##
* *Reflection: Grappling with Complexity
What's the Frequency Kenneth? Summarizing Data with Frequency Tables - Section 4: Our City Statistics Project + Homework - Creating Frequency Tables

When creating frequency tables (**Student Work 1 Frequency Table **and **Student Work 2 Frequency Table**), many groups had a difficult time initiating the task. They were confused about the different types of frequencies and how to apply these ideas to their group projects. As a way to help them grapple with this complex task, I encouraged students to look back at their notes and to use them as a tool to better understand the material.

When given the time to look though, re-process and apply their notes, students did tend to work better and were able to complete the task of developing a frequency table for their associated research question and data.

Technology also helped with this task. Using a word processor or spreadsheet application helped many groups easily create a table and organize their visual space to be able to focus on the math and to create their frequency table. I was pleased with the end results of this aspect of the project.

*Grappling with Complexity: Frequency Tables and Complexity*

# What's the Frequency Kenneth? Summarizing Data with Frequency Tables

Lesson 6 of 10

## Objective: SWBAT interpret and create frequency tables in context, including joint, marginal and conditional relative frequencies.

## Big Idea: Students will answer REM’s question by creating and interpreting frequency tables as another tool to organize and understand data!

*95 minutes*

#### Entry Ticket

*10 min*

Student will complete an entry ticket where they have to complete a free write (**Entry Ticket: What's the Frequency (Table) Kenneth?**) to elicit their understanding of the term “frequency.”

I will play REM’s song "What’s the Frequency Kenneth?” during the entry ticket. (I find that playing music in my classroom at a low level during independent work tends to help students focus.)

After a few minutes of independent work, I have students **Turn and Talk ** with a partner and then have each pair share their ideas with the class.

This entry ticket provides a good opportunity for all students to engage and participate in the conversation as it asks for their perspective on a vocabulary term and they can bring in different representations of the word that may help their peers better understand the term and main idea of the lesson.

**Academic Vocabulary:**

**Frequency**

**Relative frequency**

**Marginal frequency**

**Joint frequency**

**Conditional frequency**

*Note: place academic vocabulary on word wall as a strategy to assist students in learning academic vocabulary.

** **

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After the entry ticket, I will review a Powerpoint presentation on frequency tables (**PowerPoint: Frequency Tables**). After completing examples with students, I ask my students to complete a number of **Turn and Talks ** (see strategy folder for more information).

During this time students are actively engaged in the discussion, taking **Two Column Notes **and interacting with the material through the language domains of listening, reading, speaking and writing.

#### Resources

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After reviewing examples, I have students complete the **Collaborative Work and/or Exit Ticket: What's the Frequency (Table) Kenneth?** independently to assess their understanding of the day’s lesson.

Alternatively, the assignment can be utilized as group work. This provides students with another opportunity to work collaboratively in a small group setting on the day's learning objectives.

This particular ticket to leave asks students to differentiate and identify the appropriate type of relative frequency used to create the table/survey on Pepsi and Coca-Cola and focuses on the Math Practice standard **MP.6 **as students must tend to precision in order to interpret the table correctly.

In addition, students are asked to organize their ideas and write a well developed paragraph. See the strategy folder for more information on the **Idea Organizer **and **Writing in Math**.

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To conclude today's lesson I have students work in groups on their collaborative project: **Our City Statistics Project Overview**

For more information on the project assignment and expectations, see the **Project: Our City Statistics Assignment Sheet.**

For this particular working session of the project, I recommend that students work on creating a frequency table that is part of the requirements of the group project. To facilitate this process, I ask students to think about their data and decide what type of frequency table would best communicate their research findings to other people. I give each group about 5 minutes to discuss this. Each group then identifies what type of frequency table they are going to create and, more importantly why. Having each group share focuses on MP.3 as students are asked to navigate a group setting and work collaboratively to create and critique mathematical decisions and arguments. It would be helpful to be bale to let each group use one computer to create the frequency table.

As an alternative each group can make a table by hand and them assign one person in the group to type up the table at home (and that person could get a homework pass for the night’s homework in exchange for the group work). In this way, students are offered an opportunity to independently practice the day’s concepts in a meaningful context (group project).

For homework, students create a frequency table and respond to the following prompt: 1. Create a raw and relative frequency table for the vowels and consonants (and total letters) in your name and for the letters in the name of a friend or family member. 2. Identify the marginal, joint and conditional frequencies in the tables. This homework assignment makes the concept relevant to each student, provides some flexibility and also assesses student understanding of the material. For the relative frequency I look to see if students include an explanation of what the frequencies are relative to (type of letter, person, or total). The assignment also ties nicely into Math Practice standard MP.8 as the homework asks students to look for regularity in repeated reasoning when working with frequency tables.

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
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- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Our City Statistics Project and Assessment
- LESSON 2: Correlation and Causation
- LESSON 3: Estimating Population Percentages - It is all normal
- LESSON 4: Summing it Up: Dot Plots, Histograms and Box Plots
- LESSON 5: Making Relevant Comparisons: Comparing Populations
- LESSON 6: What's the Frequency Kenneth? Summarizing Data with Frequency Tables
- LESSON 7: Cinderella's Slipper: Scatterplots, Residuals and Goodness of Fit
- LESSON 8: How does this fit? CalculatingCorrelation
- LESSON 9: What does it mean? Interpreting linear models
- LESSON 10: Outliers and Outsiders: The Impact on Data