For this lesson students will need access to computers which have Excel or a comparable program on them. Ideally, this lesson can take place in the classroom with a laptop cart or in the computer lab.
In this lesson students apply their understanding of literal equations. In this lesson students explore "real-life" resources that make use of literal equations (rewriting known formulas) to help make people's lives easier. Start out by showing students this intro video which discusses how to calculate simple interest. This short video plants the seed for the next portion of the launch. Poll the class to determine how many students have heard of earning "interest" on a bank account.
Next, have students individually visit the website Bankrate.com calculator. This is a simple interest calculator. Show students how the calculator works by inputing some values and calculating the amount in the account after a certain amount of time. Let students have a few minutes to play with this calculator and determine some hypothetical values.
Explain to students that in this lesson they are going to be designing a program similar to the one that Bankrate uses for their calculator. The calculator works by taking values and plugging them into a certain formula. The calculator that the students will make will actually be more useful than the one on the website because the user will be able to solve for different variables.
I will go over Example 1 of the Rewriting_Formulas_Investigation with my students. I plan to have students read down to the first screenshot from Excel and have them do a turn-and-talk around why that formula would give them the volume of the prism. I will ask one or two pairs of students to share their ideas with the class.
Many students will not be familiar with the Excel program. Make sure to point out logistical items such as using "*" for multiplication. Also, explain to students that in order to write a formula they must put an "=" before they begin to type.
I have students look at the second screenshot and do a Think-Pair-Share to determine why the given formula determines the length of the prism. When students share out, I focus student responses on why the parenthesis had to be there in order to have the formula work correctly.
Teaching Point: Encourage students to write the formula out by hand first and then solve if they are having difficulty in seeing why the given operations are being done.
I will have each pair of students go down to the third screenshot and determine the formula that would be used to solve for the width of the rectangle. This task requires that students reason abstractly about the values that would be plugged into the formula (MP2). Students also need to see the structure in the original equation in order to determine which inverse operations to use (MP7).
Lastly, before moving on, I will have students make a spreadsheet like this one so that they can input the formulas for themselves. I give students a few minutes to input different values to determine if their formulas are working correctly.
Next students will begin the independent portion of the investigation. Students will determine the four formulas that would be used to determine the total amount (A), starting (principle) amount (P), Rate (r) and Time (t) based off of the simple interest formula. I encourage my students to think through the problem and organize their thinking first, before trying to construct the spreadsheet. Students can organize their work either horizontally (as shown) or vertically (similar to the Bankrate calculator).
Teaching Point: Have students copy and paste their input sections. I have them make four different sections (one for each equation) so that when answering questions they can plug in the three given values and solve for the fourth. They could also make one input section and have all four formulas as long as they delete all of their inputs each time they start a new question.
If students answer all four questions early, I have them explore the formulas further by making up some examples of their own and solving for a missing value. I ask questions like, "how long will it take me to make a million dollars?"
The Rewriting_Formulas_Practice closing activity will have students apply what they have learned to other mathematical formulas. The time available may be limited, so I may have my students finish this assignment for homework.
In the investigation, students can see why you would want to isolate a single variable. In this practice/closure, students will get to practice their algebraic manipulation skills to isolate variables in more complex equations. Whether this assignment is collected at the end of class or given as an assignment for home, I will make time for students to discuss their solutions with a partner to check for consistency.