Direct, inverse, and joint variation

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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.

F 503. Build functions and use quantitative information to identify graphs for relations that are proportional or linear F 602. Build functions for relations that are inversely proportional AF 601. Solve word problems containing several rates, proportions, or percentages AF 502. Build functions and write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) A 406. Exhibit knowledge of slope A 514. Determine the slope of a line from an equation A 513. Determine when an expression is undefined F 505. Understand the concept of a function as having a well-defined output value at each valid input value AF 701. Solve complex arithmetic problems involving percent of increase or decrease or requiring integration of several concepts (e.g., using several ratios, comparing percentages, or comparing averages)

F 503. Build functions and use quantitative information to identify graphs for relations that are proportional or linear
F 602. Build functions for relations that are inversely proportional
AF 601. Solve word problems containing several rates, proportions, or percentages
AF 502. Build functions and write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions)
A 406. Exhibit knowledge of slope
A 514. Determine the slope of a line from an equation
A 513. Determine when an expression is undefined
F 505. Understand the concept of a function as having a well-defined output value at each valid input value
AF 701. Solve complex arithmetic problems involving percent of increase or decrease or requiring integration of several concepts (e.g., using several ratios, comparing percentages, or comparing averages)

What you'll learn

Translate a variation statement (direct, inverse, joint, combined, or with a power) into an equation, find `k` from one given pair of values, and use it to answer for an unknown value
Decide the variation type from a table by testing whether `y/x` or `xy` is constant, or from an unlabelled situation, and identify relationships that fit no variation model
Distinguish direct variation, a line through the origin, from a linear relationship with a nonzero intercept, and recognize inverse variation as a curve undefined at `x = 0`
Determine the effect on the output of scaling an input, without computing `k`

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