Direct and inverse proportionality

Teacher tools for this standard

Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

"Questions will require students to solve problems by using a proportional relationship between quantities, calculating or using a ratio or rate, and/or using units, derived units, and unit conversion." "Understand and use the fact that when two quantities are in a proportional relationship, if one changes by a scale factor, then the other also changes by the same scale factor." "Apply proportional relationships, ratios, and rates in a wide variety of contexts. Examples include, but are not limited to, scale drawings and problems in the natural and social sciences." → `sat-psda-ratio-prop` "Solve problems involving derived units, including those that arise from products (e.g., kilowatt-hours) and quotients (e.g., population per square kilometer)." → `sat-psda-ratio-unit` "Solve problems involving: » a one-step unit conversion. » a multistep or multidimensional unit conversion." → `sat-psda-ratio-unit`

"Questions will require students to solve problems by using a proportional relationship between quantities, calculating or using a ratio or rate, and/or using units, derived units, and unit conversion."
"Understand and use the fact that when two quantities are in a proportional relationship, if one changes by a scale factor, then the other also changes by the same scale factor."
"Apply proportional relationships, ratios, and rates in a wide variety of contexts. Examples include, but are not limited to, scale drawings and problems in the natural and social sciences." → sat-psda-ratio-prop
"Solve problems involving derived units, including those that arise from products (e.g., kilowatt-hours) and quotients (e.g., population per square kilometer)." → sat-psda-ratio-unit
"Solve problems involving: » a one-step unit conversion. » a multistep or multidimensional unit conversion." → sat-psda-ratio-unit

What you'll learn

Identify whether two quantities vary directly, inversely, or neither (from a table, from wording, or from a context in which the word "varies" does not appear), and use the relationship and one known pair to find an unknown value
Find the constant of variation from a table (every ratio y/x constant, or every product xy constant) or from one known pair, state its units, and write y = kx or y = k/x
Apply the scale-factor property (the same factor under direct variation, the reciprocal factor under inverse variation), converting a percent-phrased change into a growth factor first
Distinguish direct variation from a linear relationship that is neither, using the doubling test and the origin test

Review first:

Slides

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