Georgia 8.FGR.5.6
The Standard
Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Georgia's K-12 Mathematics Standards · Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use distribution, combining like terms, and factoring to rewrite a linear function without changing its outputs. They explain which form makes the slope, an intercept, or a point easiest to identify.
What Mastery Looks Like
- A student can rewrite a linear function accurately using distribution, factoring, and combining like terms. They choose a form that clearly shows the slope, an intercept, or a known point, then verify that the forms match.
Common Misconceptions
- Students may think expressions that look different represent different functions. They often make sign errors when factoring, read the x-intercept in 3(x-4) as -4, or confuse slope with an intercept.
How to Assess It
- Exit ticket: Given f(x)=3x-12, rewrite it to show the x-intercept, then state the slope and both intercepts. Explain which form helped with each property.
Lesson moves
Ways to Teach It
Give pairs algebra tiles to build 3x+6, regroup them as 3(x+2), and verify both forms with three input values.
Ask: Which form, f(x)=2x-8 or f(x)=2(x-4), makes each intercept easier to see, and why?
Run a card sort matching expanded, factored, and point-based forms of the same line with its graph and property cards.
Model concert profit as P=5x-100, rewrite it as 5(x-20), and interpret $5 per ticket and the 20-ticket break-even point.
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