This is the ninth lesson in the series, Lesson Transformed, in which traditional lessons are transformed into engaging experiences for students which exemplify the premises of the Visioning Document.
Topic: Evaluating Functions
Grade Level: 9/Algebra I
Content Area: Mathematics
Objective: The students will be able to decide whether relations represented verbally, tabularly, graphically, and symbolically define a function and evaluate functions, expressed in function notation, given one or more elements in their domains.
Flipped Lesson: Students watch this video (link) from Khan Academy – What is a Function?
While watching the video, make note of the following:
- What makes a relation a function?
- Sketch an example of a graph that is a function.
- Sketch an example of a graph that is not a function.
Lesson: Students will use copies of the Function Representations Graphic Organizer (linked below) to take notes of examples provided by the teacher.
One representation of a given function will be provided by the teacher, then the students should translate the function into the other representations. Examples are linked below.
During classroom discussion, the teacher should emphasize how to evaluate a function for a given value (by substituting the value for x into the equation and simplifying), connecting the function value to the multiple representations of the function.
Practice: Evaluating Functions worksheet (link).
Objective: The students will create evidence of understanding of multiple representations of relations (represented verbally, tabularly, graphically, and symbolically) and whether each define a function. The students will also evaluate functions, expressed in function notation, given one or more elements in their domains.
Investigation: Students explore the connection between a graphical model and the real world event for which it models. The teacher launches Function Carnival by Desmos then the interactive guides the students, individually on their own devices, through the experience:
- Watch: The students watch a 10-second video.
- Graph: They graph what they see in the video.
- Iterate: Students play back the video and see how their graphical model would be represented as an animation. They update their graphs based on that feedback.
- Repeat: Students watch and graph two more scenarios.
*Note: This learning experience did not begin with the flipped video as in the traditional lesson. This transformed lesson exemplifies the opportunity to focus on the student experience in the lesson, allowing for the student to explore the content and make connections authentically, rather than through a lecture format (in which information is shared with no authentic connection). For more information, you may choose to read this blog post by Dan Meyer (link).
Exploration: Similar to Function Carnival, students compare the graphs of the height of the water in a glass against time to the corresponding video. The teacher launches Water Line by Desmos then the interactive guides the students, individually on their own device, through the experience:
- Graph: Students watch a glass fill with water and graph the height of the water v. time. They play back the video to see how well they did.
- Create: After graphing the third glass, students create their own glasses to graph.
- Challenge: Once students successfully graph their own glasses, they add the glasses to the class cupboard to challenge their classmates!
Application: Students complete President’s Pay by Yummy Math. This learning experience includes a PDF of the activity and corresponding Desmos Graphing Calculator, pre-loaded with the data from the activity. The students explore the presidential salary as the the activity opens with this information:
Surprisingly the US president’s salary has only changed 6 times since 1789. Changing the president’s salary requires an act of congress . [Given] are the 6 years of presidential salary change since George Washington became our first president.
This independent practice (President’s Pay) asks the students to create a graph of a given set of data expressed in table form. Then, the students identify specific function values in terms of the pay of a President in a given year. Finally, the students use the Consumer Price Index to explore current Presidents’ pay to past ones.
This transformed lesson was inspired by TASA on iTunes U: Algebra I – Number and Algebraic Methods (Evaluating Functions).
It is the goal of this blog series to equip teachers with skills to transfer understanding and transform their own lesson design.