Teaching CCSS.Math.Content.HSA-CED.A.4

Instructions for You

Objective: What if you could come up with a formula that could evaluate every date according to your own particular tastes and spit out a quantitative assessment of that date? Pretty sweet, no?

In this activity, students will work in groups and as a class to come up with just such a formula. Then, they'll rearrange smaller equations and the overall formula to solve for several different variables. It's good practice for isolating variables while making sure they aren't left isolated when prom rolls around.

Activity Length: 1 class period
Activity Type: Groups of 3-6
Materials Needed: Papers, pencils, large whiteboard or document camera

Step 1: Brainstorm with the class all the attributes that they look for in a date to homecoming, prom, or whatever those whippersnappers are up to nowadays. Suggest things like intelligence, sense of humor, dance skills, and a rockin' bod. (What? We know you were thinking it.)

Once you've got a good-sized list, have students pick their top 5-7 characteristics and erase the others. These characteristics will add up to an Overall Date Score. (Note: Each group will be responsible for one attribute, so make sure you have exactly as many attributes as groups!)

Step 2: Assign each of these attributes a variable (e.g., HQ for Humor Quotient, DC for Dance Capacity, MoI for Measure of Intelligence, etc.). In big, big letters, write the sum of all these variables as equal to the Overall Date Score (ODS). It should look something like this:

HQ + MoI + … + DC = ODS

Step 3: Split the entire class into groups—one group for each term in the sum—and give them five to ten minutes to come up with an equation for their specific term. They should use new variables specific to their attribute, define them appropriately, and justify their equation. We suggest they follow these guidelines:

• They should use 3-5 unique variables. Any more than that, and things get sticky.
• Numerical coefficients and fractions are A-okay.
• Variables in the denominators of fractions are okay, but they should all be linear (i.e., have exponents of 1).
• Have teams write down this equation and their variables! Otherwise, they might not remember!

For example, if they're defining HQ, they can say that , where t is the combined laughter time in seconds, j is the total number of jokes told, and p is the number of awkward pauses in conversation.

Step 4: After each group has come up with their equation, call on them to give you their equation for each term and explain it to you and the rest of the class. As they tell you the equation, replace the term in the sum with the expression it represents. This way, instead of HQ + MoI + … + DC = ODS, you'll have a much more complicated equation on the whiteboard.

Since groups came up with their expressions individually, there might be repeats in the variables used. As you write these on the board, replace these repeat variables with other variables so that each term has its own set of variables.

Step 5: Have group members isolate the equation for each of their newly defined variables (i.e., isolate the HQ equation for t, j, and p). Each team member should do this individually, but if they're struggling, have them ask their group for help.

Step 6: Now that you've got a huge equation, have students pick five variables and isolate the monster equation for those variables (i.e., isolate the ODS equation for t, j, p, and two other variables). Make sure they show their work!

Step 7: Once they're finished rearranging the equations, isolating variables, and showing their work, they'll have a formula with which to rate how well or poorly a date has gone. Of course, they might have to carry around a timer and a pad with them to take notes, but trust us: it'll all be worth it.

Instructions for Your Students

What if you could come up with a formula that could evaluate every date according to your own particular tastes and spit out a quantitative assessment of that date? Pretty sweet, no?

In this activity, you'll work in groups and as a class to come up with just such a formula. Then, you'll rearrange smaller equations and the overall formula to solve for several different variables. It's good practice for isolating variables while making sure that you aren't left isolated when prom rolls around.

Step 1: As a class, think of attributes that you'd look for in a date to a dance. What about things like intelligence? A sense of humor? Dance skills? A rockin' bod. (What? We know you were thinking it.)

Step 2: Once you've got a good-sized list, you'll narrow this down to the top 5-7 characteristics and assign them variables (like HQ for Humor Quotient, MoI for Measure of Intelligence, and DC for Dance Capacity). These characteristics will make up an individual's Overall Date Score (ODS), which is just the sum of all these terms. You'll see an equation that looks kind of like this:

HQ + MoI + … + DC = ODS

Step 3: Your teacher will separate you into groups and give you a particular attribute—one of these variables—to define. In five to ten minutes, come up with an equation for that specific term. Use new variables specific to the attribute, define them appropriately, and justify your equation. Follow these guidelines:

• Use 3-5 unique variables (any more than that, and things get sticky) and define these variables explicitly.
• Numerical coefficients and fractions are A-okay.
• Variables in the denominators of fractions are okay, but all variables should have exponents of 1.

For example, you can come up with an equation that represents HQ in terms of t (the combined laughter time in seconds), j (the total number of jokes told), and p (the number of awkward pauses in conversation). Something like that.

Once your group has come up with your equation and what these new variables represent, don't forget to write it all down!

Step 4: Once you've finished, your teacher will ask you to explain the equation and the variables to the rest of the class. He or she will also write the expression that represents your term on the whiteboard in place of the original variable.

There might also be some variables that need to be changed—just so we aren't confusing them to mean the same thing. If that's the case, your teacher will tell you what to change the variable to. Make this change on your paper, too, and use this variable from now on.

Step 5: Individually, rearrange the equation your group created for each of the new variables you defined. Show all your work! If you're struggling, ask the group or your teacher for help.

Step 6: Thanks to you and the groups around you, the original formula for Overall Date Score has transformed into kind of a monster of an equation. Pick five variables and isolate the formula for those variables. Make sure you show your work!

Step 7: Once you're finished rearranging the equations, isolating variables, and showing your work, you'll have a formula with which to rate how well or poorly a date has gone. Of course, you might have to carry around a timer and a pad with you to take notes, but trust us: it'll all be worth it.