Linear vs. Exponential Functions
Overview
The point of the lesson is for students to be able to distinguish between situations that can be modeled with linear functions and with exponential functions.
• Prove that linear functions grow by equal differences over equal intervals, and exponential functions grow by equal factors over equal intervals.
• Recognize linear situations.
• Recognize exponential situations.
Lesson
Brian-Based Lesson
| Lesson Objectives: Distinguish between situations that can be modeled with linear functions and with exponential functions. • Prove that linear functions grow by equal differences over equal intervals, and exponential functions grow by equal factors over equal intervals. • Recognize linear situations. • Recognize exponential situations. | |||
Grade: 9th Algebra 1 Time frame: One class period | Lesson Title: Linear vs. Exponential Functions | ||
Brain-based Strategies Used in the Lesson:
| Formative or Summative Assessments: Formative Assessment: An exit ticket will be given at the end of the lesson having the students show their reasoning skills. Also, will have a check-in on how they believe they are doing on the topic and why. | ||
Prior to this lesson: The information needing to be covered before this topic is how to determine what a function is, evaluating functions, and writing functions when given the slope and y-intercept. Before they enter 9th grade these students should have a basic understanding of graphing (even if it is just plotting points), key features, and slope. The unit we are working on is Linear and Exponential Functions. This topic should be taught after the students have some type of reasoning skills to determine real solutions based on context, can interpret information based on a graph, words, table, equation, and patterns. Students' mastery of that information will help them form a base of characteristics that can be used to compare to new functions. That way during the introduction to Exponential Functions they can use the previous information to understand the differences and similarities between the linear and the new function, be able to identify either function used based on the context, make sense of solutions, and identify key features. | |||
Materials: Computer and Desmos Technology materials: Desmos: (This includes their warm-up, lesson, and exit ticket) | |||
Content Core Standard: CCSS.MATH.CONTENT.HSF.LE.A.1 | |||
Technology used:
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| Time | Materials | Lesson Procedures(Include the materials & technology.) | |
| 5Mins | Intro to Exponential | Intro activity to activate schema (background information)/Warm-up/or Bell-ringer Students will start by completing 5 views of a function with a linear function. This is so they are prepared to be able to compare/contrast a linear function to that of an exponential one (which they will be learning momentarily). | |
| 5 Mins. | Introduce New Information: (Teaching)Students are given a pattern of clouds in which the hope is that they see it is increasing at an inconstant slope. They will discuss what they notice and wonder about the pattern they are seeing. From here we will do the Five Views of a function with the Exponential Function in which they will be able to see it unfound in a table, graph, and equation. | ||
| 10 Mins | Hands-on Activity Steps: (Prepare ways for students to practice the new information.)After learning what an exponential function is, students will go through a series of pictures, equations, tables, word problems, and determine if the function is linear or exponential based on the key features of each. They will also be asked to justify their answer. Each of these we will go over as a class – so that any misconceptions can be cleared up. Before ending the lesson, they will have to do a card sort in which they will be given multiple views of each function. (This they will fully on their own) | ||
| 5 Mins. | Feedback: (How will the students provide feedback?) Group activity? Instructor feedback? Feedback will be given in the Exit Ticket. Students will slide the slider to agree/disagree with the statement “I feel confident in my ability to determine if a function is linear or exponential.” They will also explain their answer. Lastly, to double-check their memory they will give me one way they know a function is linear and one way they know a function is exponential. | ||
| Homework or in-class assignment | Assessment(s): (assignments and/or activities)
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