CCSS.Math.Content.HSF-LE.A.1b
The standard
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Common Core State Standards for Mathematics · Construct and compare linear, quadratic, and exponential models and solve problems
What this standard means
Students need to spot when a relationship is linear. They should see that equal steps in the input make equal changes in the output. They should describe the rate, name the units, and connect it to a table, graph, equation, or situation.
Mastery looks like saying, “It goes up by 3 each hour, so the rate is constant,” and backing it up with evidence. Students often confuse a steady increase with a constant rate. They may also ignore unequal input intervals or describe the starting value instead of the rate of change.
Ways to teach it
- Give pairs a stack of table cards and have them sort into constant rate and not constant rate, then justify two choices.
- Ask students to write: How can you prove a phone plan cost changes at a constant rate per gigabyte?
- Show a four-row table with one missing value and ask students whether it could represent a constant rate, with evidence.
- Use taxi fare data with miles and total cost, then ask students where the constant rate appears in the table and equation.
Plan a lesson for CCSS.Math.Content.HSF-LE.A.1b
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Related standards
- CCSS.Math.Content.7.RP.A.2
Recognize and represent proportional relationships between quantities.
- 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.6.RP.A.3b
Solve unit rate problems including those involving unit pricing and constant speed.
- CCSS.Math.Content.7.RP.A.2b
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.