Unit Title:Community and Communication 3 Weeks

/ Math
Lesson Plan
Teacher:6th Grade Math Teacher / Grade:6th Math I-A
Lesson Title: Communicating through Statistics
STRANDS
Statistics and Probability
LESSON OVERVIEW / Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
Statistics is a mathematical tool for communicating. Throughout this unit, students will learn how to analyze data and share their findings. This unit makes use of real-life statistics. Students will explore bar graphs, line plots, line graphs, measures of center and measures of variation. The community aspect of statistics will be brought out as we extend statistics to include Social Studies (data about our communities) and Science (data about our habitat), as we display and write a written analyze the data found in the two academic areas in our iBook.
MOTIVATOR / Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
Watch “Why Statistics” video in the Resource Folder. This video compares Statistics to a microscope. This video is motivational because it explains the need for studying statistics and how statistics is used in the real life.
DAY /
Objectives
(I can….) /

Materials & Resources

/

Instructional Procedures

/ Differentiated
Instruction /

Assessment

1 / I can use a sampling to gain information about the population. / Prior to class, collect all the birthdays of all of the students. Just month and date.
Copy of the birthday data for the classes.
Materials for Differentiated Instruction – Remediation:
Allow students to use the links listed in the lesson to create their graphs.
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do use a sampling to gain information about a population? / Differentiated Instruction – Remediation::
Allow students to use the links listed in the lesson to create graphs.
Give the students the data in a frequency table and have them analyze the data.
Differentiated Instruction – Enrichment:
Have students research the difference between bar graphs and histograms. / Formative Assessments: Informal observations
Responses to activities
Ticket Out the Door Responses.
Homework
Performance Assessment:
Graphs created by students
Birthday Bar Graphs
Set: Find examples of different types of graphical representations from the text or newspaper. Display these for students via posters around the room, handouts, or projection. Discuss in general terms how these graphs are used. The following websites allow you to make your own graphs, and some allow you to print.
“Create a Graph”
Shodor Education Foundation
National Library of Virtual Manipulatives:
NCTM Illuminations
Gather real world frequency tables from the newspaper or other sources.
In small groups, pairs, or as a class, discuss each real world frequency table to determine:
What questions can we pose about this data?
What would be appropriate graphical representations for this data?
Teaching Strategy:
  • Hand out copies of the Birthday data collected in a previous class.
  • Allow students time to review the data and answer the following questions:
What questions can we pose about this data?
How should we organize the data?
What would be appropriate graphical representations for this data?
Record the groups’ comments on the board or on poster paper.
  • Suggest that we ask the question: How many students in each homeroom have birthdays in each month of the year? This question will be answered by creating a frequency table, followed by a bar graphto display the data.
  • Explain the similarities and differences among frequency tables, bar graphs and bar graphs. Sources include:
Websites mentioned in the “Hook” section.
A presentation introducing bar graphs and histograms can be found at
“Length of Cats” activity from NCTM Navigating Through Data Analysis in Grades 6-8 for analyzing bar graphs
  • Give the students rulers and graph paper or a copy of the BirthdayActivity graphic organizer. The charts can be done individually, in pairs or in groups. Here is an example of a graphic organizer.

Students use the copied data lists to summarize the data onto the frequency table.
  • From the frequency table, students create a bar graph, including a legend and other appropriate labels.
  • Model the first portion of this graphing activity and then monitor for accuracy as the students work, answering questions and clarifying misconceptions.
Summarizing Strategy:In the last 5 minutes of class, students share what they discovered so far about the birthday statistics of their team.
Assign practice problems for homework.
2 / I can use a sampling to gain information about the population. / Graph Paper
Calculators
Materials for Differentiated Instruction – Remediation:
Allow students to use the links listed in the lesson to create their graphs.
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do use a sampling to gain information about a population? / Prompting
Grouping
Differentiated Instruction – Remediation:: Give students a frequency table and ask the students to analyze the data.
Differentiated Instruction – Enrichment: Have students create circle graphs of the birthday data. / Formative Assessment:
Informal observations
Responses to activities
Ticket Out the Door Responses.
Homework assignment on line plots.
Birthday Line Plots
Set: In small groups, the students discuss how the data for one homeroom compares to the data of the total team.
Teaching Strategy:
  1. Ask the students to think about this question. Is there anyone else in your homeroom that has the same birthday as you? What about on in the 6th grade?
  2. Have students think-pair-share about what the pros and cons are for using a bar graph. Ask students to suggest other ways that we might be able to display this data. Have them discuss and research other ways to display this data.
  3. Turn the discussion around to a line plot. Model for the students how to create a line plot. After modeling, give the students some data to display in a line plot. Have the students’ compare their line plots to those at their tables.
  4. Have the students put the entire grade level’s birthday data into one line plot.
Summarizing Strategy: Have each student writes a paragraph in his/her journal explaining how the birthday data compares for a homeroom versus the whole 6th grade. Answer the following question in complete sentences: In your opinion, which data representation (frequency table, bar graph or line plot) displays our birthday data the best and why?
Assign practice problems for homework.
3 / I can use a sampling to gain information about the population. / Graph Paper
M&M Snack Pack for each student.
A copy of “It’s in the Bag” for each student (See Resource Folder).
Materials for Differentiated Instruction – Remediation:
Calculator
Materials for Differentiated Instruction – Enrichment:
Compass
Protractor / Essential Question: How do use a sampling to gain information about a population? / Prompting
Grouping
Differentiated Instruction – Remediation:: Allow students to work with one color instead of an entire bag.
Differentiated Instruction – Enrichment: Have students create a circle graph of their data using a compass and a protractor. / Formative Assessment:
Informal observations
Responses to activities
Homework
Ticket Out the Door
Using M&Ms to Model Sampling of a Population
Set: Show the students a video about the M&M factory (See Resource Folder).
Teaching Strategy:
  • Ask students what they know about taking a census for the population for the United States. Discuss the idea of sampling to estimate the size and characteristics of a larger population. Information about the census can be found at A discussion about counting different types of animals in the wild may also be used to introduce the subject of sampling a population.
  • 2. Give each student a small bag of standard M&M’s, about 25 per bag. Handout “It’s in the Bag” to each student (See Resource Folder).
    Variation due to time constraints: To accommodate students who may not be able to complete the task in the allotted amount of time, teachers could have them work with only one color rather than with all six. This reduces the amount of counting needed and may benefit students who need more time to complete the task.
    NOTE: Because of peanut allergies, teachers may want to use Skittles instead of M&M’s. Even plain M&M’s may cause a reaction in cases of severe peanut allergy because they are processed near Peanut M&M’s.
Summarizing Strategy: Ticket Out the Door
The human body has a total of 206 bones. The number of bones on each of the following parts of the body is listed in the following frequency table. Find the % of total bones for each body part.
Types of Human Bones / Number / % of Total
Skull / 29
Spine / 26
Ribs & Breastbone / 25
Shoulders, Arms & Hands / 64
Pelvis, Legs, and Feet / 62
Assign practice problems for homework.
4 / I can identify the center of the data and explain which measure of central tendency is the best of a given set of data. / Mean, Median, and Mode Song (See Resource Folder)
Materials for Differentiated Instruction – Remediation:
Supply students with an advanced organizer to keep track of their notes. (See Resource Folder)
Materials for Differentiated Instruction – Enrichment:
iPad / Essential? What is meant by the center of data set? How is it found and how is it useful when analyzing data? / Differentiated Instruction – Remediation:: Supply students with an advanced organizer to keep track of their notes. (See Resource Folder.)
Differentiated Instruction – Enrichment: Have students research mean, median, and mode in the news. Have them critique the information they find. / Formative Assessments:
Informal observations
Ticket Out the Door
Short homework assignment
Mean, Median, and Mode Jigsaw
Set: Watch the Mean, Median, and Mode Song (See Resource Folder)
Teaching Strategy: Have students Think-Pair-Share on what the center means. Lead a brief discussion on the Measures of Central Tendency.
Explain a Jig-Saw Lesson to the students. Have the students number off at their tables. Group #1 will learn all about mean. Group #2 will learn about median. Group #3 will learn about mode. Have students transition into their learning groups. Their task in their learning groups is to learn all they can about their topic. In particular, they need to learn:
  1. How do you calculate (Mean, Median, Mode)?
  2. What situation would be the best to use (Mean, Median, Mode)?
  3. What situation would not be best to use (Mean, Median, Mode)?
Give the groups enough time to research these questions. Remind students that they will need to be able to go back to their table groups and teach their table all about their subject.
When the groups are ready, send them back to their table to teach each other about their specialized subject. Give students problems to work out on Mean, Median, and Mode as a group. Have them discuss which measure of central tendency is appropriate for each situation.
Summarize: Ticket Out the Door: Describe a situations when the mode is the best measure of central tendency.
Assign practice problems for homework.
5
Project Day 1 – refer to Unit Plan
Topic – iBook Community Guide
6 / I can describe the variation of a set of data. / Calculator
Paper
Pencil
Materials for Differentiated Instruction – Remediation:
Graphic Organizer on Measures of Variation (See Resource Folder)
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do I describe variation of a set of data? / Differentiated Instruction – Remediation: Supply students with an advanced organizer to keep track of their notes.(See Resource Folder)
Differentiated Instruction –Enrichment: Have students research real-world examples of variation. / Formative Assessment:
Informal observations
Responses to activities
Ticket Out the Door Responses.
Measures of Variation
Set: Watch the video on using the Measures of Variation to analyze data (See Resource Folder).
Teaching Strategy:
  • Define measures of variation.
  • Model how to find the measures of variation for the students. Students need to identify the minimum, lower quartile, median, upper quartile, and the interquartile range. After a few modeled examples, guide the students through some examples, and then allow them to collaborate on some examples. Finally, ask them to work out some examples on their own.
  • Model how to find outliers for students. Guide students through a few examples, allow them to do some examples collaboratively, and then do some examples independently.
Summarizing Strategy:
Ticket Out the Door: Have the students compare and contrast the measures of central tendency and the measures of variation. As the students discuss this within their table groups, monitor their discussion for accuracy, answer questions and clarify misconceptions.
7 / I can construct and read a box-and-whisker plot. / Real-World Data for Box-and Whisker Plots
Calculator
Graph Paper
Pencil
Ruler
Materials for Differentiated Instruction – Remediation:
Supply students with an advanced organizer to keep track of their notes. (See Resource Folder)
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do I construct and read a box-and-whisker plot? / Differentiated Instruction – Remediation: Supply students with an advanced organizer to keep track of their notes (See Resource Folder).
Differentiated Instruction – Enrichment: Have students research real-world examples of box-and-whisker plots. / Formative Assessment:
Informal observations
Responses to activities
Ticket Out the Door Responses.
Box-and-Whisker Plots
Set: Show the students the Box and Whisker Plot Video from Khan Academy (See Resource Folder).
Teaching Strategy:
  • Review finding the minimum, lower quartile, median, upper quartile, maximum, and any outliers.
  • Next, model for the students how to create a Box-and-Whisker Plot. Begin with identifying the minimum, lower quartile, median, upper quartile, maximum, and any outliers. Plot these numbers on a number line and connect the dots to create a box-and-whisker plot. Do some examples with and without outliers.
  • After modeling this for the students, guide the students through a few examples. Then have the students work collaboratively to complete a few examples, and finally do a few examples independently.
  • After each example, ask students to discuss what the data means. They will look at the shape of the data, where the lower quartile, median, and upper quartile are.
Summarizing Strategy:
Ticket Out the Door: Give the students a set of data to create a box-and-whisker plot.
Assign practice problems for homework.
8
Project Day 2 – refer to Unit Plan
Topic – iBook
9 / I can choose and create appropriate graphs to represent data. / Graph Paper
Who was the Greatest Yankee Homerun Hitter (See Resource File)
Materials for Differentiated Instruction – Remediation:
Laptop with Excel
Stem and Leaf Plot Advanced Organizer (See Resource Folder)
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do I choose and create appropriate graphs to represent data? / Grouping
Prompting
Differentiated Instruction – Remediation:: Supply students with a Stem and Leaf Advanced Organizer (See Resource Folder).
Cut back the number of baseball players.
Use Excel to create the graphs
Differentiated Instruction – Enrichment: Allow students to research a non-Yankee baseball player and see how they compare. / Formative Assessments
Informal Observations
Tickets Out the Door
Summative Assessment
Performance Assessment:
Students’ Stem and Leaf Plots
Who was the Greatest Yankee Homerun Hitter?—Stem and Leaf Plots
Set: Who do you think is the best player in Major League Baseball? Why do you think that he is the best? What did you base that decision on? (The teacher guides the discussion.)
Teaching Strategy:
  • After asking the Hook questions, show the students the table for the “Who was the Greatest Yankee Homerun Hitter?”(See Resource Folder) task and ask them to skim these records.
  • The students complete part 1 of this task, answering the following questions: Which player appears to be the greatest home run hitter? Why did you choose this player?
  • After the students have written their answers, have the students turn to their tables and discuss their answers and come up with an answer for the table. Finally, have the tables share their answers.
  • Tell the students that we are going to learn about Stem and Leaf Plots today. Have them turn to their table and discuss what a Stem and Leaf plot is. They may research this.
  • Work through some examples for the students. Model for the students, guide the students, and then allow them to work independently.
  • Ask students to create a Stem and Leaf Plot for the baseball players.
Summarizing Strategy: Ticket Out the Door: Have students answer the first essential question. Remind them that the purpose of a stem and leaf plot is to analyze data.