# Using Technology with Normal Model

## Objective

SWBAT use a graphing calculator to determine population percentages and percentile values for a normal distribution.

#### Big Idea

The Empirical Rule helps us know the percent of values that are one or two standard deviations from the mean, but what do we do for 1.33 SDs?

## Warm-Up

15 minutes

While I circulate around the room checking homework and scoring it with the homework rubric, students practice using their calculator to produce graphs of data. Warm-Up Describe Univariate Distributions asks students to create graphs on the calculator, describe univariate distributions and compare two distributions.

## Direct Instruction in Using the Graphing Calculator

20 minutes

I use the presentation Normal Distribution with Tech to show my students why we need more than the Empirical Rule, and to teach them how to use the graphing calculator to find population percentages and percentile values.

My goal is for students to understand that the Empirical Rule is great for making predictions about values that are a whole number of standard deviations from the mean, but that the graphing calculator or other tech tool allows us more flexibility.

## Practice Activity: Using the Graphing Calculator with the Normal Model

45 minutes

After my students have learned the procedures for calculating population percentages and percentile values using the graphing calculator, I have them work in their table groups (usually groups of four) to complete Normal Probability Match.  This is a set of cards with a set of normal distribution questions on the front of the cards and a set of answers on the back.  The answer on the back is for a question other than the one on the opposite side. Students will need to use the graphing calculator to answer these questions [MP5].

Students start by putting all cards face down (answers showing) on the table.  They turn one over and determine the answer to the question.  They then look for this answer amongst all the cards on the desk.  When they find the answer they turn that card over and repeat the process.  If they answer correctly, they are able to turn all the cards over and end with the card they started with.

As students work I circulate around the room, using the 3 Cup System to determine where my help is needed [MP1].

## Assignment

10 minutes

In preparation for the next day's lesson, I ask my students to collect some data at home.  I show them my "special coin" that my husband brought me back from Papua New Guinea.  I tell them that it is special because it lands on heads more often than it lands on tails.  We discuss how I could prove to them that my coin is special.  I ask them if flipping the coin 100 times and landing on heads 60 times would convince them.  We continue this discussion and I tell them that for homework I want each student to flip a fair coin 100 times TWICE and come to class with the number of heads they got.  The following day we will make a dot plot of these numbers to try to get a good idea of the number of heads that would surprise them.

The idea behind this activity is to help my students understand the nature of a hypothesis test.  Comparing what actually happens with what we expect to happen with a fair coin is the basis of the hypothesis tests that students will study in formal statistics.