What's My Rule?

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SWBAT to assign a rule/equation to given a table of data.

Big Idea

Looking for patterns is just the start of this wonderful activity that helps students begin to see relationships in given data sets and express those relationships as equations or rules.

Warm Up

5 minutes

For Warm Up today, I have selected several problems that require students to apply previously learned rules of exponents. Negative exponents continue to confuse students, so I intentionally bring them back at least once a week.  I also included two problems that involve computations with scientific notation.  By providing spiral review of these problems, students gain confidence in their probelm-solving abilities.

What is a function?

7 minutes

Understanding a function is the main idea of this entire unit, so I want to give focus to this key academic vocabulary.  I provide the definition of a function for students to include in their journal.  I then go on to show an example and a non-example of a function (represented by two different  data sets) so that students have a visual representation of the definition.  Although the students can easily identify the non-function having a double input value, it is not until I plot the points on the graph that they see it graphically.  I briefly mention the vertical line test and show how the non-function does not pass the test.  I will address the vertical line test again later in the unit, so I don't spend time practicing it in this lesson.

Let's Play: What's My Rule?

24 minutes

Next, I introduce today's activity, a game called "What's My Rule?".  I reveal a table of values in which I have shaded the y-values from student view.  I explain that for each input, something is going to happen to change the number.  Their job is to figure out what is happening based on the y-value (output) numbers.  I explain the rules of the game:  First, no one can call out the rule.  They can only say the word "rule" at which point I will call on them to tell me the next output.  After they call the output, I reveal it.  If they are correct, I tell them they have the rule. If they are incorrect, I encourage them to keep thinking. I continue with other students until we have revealed the entire chart.  I then ask for a volunteer to give me the rule.

The rules for the first four data tables are very simple and student confidence builds quickly. Then, I reveal table #5, which has a two-step rule applied.  This stumps students for a bit, but eventually someone calls, "rule", so we test their idea. 

If students get stumped, I explain that sometimes, a rule has two steps, like a two-step equation.  This generally gets students headed in the right direction. 

Closure: Ticket Out the Door

6 minutes

For closure, I want students to create their own rule and then fill in a corresponding t-table.  I distribute note cards and tell them to create a rule in slope-intercept form on the front and a table of values for that rule on the back.  I model an example on the smartboard so they know what to do.  As they leave class, I collect these cards. My plan is to use them in the next day's lesson.