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# Analyzing Linear Practice Data with Center and Spread

Lesson 9 of 20

## Objective: SWBAT interpret differences in center and spread for three different data sets.

**Opener**

Two days ago, students made predictions about how they would fare on Linear Practice #3 (LP3), before having one more go at that challenge. When today's class opens, I present each class with their real results from that third and final trial, and instruct students to construct a box plot of the data. Students should be able to sketch this final box plot on their Comparing Box Plots handout from two days earlier, and to compare the real data to the predictions they made then. Engagement is high as students complete this task, because the data comes directly from within the class and because kids want to see how well their predictions held up.

We have some fun as I ask, "How did we do?" I mean this question is both ways: how did everyone fare on LP3, and how accurate were the predictions made by students? Just like that, we're comparing box plots, and interpreting the data!

**Notes**

When students are done constructing their box plots, I spend a few minutes talking about representations of data on the number line. I start with measures of center. "What are the three measures of center?" I ask, and noting how quickly and comfortably students can answer this question, I ask which of the three we can see on a box plot. In this particular representation, of course, we can see the median but not the mode or mean. If students are confident with what we've done so far today, I might ask them to calculate the mean of the LP3 scores, and then to plot a point representing the mean on their box plots, which can lead to a discussion of how we might intuitively estimate where the mean falls in a data set.

Each of the three types of stat plots we're currently studying - box plots, dot plots, and histograms - have strengths and weaknesses relative to each other. I want this conversation to move in that direction, but I also want students be the ones having such ideas.

After discussing center, we move on to spread. I ask students to name the two measures of spread that we're studying here - range and IQR - and then to show how these two measures appear on a box plot.

On the flip side of the Comparing Box Plots handout, students can record the center and shape for each data set. They should have done this for Linear Practice trials #1 and #2 in a previous class, so now they can record the data for LP3. As this happens, I again reiterate that the mean and mode are not visible in the box plots on the front of this page. The data is displayed at the front of the room however, so students should be able to make these calculations.

You'll also notice that I've left room for shape at the bottom of this handout. If there is a critical mass of curious students, I'll address this topic, but this year I let it slide in most of my classes. I've chosen instead to stick to the intuition available when we compare and interpret differences between center and spread, and to give shape a passing treatment for now.

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Now we step back from the curriculum for a few moments to celebrate successes and build some community. First, I give some "data driven shout outs". As shown on these slides, I recognize students who improved the most from Linear Practice #2 to Linear Practice #3, and to the students who got the most work done on yesterday's Delta Math assignments. I'm emphasizing improvement and hard work, and as a result, there are students in every class who get a shout out even though they're not the type to usually earn such recognition, and this goes a long way toward building community. I can count on kids wanting to take pictures of their name on the board, so they can go home and share that success.

Next, we choose a mascot. One of the questions on yesterday's survey asked students to suggest a mascot for their class. I post a list of all student responses, and then run a few rounds of voting until we've identified a winner. It's lighthearted and fun. One of my favorite constructs is to ask the class if they'd "really like to be known as __________________," and I fill in the blank with the most absurd option.

Once the kids make their choice, it gives me another way to refer to a class. Moving forward it's so much more fun to greet my "Ninjas" every morning than "Period 1 Algebra".

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#### Data Preview!

*13 min*

Depending on how quickly we move through the first two parts of today's class, we might have a little time to take a peek at some of the data sets from yesterday's Stats Survey.

Kids are usually excited to see the data from yesterday's survey, and often the first few sections of today's lesson can pass pretty quickly. So in my back pocket I've prepared some results from yesterday's survey for our perusal.

If it's an especially task oriented class, I ask kids to make a dot plot of one of these sets. If they like to shoot the breeze and talk about ideas, then I just post each for a few minutes and we chat about what we see. I find that it helps to mix the pace once in a while, and today's loose, Friday agenda serves to build an upbeat culture that we can maintain no matter how hard we have to work.

#### Resources

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- UNIT 1: Number Tricks, Patterns, and Abstractions
- UNIT 2: The Number Line Project
- UNIT 3: Solving Linear Equations
- UNIT 4: Creating Linear Equations
- UNIT 5: Statistics
- UNIT 6: Mini Unit: Patterns, Programs, and Math Without Words
- UNIT 7: Lines
- UNIT 8: Linear and Exponential Functions
- UNIT 9: Systems of Equations
- UNIT 10: Quadratic Functions
- UNIT 11: Functions and Modeling

- LESSON 1: The Game of Greed and an Intro to Statistics
- LESSON 2: Creating Box Plots and Generating Data
- LESSON 3: Introducing Delta Math and Getting Better at Solving Equations
- LESSON 4: Data and Plots on the Number Line
- LESSON 5: Making Data to Fit a Representation
- LESSON 6: Jigsaw: Histograms With Differently Sized Bins
- LESSON 7: Comparing Box Plots and Making Predictions
- LESSON 8: Generating Data and Stats Practice
- LESSON 9: Analyzing Linear Practice Data with Center and Spread
- LESSON 10: Group Quiz: Plots on the Real Number Line
- LESSON 11: Problem Set: Texting vs. Social Media
- LESSON 12: Background Knowledge: Percentages and Practice
- LESSON 13: Where Does My Stuff Come From? Part 2: Organizing Data
- LESSON 14: Where Does My Stuff Come From? Part 3: Two Way Frequency Tables
- LESSON 15: Social Media Problem Set #2
- LESSON 16: Where Does My Stuff Come From? Part 4: U.S. Trade Data
- LESSON 17: Where Does My Stuff Come From? Part 5
- LESSON 18: Where Does My Stuff Come From? Part 5, Day 2
- LESSON 19: Writing Prompt Assessment: Which Basketball Player Would You Choose?
- LESSON 20: Unit 2 Exam