CCSS.Math.Content.HSF-BF.A

CCSS.Math.Content.HSF-BF.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSF-BF.A.1

  Write a function that describes a relationship between two quantities

• CCSS.Math.Content.HSF-BF.A.1a

  Determine an explicit expression, a recursive process, or steps for calculation from a context.

• CCSS.Math.Content.HSF-BF.A.1b

  Combine standard function types using arithmetic operations.

• CCSS.Math.Content.HSF-BF.A.1c

  (+) Compose functions.

• CCSS.Math.Content.HSF-BF.A.2

  Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

01

What Students Need to Do

Students identify input and output quantities, choose variables, and write a function rule that fits a given relationship. They use a table, graph, equation, or description to justify the rule and set a sensible domain.

02

What Mastery Looks Like

Given a situation, students can choose a suitable function type and write a correct rule. They can explain each variable and parameter, state a sensible domain, and use the function to predict values.

03

Common Misconceptions

Students may reverse the input and output or leave out a starting value. They may use repeated addition for percent growth, choose an unsuitable function type, or give a domain that includes impossible values.

04

How to Assess It

Exit ticket: A gym charges a $25 sign-up fee and $18 per month. Write C(m), state a domain for one year, find C(7), and explain both numbers.

1. 01

   Give groups stacked cups, rulers, and a recording table, then have them measure stack heights and write a function for any number of cups.

2. 02

   Ask students to compare two phone plan rules and write which plan costs less for different amounts of data.

3. 03

   Run a card sort matching six situations with their tables, graphs, equations, and reasonable domains.

4. 04

   Have students use a local taxi fare or delivery fee to write a cost function and calculate three sample trips.

• CCSS.Math.Content.HSF-IF.B.4

  For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs show...

• CCSS.Math.Content.8.F.B.4

  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of...

• CCSS.Math.Content.8.F.B

  Use functions to model relationships between quantities.