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.
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.
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.
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.