Maryland Math 8.AT.D.10.b
The Standard
- 8.AT.D.10
- Construct and interpret a linear function to model a relationship between two quantities.
Interpret the rate of change and initial value in the context of the problem.
Maryland College and Career Ready Standards for Mathematics (2025) · MODEL WITH FUNCTIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain how much the output changes for each one-unit increase in the input. They explain what the output is when the input is zero, using the situation and its units.
What Mastery Looks Like
- Given a tank that starts with 20 liters and loses 3 liters each minute, a student says the rate is negative 3 liters per minute. They say the initial value is 20 liters, the amount in the tank at zero minutes.
Common Misconceptions
- Students may read a negative rate as a negative amount in the tank, rather than an amount lost each minute. They may call the first value shown in a table the initial value, even when the table starts after zero minutes.
How to Assess It
- Show a table with time in minutes of 0, 2, and 4, and water in liters of 20, 14, and 8. Ask: What are the rate of change and initial value, and what does each mean here?
Lesson moves
Ways to Teach It
Start with 20 cubes, remove three each round, and have students record the amount left in a table.
Ask students to write why a tank losing 3 liters per minute can have a negative rate but a positive starting amount.
Give pairs cards showing tank tables and cards describing starting amounts and rates, then have them match the cards.
Show a taxi fare of $4 plus $2 per mile, and ask students to label both amounts on a fare graph.
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