CCSS.Math.Content.HSF-IF.B.6
The standard
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Common Core State Standards for Mathematics
What this standard means
Students need to find how much a function changes, on average, over an interval. They should do this from an equation, a table, or a graph. In plain terms, they are finding the slope between two points and explaining what it means in context.
Mastery looks like choosing the correct two input values, finding the matching outputs, computing change in output divided by change in input, and naming the units. Students often mix up input and output, subtract in different orders, or give only a number without saying what it means.
Ways to teach it
- Give pairs a table of water height over time and have them calculate average rates for three different time intervals.
- Ask students to explain why the average rate from 0 to 10 seconds may differ from the rate from 10 to 20 seconds.
- Show a graph with two marked x-values and have students estimate the average rate of change on a sticky note.
- Use a rideshare fare table and ask students to find the average cost per mile over different trip lengths.
Plan a lesson for CCSS.Math.Content.HSF-IF.B.6
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Related standards
- CCSS.Math.Content.HSF-LE.A.1c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
- CCSS.Math.Content.HSS-ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
- 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.HSF-LE.A.1b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.