Lesson objective: Extend understanding of unit rate for proportional relationships to rate of change for general linear functions.
Students bring prior knowledge of unit rate from 7.RP.A.2.B. This prior knowledge is extended to rate of change as students compare a proportional linear relationship to a non-proportional linear relationship. A conceptual challenge students may encounter is not all linear relationships are proportional, yet we can still use ideas from proportional relationships.
The concept is developed through work with a table of values, which helps students to observe changes in input values and output values side by side, and facilitates understanding that these changes are related.
This work helps students deepen their understanding of operations because, whereas calculating unit rate only required division of any output value by its corresponding input value, calculating rate of change involves dividing the differences of output values and input values.
Students engage in Mathematical Practice 7 (Look for and make use of structure) as they identify the relationship between the changes in the input and output values, and use this information to find missing values in the linear relationship.
- equivalent ratios
- rate of change
- unit rate
Algebra I - Rate of Change and Slope
Common Core Aligned Lesson Plan with Homework
This lesson plan includes:
-Lecture Notes (PDF, PowerPoint, and SMART Notebook)
-Blank Lecture Notes (PDF and SMART Notebook)
-Lecture Handout (PDF)
-Answer Key (PDF)
-Find the slope of a line.
-Determine if a function is linear based on a table of values.
Common Core Standards:
F.IF.6 - Calculate and interpret the average rate of change of a function over a specified interval. Estimate the rate of change from a graph.
F.LE.1a - Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F.LE.1b - Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
----Chapter: Linear Functions----
Determine the Equation of a Line
Linear Functions Lesson Plan Bundle
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© Ashley Spencer, 2015
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The Common Core Standards were written and developed by The National Governors Association Center for Best Practices and Council of Chief State School Officers. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
This product is the work of Ashley Spencer (“Infinitely Pi Learning”). It is intended to support the implementation of the Common Core Standards. Any claim of alignment is the personal opinion of Ashley Spencer (“Infinitely Pi Learning”) and is not necessarily the opinion of the National Governors Association Center for Best Practices and Council of Chief State School Officers. No approval by, nor the association with, the creators of the Common Core Standards is intended or implied.
Lecture - 12, HW - 2