Maryland Math F.BF.A.1.c

MathGrades 9–12BUILDING FUNCTIONS

The Standard

F.BF.A.1: Write a function that describes a relationship between two quantities.

Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

Maryland College and Career Ready Standards for Mathematics (2025) · Build a function that models a relationship between two quantities.

Teacher's field guide

What This Standard Means

What Students Need to Do: Students use the result of one rule as the input to another. They choose an order that makes sense, calculate the result, and explain what it means.
What Mastery Looks Like: Given P(h)=15h+10 dollars and D(p)=0.9p, a student writes D(P(h))=0.9(15h+10). They find D(P(2))=36 dollars and explain that the discount applies to the full price.
Common Misconceptions: Students may reverse the rules without checking whether the units fit. Some multiply the two rules instead of putting one result into the other, or apply a discount to only part of a price.
How to Assess It: Exit ticket: A ride costs F(m)=4+2m dollars, and a coupon takes 3 dollars off with C(p)=p-3. Find C(F(5)) and explain why F(C(5)) does not fit the units.

Lesson moves

Ways to Teach It

Give pairs cards L(n)=3n cups of lemonade and B(c)=c/2 bottles; they pass an n=4 slip through both cards.
Ask pairs to write why a rule needing miles can take a distance result but cannot take a price result.
Teams race to order cards d(t)=30t miles, F(d)=2d dollars, and S(p)=1.1p dollars, then evaluate the chain at t=2.
Give students a phone plan P(g)=20+5g dollars and sales tax S(p)=1.06p; have them calculate S(P(4)) and explain the bill.

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