## Problem- Square Root verse Absolute Value - Section 2: Standard Deviation

# A New Way To Measure Spread- Standard Deviation

Lesson 3 of 6

## Objective: Students will be able to find the standard deviation of a population or a sample of a population.

#### Warm Up and Homework Check

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Standard Deviation asks students to evaluate whether the mean, median or mode is the most appropriate measure of center. This is a direct introduction into the day's lesson.

I also use this time to correct and record the previous day's Homework.

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#### Standard Deviation

*35 min*

My goal for this lesson is to re-access my students' prior knowledge on basic statistics and then extend into standard deviation. The first Task gives the last five test scores for three separate students. I ask them to identify the statistical information that can be used to compare the test scores. My goal is that they come up with the mean, median, mode, range, and inter-quartile range. I have set up these data sets so that the mean and median are identical on all three. The students will see the need for another way to compare the data. The inter-quartile range is informative, but it only gives a certain picture of how the data is spread. Here is where I introduce standard deviation as a new measure of spread.

I then demonstrate the method of finding standard deviation with a simple set of data about number of Pets. Please watch my Video Narrative explaining how I maximize student thinking during a demonstration. We then formalize the formulas for finding standard deviation for both a population and a sample.

Next, I give them some experience finding standard deviation using the original test samples from the beginning of the lesson.

Students often wonder why the square and square root are used when the absolute value seems more intuitive. I pose this question to the students if they haven't already asked it. After they have discussed it with their partner, I offer a Problem that demonstrates the effectiveness of square roots verses absolute value (**Math Practice 7**). My example was based on the a wonderful example from the website Math Is Fun.

The final task uses data gathered from the class. This type of problem is very powerful in getting student buy-in as well as to increasing engagement.

Detailed presentation notes are located in the PowerPoint.

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#### Exit Ticket

*5 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to find the standard deviation of a data set.

#### Resources

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This assignment allows students to practice finding the standard deviation. They find the standard deviation of a population and then for two samples from another population. They compare and contrast the results of the two samples (**Math Practice 3**).

The problems on this assignments were adapted from a great problem from the CK12 website. This website offers amazing online textbooks for mathematics.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review