##
* *Reflection: Discourse and Questioning
What's Your Frequency? Analyzing and Creating Frequency Tables and Line Plots - Section 1: DO NOW

Before the students started working independently on the Do NOW, I wanted to hear from them to get a clear understanding of what they know and how they bring it all together. So I decided to use a "popcorn" style of answer questions and asking quesitons to get more of the students talking about the measures of central tendency. Here's how it worked. I asked the students to think about the mean. I gave them 10 seconds of think time. Then I told them that they could start whenenver they were ready. They were allowed to say one sentence about what they know about the mean. Once they said their one statement, they had to "send it" to someone else even if that person did not have their hand raised. I facilitated the conversation, but did not get involved in the discussion unless they said something completely wrong. I encouraged students to use their sentence stems: I agree, I disagree, I want to build upon or I want to clarify. This was a big success! More students got to participate and as we covered all the components, I would have the last student summarize what was said. This way they had to pay attention to the conversation. We did this for all measures: mean, median and mode.

Here's what I heard (and wanted to hear!)

Mean: measure of center, add up all of the data values and divide by how many values you have, most affected if there is an outlier, and the value of the mean stands for everyone getting the same amount

Median: measure of center, middle number when the data is arranged small to large, you cross off in pairs from small to large, not affected by an outlier because we get rid of it right away with the crossing off, and it means that 50% of the observations are on one side and 50% on the other side. Additionally, they said that you can only have one median so if you are left with two numbers you have to find the mean of those numbers in order to find the median.

Mode: measure of center, occurs most often, you can have one mode, no mode or more than one mode, not affected by the outlier, and you can't use zero for a mode because zero is a numerical value.

After we spoke about the mode, I asked the students a real life question. "When would someone in the real world want to use the mode over the other measures of center?" Again, I was impressed with their responses.

Examples,

Competing restaurants would use the mode because they may want to count #'s of customers

Television stations use the mode to see which shows are watched the most.

Apparell stores use mode to find out which brands are sold the most.

We had some really good discussion about Sweeps week in TV. I enjoyed their insight and they were able to apply this to their own lives all while deepen their understanding of the uses of the measures of central tendency.

*Hearing their side....*

*Discourse and Questioning: Hearing their side....*

# What's Your Frequency? Analyzing and Creating Frequency Tables and Line Plots

Lesson 6 of 23

## Objective: The students will be looking at data to create, analyze and describe frequency tables and line plots (dot plots).

## Big Idea: The students will be working with frequency tables and turning them in to line plots. They will be describing the data and making observations from the tables.

*80 minutes*

#### DO NOW

*10 min*

*DO NOW:*

The beginning part of this lesson is applying their knowledge of the measures of central tendency. I choose this problem because I wanted to see what students could identify that the mean would be most affected by the outlier without having to calculate out the measures. Students who know the mean is most affected by the outlier understand that when you have a number that is far away from the other data values it will affect the mean the most. These students will not have to use the mean algorithm with and without the data value to understand the concept. A good way to get students talking about this is to do a partner share. (It may not always work on nicely for pairs) Have students that did not have to do any calculations partner up with students that needed to do the calculations for mean. This is a good way to let the high achieving students share their knowledge and understanding.

*expand content*

#### Analyzing Frequency Tables

*55 min*

The lesson middle focuses on direct guided instruction. Students will be looking at frequency tables with a variety of data (both numerical and categorical). They will be required to create their own frequency tables using intervals. Additionally, it will be important to address a few questions to relate this to 6.SP.B.5

- Students should be able to report how many people were surveyed
- Students should be able to describe the data (shape, center, and spread)
- To challenge, have students find the mean, median, mode and range of the data from the line plot

The student will work through a few tables and graphs with the teacher and then they will be given two opportunities to create and analyze on their own. During this time, the teacher’s role is a facilitator. Allow students to work on their own or solicit the help of other students. To check for understanding, it may be beneficial to have students report back their findings to the group (team check) or to the whole class. When team checking, remind students to incorporate speaking and listening strategies, to use mathematical language **(SMP6) **and to support their answer with a reasonable argument **(SMP3)**

After students have completed creating their tables, have them work on the final two questions in the power point. This can be shared as whole group or in partners or use **think-pair-share** to get more thoughtful responses.

Question 1: Students should be able to say that there cannot be an overlap of numbers when using intervals. Intervals need to be equal too

Question 2: Students should see that Caleb did not read the plot correctly. The numbers on the number line indicate the ages of campers and the x’s indicate how many campers. Caleb read the line plot incorrectly.

*expand content*

#### Closure

*15 min*

Before starting on the TV worksheet, ask the students the following questions to assess understanding of the learning objective. Questions will be discussed whole group.

- What components need to be in a frequency table (category, tally, frequency, and title)
- Could you find the mean, median, mode and range from a frequency table?
- When using intervals, explain what that would look like?
- What can’t you determine when using intervals?
- What components are in a line plot? (number line, x’s or dots, title)
**Can you find the mean, median, mode and range in a line plot?**- Can you tell how many people were surveyed in a line plot or frequency table?
- How are a line plot and frequency table alike?

**Question #6:** There is a common misconception when working with line plots and finding the mean. Students have difficulty making the connection that the amount of x’s indicates the frequency of the event happening. Hit this question hard. Get kids to tell you how to find the mean (add up all of the data and divide by how many) then tell them to think about a line plot (what do the x’s represent). So, if we want to find the mean, how would that look when writing it out? Also, ask the students if there is a large number of data values, can we simplify the amount of information going in to the calculator? My students want to put every number in the calculator and they run out of space. We talk about trying to simplify our calculations. I ask them how to simplify repeated addition, looking to get them to say multiplication. So some students will write the value amount of the data above the x’s and then put that in the calculator.

**(TV watching, Navigating though Data Analysis in Grades 6 – 9, NCTM)**

Allow students time to work on the TV watching worksheet. This is an application problem that involves components learned thus far. If students do not finish, they may take it home to complete.

If they are done, have the students compare answers with a partner or discuss whole group. This could also be done as the DO NOW for the next day.

*expand content*

The margins somehow got shifted and make this pdf document impossible to copy. I like this lesson, if it could be fixed, great! Thanks.

Joy Kovnat

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- LESSON 1: Statistically Speaking....
- LESSON 2: What Does the Data Tell Us? Describing Data
- LESSON 3: Describing Data Activity
- LESSON 4: Analyze this! Mean Median Mode and Range
- LESSON 5: Analyze This Part 2!
- LESSON 6: What's Your Frequency? Analyzing and Creating Frequency Tables and Line Plots
- LESSON 7: Line Plot Activity
- LESSON 8: Box and Whiskers... Analyzing and Creating
- LESSON 9: Box and Whiskers Activity
- LESSON 10: Hilarious Histograms. Analzying and Creating
- LESSON 11: Histogram activity
- LESSON 12: Mean absolute deviation. What does it mean?
- LESSON 13: What's in your name?
- LESSON 14: Misleading_Leading_Graphs
- LESSON 15: Say it with Stats! Review
- LESSON 16: Bar none. Analyzing and creating bar graphs
- LESSON 17: Bar Graph Activity
- LESSON 18: Analyzing and Creating Circle Graphs
- LESSON 19: Circle Graph Activity
- LESSON 20: Line me up. Analzying and Creating Line Graphs
- LESSON 21: Line Graph Activity
- LESSON 22: Places Everyone. Analyzing and Creating Stem and Leaf Plots.
- LESSON 23: Stem and Leaf Plots_Activity