opinions together and independently.

Lesson Plan:

Tuesday:

As students enter class, have two graphs on the board. Both will show the same average rate of speed. Graph 1 will show someone starting quickly and slowing down. Graph 2 will show someone starting slowly and speeding up.

Give out Persuade Your Peers cards to three or four students. Allow them to review for a minute or two, and then ask them to try to persuade others to believe that they are accurately interpreting the graphed information.

Each persuader will have two minutes to explain. After all explanations are given, ask the class which is correct and why. What can we tell just by looking at these graphs? What goes on the x-axis? What goes on the y-axis? (rise over run, slope, rate)

Ask a student to demonstrate what the graphs are saying. Are these interpretations correct? Talk about average speed vs. instantaneous speed. Both graphs show the same average speed, but looking from point to point we see that one starts slow and the other starts fast. Analyze the rate of change between points. Can we ever have a negative rate of change? What would that look like? Can students provide real-life examples?

Hand out homework worksheets regarding reading graphs and finding rate of change. Have students start working on them in class. Float to see if students understand the material or if they are having difficulty. Review the first few answers together, the remainder is homework due Wednesday.

Wednesday:

Show a graph with three lines – the first line will have a constant rate of change, the second will be increasing at different positive rates of change, and the third will have a negative rate of change at some point on the line.

Ask students to look at the graphs and see what they can figure out without any additional information. While they are doing this, have students take out the homework for a grade. Check homework for progress. Are there any questions on the homework?

What can the students tell me about the lines on the graph (Line 1, Line 2 and Line 3)? How do they know? Justify answers.

Have graphs set up on PowerPoint with data collected on snow tubing field study from each of the four science classes.

What can we tell just by looking at each graph independently? When we look at all four graphs, do we see any patterns? What does this tell us about the information we collected? Should all four graphs look exactly the same? Why or why not? What is the average speed of each graph? What about the rate of change from point to point?

Ask students to provide the rate of change formula and have them practice using this with the points on the graphs of the field study data. Float around the room to check understanding/answer questions and then look at a few points together.

No homework.

Assessment:

Evaluate student understanding of rate, rate of change and analyzing graphs through:

Persuade Your Peers activity. Do students have misunderstandings about reading information graphically?

Listening to class discussion around reasoning and analysis of graphs. Homework worksheet. Overall, making sure that the arguments are logical and can be justified mathematically. While

specifically looking for any misunderstandings of vocabulary or mathematics being presented.