About This Chapter
Standard: 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. (CCSS.MATH.CONTENT.8.F.B.5)
About This Chapter
Integrate these video lessons into your regular math curriculum to accentuate the important skills related to the connections that may exist between functions. Teach your students all about functional relationships and their graphs. After working through this chapter's topics, your 8th graders will feel secure in the following content:
- Quantitative variables
- Graphs used to express qualitative features of functions
- Drawing, reading and interpreting graphs
You can be sure that your class has mastered functional relationships when learners are able to explain the concept of quantitative variables, describe how graphs indicate relationships and draw graphs based on a function's qualitative features. These skills might serve students well in high school and college math courses. The strategies might also be useful when evaluating or performing research in a wide variety of areas.
How to Use These Lessons in Your Classroom
Here are a few lesson ideas that you might want to add to your arsenal, in efforts to meet the Common Core Standards.
Compare Qualitative and Quantitative Measurement
After sharing this chapter's lessons, review the concept of qualitative vs. quantitative research and measurement. Look at examples and lead a classroom discussion of to which category each belongs. Explain the possibility of mixed methods.
Divide your class into small groups. Each group will be tasked with devising a survey based on two chosen variables. They should then plot their results on graphs to determine whether there's a relationship between their variables. Students could present their findings through oral presentations with visual representations of their graphs.
Estimates vs. Predictions
Present a graph with a pattern based on a quantitative survey topic of wide interest among your students. Guide their understanding of estimates that might be made based on that information and predictions that could be inferred by extending the line. Discuss. Ask students to determine whether their graphs from the previous lesson offer the opportunity to make estimates or predictions.
1. Describe the Functional Relationship Between Quantities
In this lesson, you'll learn how to look at a graph, table, or function written mathematically and verbally describe the functional relationship shown. For example, you'll learn to describe whether the function is increasing or decreasing.
2. Draw a Graph Based on the Qualitative Features of a Function
Learn how to sketch the graph of a function based on a description of its behavior. You can do this even if you don't know any exact numbers for the input or output values!
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Other chapters within the Common Core Math Grade 8 - Functions: Standards course