Exponential Growth Functions Using Percents
1 Hook/Attention Grabber
Show a video that demonstrates exponential growth and how large populations and/or bank accounts can get with exponential growth. Stop the video at pre-determined stopping points and have students answer questions about the segment of the video they just watched.
Students will answer questions when the teacher stops the video.
2 Direct Instruction
1.) Have students recall the components of an exponential growth function. 2.)Model how to write exponential growth functions using percents. Teacher will emphasize how to correctly write the percent in the growth function. Review notes and have students add more information if necessary. Summarize the parts of an exponential function and what is needed in a growth function. 3.) Compare/contrast Exponential and linear functions using a Google doc that all students will have access to and can contribute to.
Students will keep track of all information for the direct instruction in notability with color -coded examples of each part of the exponential function. Students will compare and contrast exponential and linear functions using a venn diagram that is in a Google doc that all students can contribute to. Students will open the Google doc that the teacher had previously shared and given them editing rights to.
3 Guided Practice
Review questions on converting percents to decimals in the exponential function. Teacher will run Socrative teacher paced and will go over each question after the students have answered it. The teacher will use the app to visually see how many students are getting a question wrong. If not as many students got a particular question wrong, less time will be spent going over that question.
Students need to download the app or go to the website and enter in the teacher room number. The questions will pop on their screen. These multiple choice questions will involve converting percents to decimals. They will become increasingly more difficult and the last question will be about finding a growth factor.
4 Independent Practice
Students will work in groups on the population growth examples. Students will create a model for their scenario and then then post their problem, explanation and solution to the class padlet. Students will verbally explain their problems to the class.
Students will complete their work and then take a picture of their work to add to the class padlet. Students will have a resource of multiple problems and solutions. They can add the link to the padlet in their notes.
5 Wrap Up
Teacher will pose one final scenario on the board. Students will write their response on an exit card. The teacher will take pictures of the exit cards and display them on the board during the next class and ask students which solutions are correct and why. The teacher will also highlight common mistakes. Student names will not be displayed on the board. The teacher will know who completed each card, but the students will not.
Key Standards Supported
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Linear, Quadratic, And Exponential Models
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).