##
* *Reflection: Real World Applications
Playing with Measures of Central Tendency - Section 4: Closure and Ticket to Go

In addition to the closure, I wanted to see if students could apply what they had learned about the mean to a new situation. I told students that a student in math class had an average of a 70% as his grade. I asked for a volunteer to explain what it meant to have an average of 70%. I wanted to make sure that students understood the process of calculating the mean.

Then I presented three situations: a) on the next test this student gets a 90%, or b) on the next test this student gets a 75%, or c) on the next test the student receives a 65%. For each situation I asked students to predict whether the new test grade would cause the mean to increase, decrease, or stay the same. I had students use their thumbs to express their opinion. Students were engaging in **MP2: Reason abstractly and quantitatively **and **MP8: Look for and express regularity in repeated reasoning.** After students expressed their opinions I called on a few students to explain their reasoning. I wanted students to connect with their work during the lesson to realize how the mean would change when there is a new value added to the data set.

*How will it affect the mean?*

*Real World Applications: How will it affect the mean?*

# Playing with Measures of Central Tendency

Lesson 11 of 22

## Objective: SWBAT: • Calculate the mode, mean, and median of a data set. • Make a prediction of how a new value will affect the mean, median, and mode. • Explain how a new value in a data set will affect the mean, median, and mode.

## Big Idea: What will happen to the mode, median, and mean of data set when you add a new value? Students work to make predictions and understand how new data will affect measures of central tendency.

*50 minutes*

#### Do Now

*8 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to analyze a line graph in order to answer questions. Scholastic News has a 5^{th}-6^{th} grade edition that typically includes a graph on its back page.

I ask for students to share their thinking. I am interested to hear about the strategies students used to determine the answer to question 3. I ask students what we should get when we add up all parts of a circle graph. I want students to understand that the entire circle graph represents 100%. I also want students to realize that this circle graph is not accurate because the sum of all of the pieces is 99%. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others**.

*expand content*

#### Review

*8 min*

I have students work in partners to complete this review from the previous lesson. The most common mistakes I see are that students confuse the median, mean, and mode. I want to make sure students understand what each term means and how to find it. Another common mistake is that students divide the new sum by 5 rather than 6.

Problem two gets to the big idea of this lesson. It is important that before calculating the changes, students make predictions. I ask students to share out their findings for problem 1 and 2. I ask students:

- Why did the mode and the median stay the same?
- Why did the mean change?

I want students to understand that the mode stayed the same, since $3 is still the value that occurs most often. The median stayed the same, since $3 is still in the middle. The mean increased because we added a game that was more money. Our new sum was $30, and we divide it by 6 since there are now 6 games. Some students may not see this pattern yet, and that is okay. I want students to start to recognize and anticipate how changes will affect the mode, median, and mean of a data set during their group work.

#### Resources

*expand content*

#### Buying Games

*22 min*

**Notes:**

- Before this lesson, I use the exit tickets from the previous lesson to
**Create Homogeneous**groups of 3-4 students. - I copy sheets A-E and place them in the back of the room.
- Each group also gets a
**Group Work Rubric.** - I create and
**Post a Key.**

Students move into groups and I pass out materials. We work together to calculate the mean, median, and mode of the six games. I have a volunteer read the directions for the groups. I make sure that students understand that with each new problem, they are starting with the original set of six games and making a change.

Students work in their groups while I walk around to monitor student progress and behavior. Students are engaging in **MP2: Reason abstractly and quantitatively, MP6: Attend to precision, **and** MP8: Look for and express regularity in repeated reasoning.**

If students are struggling, I may ask them one or more of the following questions:

- How do you calculate the mode/median/mean?
- What do you think will happen with this new piece of information? Why?
- How did your prediction compare with the new mode, median, mean? Why is this?

If students are on track and need some extension I may ask them one or more of the following questions?

- What will happen if you add another game that is more than the original mean? Prove it.
- What will happen if you add another game that is less than the original mean? Prove it.
- What will happen if you add another game that is the same price as the original mean? Prove it.

When students finish a page, I quickly check in with them. If they are on track, I let them use the key to check their work and move on. If groups complete all of this work, they can work on the challenge problems.

*expand content*

#### Closure and Ticket to Go

*12 min*

I ask students to share what patterns they noticed when they added a new game to the original six games. Students participate in a **Think Pair Share**. I want students to be able to anticipate how a new piece of information will affect the mode, median, and mean of a data set. Students are participating in **MP3: Construct viable arguments and critique the reasoning of others **and** MP8: Look for and express regularity in repeated reasoning**.

If I have time I ask students, “What if we add one game to the original set and the new game causes the mean to change from $7 to $8. How much did the new game cost?” Students participate in a **Think Pair Share**. I am interested to see the strategies students use. Students should be able to understand that the new game must be more than the original mean of $7. Some students may guess and check. Other students may work backwards and realize that the sum of the 7 games must equal $56, since 56 divided by 7 equals $8.

I pass out the **Ticket to Go **and the **Homework.**

*expand content*

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: 100 Students Project: What If The World Were 100 People?
- LESSON 2: 100 Students Project: What do we want to know about our students?
- LESSON 3: 100 Students Project: Revising Questions & Planning the Survey
- LESSON 4: 100 Students Project: Conducting the Survey
- LESSON 5: 100 Students Project: Tallying Data and Brainstorming about Presentations
- LESSON 6: 100 Students Project: Analyzing Survey Results
- LESSON 7: 100 Students Project: Presenting Your Findings
- LESSON 8: 100 Students Project: Project Reflection
- LESSON 9: Median, Mode, and Range
- LESSON 10: Mean
- LESSON 11: Playing with Measures of Central Tendency
- LESSON 12: Choosing the Best Measure of Center
- LESSON 13: Show what you know
- LESSON 14: Introduction to Box Plots
- LESSON 15: Box Plots and Interquartile Range
- LESSON 16: Arm Span Day 1
- LESSON 17: Arm Span Day 2
- LESSON 18: Mean Absolute Deviation
- LESSON 19: Comparing Mean Absolute Deviation
- LESSON 20: Selecting Measures of Center and Variability
- LESSON 21: Statistics Jeopardy
- LESSON 22: Unit Test