March 21, 2012

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Unit 3 Descriptive Statistics The first four lessons (3.1-3.4) provide the instruction and practice that supports the culminating activity in the final unit project.

Lesson 3.3 Interpret Linear Models

- Mathematics > General
- Mathematics > Algebra

- Grade 6
- Grade 7
- Grade 8

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**Standard Clusters**

1. Summarize, represent, and interpret data on a single count or measurement variable. (Common Core Standards: S.ID.1, S.ID.2, S.ID.3)

2. Summarize, represent, and interpret data on two categorical and quantitative variables. (Common Core Standards: S.ID.5, S.ID.6)

3. Interpret linear models. (Common Core Standards: S.ID.7, S.ID.8, S.ID.9)

**Teacher Resource Materials:**

- Statistics (Sal Kahn video)
- Linear Equations (Sal Kahn video series)
- Predicting with Linear Models (Sal Kahn Video)
- Topic 3: Linear Regression (Extension Activity)
- Linear Equations in the Real World (Extension Activity)
- Linear Modeling – Modeling CO2 Levels (Extension Activity)
- Website for sports data: http://www.amstat.org/sections/SIS/Sports%20Data%20Resources/
- http://mlb.mlb.com/index.jsp/

- Lesson 1: Linear Models (lesson)
- MLB 2011 Regular Season Data (Word version or Excel version)
- Vocabulary Page (complete)

**Instructional Materials for Students (Print one copy for each student)**

- Vocabulary Page (blank)
- Linear Models Check-Up (Assessment)
- MLB 2011 Regular Season Data
- Homework (one per student)

**Time: **50-minutes session

**Lesson Objective:**

**Students will:**

· Use linear models to interpret data.

**Lesson Content**

1. Background Building Activity for Students (5 minutes)

a) Vocabulary Building:

Print out one copy of the Vocabulary Page (blank) for each student. Review the descriptive statistics vocabulary words with the whole class prior to the warm-up problem. Students will create their own definitions including a visual representation.

b) Warm-Up problem:

Display the MLB 2011 Regular Season Data table on the overhead or chalkboard and provide each group with a hard copy.

Ask students to write 3 observations about the data (encourage them to use what they learned in the previous lessons, i.e. mean, median, mode and range).

c) Discuss:

What observations can be made when given data like this? Students should be able to compute mean, median, mode, and range of any of the columns. (Note: the data is just the top 50 hitters for 2011; additional data can be found at http://mlb.mlb.com/stats/

2. Focus Question based on today’s lesson (25 minutes)

Today’s focus question (write it on the board)

*What real-world data can be represented using a linear model? *

a) Whole group presentation and class discussion: Often there is a relationship between data values. Students will continue to explore the 2011 Regular Season data. Ask students to suggest what data may be related. Lead students to consider the relationship between:

- Homeruns and RBI’s
- Games played and hits
- Strike outs and at bats

Explain that plotting the data in a scatter plot can lead to a linear relationship. Once the line has been identified, an equation can be found. This model can then be used to summarize the relationship, and then predict other data points.

b) Small Group Activity (Teacher observes students while they work to check for understanding.)

Ask students to form groups of 3 students (a group of two will work as well). Provide each group with 2011 Regular Season Data and ask students to choose two quantities to compare. Students will graph the data and determine if there is a linear relationship. (Does the data seem to fall along a ‘line’?) Students draw the best-fit line through the data. Using the y = mx + b (where m = slope and b = y-intercept), student groups write the equation of the line.

Note: If the data does not appear to have a correlation, ask the group to choose different quantities to compare.

While the students are working, the teacher checks for understanding by observing students while they are working in small groups.

c) Individual Activity:

After students have discovered the linear equations that represent the given relationship, ask students to make a prediction based on the line.

For example: If the relationship homeruns and RBI’s appeared to be linear, the student could predict the number of RBI’s for a player hitting a given number of homeruns. (If player “x” hits 12 homeruns in the season, he will have 8 RBI’s)

3. Whole class discussion (10 minutes)

a) Students share equations and predictions with the rest of the class. Students can challenge each other to make additional predictions based on the linear equations.

b) Algorithm:

- Plot the points on a coordinate grid (the independent variable is on the x-axis and the dependent variable is on the y-axis)
- Draw a best-fit line through the data points
- Identify the y-intercept (point where the line crosses the y-axis)
- Identify the slope: find to points on the line; use the equation slope is the difference in the y-values divided by the difference in x-values.

The equation for the line is y = mx + b, where m = slope and b = y-intercept

4. Assessment Activity (5 minutes)

Provide each student with a copy of the Linear Model Check-Up. Allow time to for students to complete the assessment. Assess understanding by checking student responses. Graphs and equations may vary slightly as students draw the best-fit curve. Accept any answers that are reasonable.

5. Extension Activities:

Topic 3: Linear Regression Students have the opportunity to create and conduct a market research survey. Students will also investigate the concept of linear regression using a mathematical model.

Linear Equations in the Real World Students will write linear models to represent the population growth in California; they will write an equation that models Hooke’s law and find an equation that helps calculate the shipping charged by a company.

Linear Modeling – Modeling CO_{2} Levels Students will explore the levels of carbon dioxide (CO_{2}) in the atmosphere over time.

6. Homework assignment for additional independent practice

Homework – Linear Models Students practice graphing and interpreting data.

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