Unit Title:Community and Communication Three Weeks

/ Math
Lesson Plan
Teacher:6th Grade Math Teacher / Grade:6th
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 explain what a statistical question is. / 5 Statistical Questions and 5 Non-Statistical Questions in an envelope for each group. Examples in resource folder.
Materials for Differentiated Instruction – Remediation:
3 Statistical Questions and 3 Non-Statistical Questions in an envelope for each group.
Materials for Differentiated Instruction – Enrichment:
iPad
Paper / Essential Question:
1. What is a statistical question?
2. How does it differ from a non-statistical question? / Prompting
Grouping
Differentiated Instruction – Remediation: Have students sort 3 Statistical and 3 Non-Statistical Question
Reduce the number of questions for the students to put on their posters.
Differentiated Instruction – Enrichment: Have students research the difference between a biased and unbiased question. / Formative Assessment:
Informal observations
Discussion
Ticket Out the Door
Class Discussion
Homework Assignment
Statistical Questions vs. Non-statistical Questions
Set: Ask student to define statistics.
Teaching Strategy:
  • Give the students an envelope that contains 5 statistical questions and 5 non-statistical questions. Ask the to sort the questions into two categories. Do not give students the categories of how you would like them sorted. Their only directions are to sort them into two categories and be able to defend why they made the categories they did. Give the students about 5 minutes to complete this sort with their table group.
  • Share with the students the proper sorting of the questions. Ask them to compare how they sorted them to how they were supposed to be sorted. Ask them to discuss the criteria for the two categories within their table groups.
  • Bring the group back together and discuss what they thought the criteria for each of the categories was. Explain to the students that a statistical question is a question designed to collect data and the data that is collected should vary. This is unlike a question that has a specific answer.
  • Go through the examples of statistical questions from the sort. Explain how each is designed to collect data that varies. These could include:
    How tall are the members of the high school basketball team?
    How old are the members of the city council?
    How many hours do you spend studying each night?
    What are the ethnic backgrounds of the students in my school?
Notice that each question anticipates various answers.
  • Go through the examples of non-statistical questions. These could include:
    What’s the mascot of Dobyns-Bennett High School?
    Who was the first president of the United States of American?
    What day is Halloween?
    Notice that each question anticipates a specific answer.
  • Within their groups, ask students to brainstorm their own statistical questions. Ask the students to come up with 4 statistical questions. Then ask the students to come up with 2 non-statistical questions. When the students have generated their 6 questions, ask them to share their 6 questions with you. They should support their selection of these questions. When their questions have been approved, give each group a piece of chart paper. Ask them to write their questions in any order on a piece of chart paper. Hang the chart paper up when they are done.
  • When everyone is done, ask the students to do a gallery walk and review each of the posters. They are to pick out the four statistical questions.
Summarizing Strategy: Ticket Out the Door: Ask students to explain the difference between a statistical question and a non-statistical question.
Assign practice problems for homework.
Adapted from
Muschla, Gary Robert; Muschla, Judith A.; Muschla, Erin (2012-03-21). Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8 (Jossey-Bass Teacher) (Kindle Locations 1587-1593). John Wiley and Sons. Kindle Edition.
2 / I can display numerical data on a line plot. / Presidential Ages (See Resource Folder)
Graph Paper
Pencil
Paper
Materials for Differentiated Instruction – Remediation:
Graphing Calculator
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do I display numerical data on a line plot? / Grouping
Prompting
Differentiated Instruction – Remediation: Allow students to use a graphing calculator to create their line plots.
Allow students to do a fewer number of presidents, vice-presidents, and first ladies.
Differentiated Instruction –Enrichment: Have students research the ages of the 50 Governors in the United States of America.Are Governors often younger than Presidents? How many of the Presidents of the 20th Century were Governors? / Formative Assessments:
Informal observations
Discussion
Ticket Out the Door
Homework Assignment
The Ages of the Presidents
Set: Dot Plot vs. Line Plot (See Resource Folder)
Teaching Strategy:
  • Ask students about the ages of the oldest and youngest Presidents of United States of America in the 20th century.
  • Have students open the Presidential Ages (See Resource Folder) table on their iPads.
  • Pass out graph paper and have the students draw a horizontal and vertical axis. Explain that we will be making line plots of the data.
  • Have the students look at the data of the Age of the Presidents, and discuss the range of data. What would be appropriate intervals to group the Presidents? You may want to use intervals of 5 years. (40-44, 45-49, 50-54, etc.)
  • Have them mark the vertical axis with intervals of 1. (1, 2, 3, 4 etc.)
  • Be sure the students have labeled their axis and titled their graph.
  • Have them place an “X” in the correct category for each President according to their age.
  • Once the line plot of the President has been completed, ask the students to work in their table groups on the line plot of the Vice-Presidential Ages. Be available to guide the students as needed. Finally, ask the students to complete the First Lady Ages on their own.
  • Have the students compare the 3 line plots. Discuss the similarities and differences. What conclusions can be drawn from the graphs?Overall, are Presidents or Vice- Presidents often older when they are elected to office? What would you consider to answer this question? Discuss how you cam to your conclusions.How do First Ladies compare in age to Presidents and VP’s? Are they often younger or older than the other two groups?Notice the intervals for each graph. Does the fact that the First Ladies have intervals included that are younger than those on the other graphs influence your conclusions? Would the fact that the VP’s have intervals included that are older then the Presidents line plot lead to a conclusion that VP’s are on average older than the Presidents are?
Summarizing Strategy:
Have the students write a paragraph or two discussing their conclusions of the discussion regarding the Presidents and age. Students should use the data and line plots as evidence to support their conclusions. The paragraph should also include a description as to how a line plot is constructed and how the data is organized into intervals.
Assign practice problems for homework.
3 / I can identify the center of the data and explain which measure of central tendency is the best of a given set of data. / Materials for Differentiated Instruction – Remediation:
Supply students with the Mean, Median, and Mode Graphic Organizer to keep track of their notes.
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question:
1. What is meant by the center of data set?
2. How is it found?
3. How is it useful when analyzing data? / Differentiated Instruction –Remediation: Supply students with the Mean, Median, and Mode Graphic Organizer to keep track of their notes.
Differentiated Instruction – Enrichment: Have students research mean, median, and mode in the news. Have them critique the information they find. / Formative Assessments:
Informal observations
Discussion
Ticket Out the Door
Mean, Median, and Mode Jigsaw
Hook: Watch the Mean, Median, and Mode Song (See Resource File)
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.
Summarizing Strategy: Ticket Out the Door: Describe a situation when the mode is the best measure of central tendency.
Homework: We are going to be learning about our community of students at Innovation Academy. Think about something you would like to learn about our community. Write a statistical question. Though we are looking for a statistical question, the questions should have a numerical answer.
4 / I can describe a set of data by its center, spread, and overall shape. / Graph Paper
Differentiated Instruction – Remediation:
Excel on MacBook Air
Graphing Calculator
Materials for Differentiated Instruction – Enrichment:
iPad or MacBook / Essential Question: How do I describe a set of data by its center, spread, and overall shape? / Prompting
Grouping
Differentiated Instruction – Remediation: Allow students to use technology to create the line plot. Allow students to use calculators.
Differentiated Instruction – Enrichment: Have students decide on something they would like to research about our community at IA. An example, how do IA students learn best? Have them do background research, come up with survey questions to handout to students, analyze the data, and finally write a conclusion. / Formative Assessments:
Observations
Discussions
Ticket Out the Door
Performance Assessment:
Presentation of Findings
Our IA Community
Set: Watch this video called I use Statistics Everyday (See Resource Folder).
Teaching Strategy:
  1. Group students in groups of two. Ask the students to compare questions they were supposed to write for homework. Ask them to decide on one question to use. Once they have decided on the question, they are to bring the question to the teacher for approval. Make sure the questions are statistical questions and appropriate.
  2. Once the questions have been approved, ask the students to ask ten students in the class.
  3. When the students have collected their data, ask them to describe their data in the following ways:
  1. By its center.
  2. By its spread.
  3. By its shape.
  1. Review the steps for sketching a line plot with students. This will aid students in finding the shape of their data.
  2. Have students share their results with the class. Ask and discuss the following question: Did any group pose a statistical question that could not be analyzed by its center, range, or shape?
Summarize: Give the students a set of data and ask them to describe it by its center, spread, and shape.
Assign practice problems for homework.
Adapted from Muschla, Gary Robert; Muschla, Judith A.; Muschla, Erin (2012-03-21). Teaching the Common Core Math Standards with Hands-On Activities, Grades 6-8 (Jossey-Bass Teacher) (Kindle Locations 1587-1593). John Wiley and Sons. Kindle Edition.
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 – Enrichment:
Supply students with a graphic organizer to keep track of their notes. (See Box and Whisker Plots in the Resource Folder)
Calculators
Materials for Differentiated Instruction – Enrichment:
iPad / Essential Question: How do I describe variation of a set of data? / Grouping
Prompting
Differentiated Instruction – Remediation: Supply students with an advanced organizer to keep track of their notes.
Use of Calculators
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 titled “Using the Measures of Center and Variability” (See Resource Folder).
Teaching Strategy:
  1. Define measures of variation.
  2. 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.
  3. 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.
Assign practice problems for homework.
7 / I can use measures of center and measures of variability to summarize data sets in context. / Calculator
Paper
Pencil
Materials for Differentiated Instruction – Enrichment :
Supply students with the Mean Absolute Deviation graphic organizer (See Resource Folder) to keep track of their notes.
Calculators
Materials for Differentiated Instruction – Enrichment :
iPad / Essential Question:
1. What is Mean Absolute Deviation (MAD)?
2. How can it help me describe a set of data? / Grouping
Prompting
Differentiated Instruction – Remediation: Supply students with the Mean Absolute Deviation graphic organizer (See Resource Folder) to keep track of their notes.
Use of Calculators
Differentiated Instruction – Enrichment : Have students research real-world examples of variation. / Formative Assessment:
Informal observations
Responses to activities
Ticket Out the Door Responses.
Mean Absolute Deviation
Set: Give students 5 sets of data to find the mean, median, and mode of.
Teaching Strategy:
  • Ask student to define deviation. Discuss with the class what deviation is. Deviation is the amount by which a single measurement differs from a fixed value such as the mean.
  • Give the students the following example. Eight students were asked how many text messages they sent in one day. The students answered: 52, 59 48, 54, 60, 58, 55, and 62.
  • Ask the students to find the mean of the data set.
  • Next, ask them what the difference between the mean and 52 is. Then ask them what the farthest data point from the mean is. Finally, ask them to decide if the data is close to the mean or is it far from the mean.
  • Explain to the students that a tool for describing how spread out a set of data is Mean Absolute Deviation. It is a single number that describes how close a data set is to the mean. The smaller the Mean Absolute Deviation, the closer the data set is to the mean.