Experience First

This experience can begin in groups.  They should be able to work through questions 1 through 5 in their groups without much assistance, but walk around to ask them to explain their answers to 3. We want the students to understand that a person can spend any amount of time between 0 minutes and 10 minutes, not including 10, in the restaurant.  It would be impossible to list all possible values between 0 and 10 since any amount of time is an infinite amount.  We will use the number lines in 4 and 5 to visualize interval notation.

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Formalize Later

During the debrief, the distinction between natural numbers, integers, and real numbers will come up.  This is not one of the learning targets for today, but remind the students of the properties of the different groups while walking around during the experience.  They may also need a refresher on how to write compound inequalities (0 < t < 10) in order to understand the algebraic notation.

Use the number line to help the students visualize when to use parentheses in interval notation and when to use bracket.  They should always use parentheses with infinity, since infinity is not an actual number than can be “included.” in an interval.

The symbol for a union of two intervals (U) is necessary in the Check Your Understanding, so give a quick example while filling in the Important Ideas box or help the students with 3c and 3d in the CYU.