Intro to Slope / Rate of Change
Use a backchannel such as TodaysMeet to brainstorm around the essential question: Can we use information to predict the future? Students might give their opinions on whether they believe we can or cannot truly predict the future, give examples of how we try to predict the future in daily life, or posit what kind of information we might need to predict future events.
Students can talk about the question in small groups, post their thoughts, and read others' insights on the backchannel. At the end of the lesson, students can revisit their thoughts and how they relate to what they have learned.
2 Direct Instruction
The "Domino Effect" lesson on Mathalicious is available for free and is a fantastic introduction to the concepts of slope and y-intercept based in a topic every middle school student loves - pizza! Students will use information from Dominos to create graphs, and see how each topping affects the price of the pizza. They then answer questions about the essential features of the graph: what does the y-intercept represent? What does the slope of the line mean?
3 Guided Practice
Start with the video "Slope and Rate of Change" to give students guided examples of finding the slope of a line from a graph or set of ordered pairs. Students can then explore related problem solving videos in small groups or under guidance from the teacher.
As an alternative or extension activity, have your students hit YouTube or another video sharing service, and find their own videos of guided problem solving. They can then share the videos they think are most helpful with their classmates.
4 Independent Practice
Students can practice finding the slope of a line from a graph or from two points using 8th grade skills V.9 and V.10. IXL gives feedback when a student gets a problem correct or incorrect, provides a SmartScore to let students know how they are doing overall, and gives prizes when students master each skill. Best of all, the teacher can see all students' usage statistics, such as time spent on each problem and rate of accuracy.
Twitter is a great way for students to boil down what they have learned into 160 characters. To put everything together from this experience, have students find Creative Commons licensed images of linear graphs. Then, they can tweet the picture with a brief qualitative statement about the essential features of the graph. What does the y-intercept represent? What change does the slope represent? Where might the graph be going?
Key Standards Supported
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
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 or 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.
Describe qualitatively the 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.