Free Variation Of Magnitudes: Directly And Inversely Proportional Or Non-Proportional. Lesson Plan for 8th Grade Students

Topic: Variation of magnitudes: directly and inversely proportional or non-proportional.

Objectives & Outcomes

• Identify the magnitude of a relationship as direct or inverse proportional.
• Perform calculations to find the relationship between magnitudes in a problem.
• Use proportional relationships to solve real-world problems.

Materials

• Graph paper
• Pencils or pens
• Calculator (optional, if working with real-world problems)

Warm-Up

• Have students draw a graph with two axes, one for "magnitude of A" and the other for "magnitude of B".
• Have them label one end of the graph "magnitude of A=0" and the other end "magnitude of A=infinity".
• Have them label one end of the graph "magnitude of B=0" and the other end "magnitude of B=infinity".
• Ask them to think about different scenarios in which the magnitudes of A and B might change, and write their scenarios on the graph, labeling each one with a letter (e.g. "A increases", "B decreases", "both increase", "both decrease", etc.).
• Have a discussion about the different scenarios and what they might mean for the relationship between A and B.

Direct Proportional

• Ask students to consider a scenario in which the magnitudes of A and B are directly proportional, such as "A increases by a factor of 2, and B also increases by a factor of 2".
• Ask them to draw a new graph, this time with "magnitude of A" on the x-axis and "magnitude of B" on the y-axis.
• Have them plot points corresponding to different values of A and B, using the graph they drew earlier as a guide.
• Have them write an algebraic expression for the relationship between A and B, based on the points they plotted.
• Ask them to consider different scenarios in which the magnitudes of A and B might be directly proportional and write these on the graph, labeling each one with a letter (e.g. "A increases by a factor of 2, and B also increases by a factor of 2", "A increases by a factor of 3, and B also increases by a factor of 3", etc.).

Guided Practice

• Provide students with another scenario in which the magnitudes of A and B are directly proportional and have them work in pairs or small groups to plot points, write an algebraic expression, and label their graphs with letters.

Independent Practice

• For the independent practice, students will be creating their own scenarios in which two or more magnitudes are either directly or inversely proportional. They will be working independently or in small groups to create their scenarios, plot points, write an algebraic expression, and label their graphs with letters.

Closure

• As a class, the students will come together to share their work with the rest of the class. They will present their scenarios, their graphs, and their algebraic expressions. They can then discuss the different strategies they used to identify the proportionality between the magnitudes, and how they integrated this with the thematic unit Algebra.

Assessment

• To assess the students' understanding of the material, a written or oral quiz could be given. This would include multiple-choice and fill-in-the-blank questions that ask the students to identify proportional or inversely proportional magnitudes and explain their reasoning. It could also include problems for the students to solve that would require them to identify the proportional or inversely proportional relationships between the given magnitudes.