Illuminations: Looking Back and Moving Forward

Looking Back and Moving Forward
In this lesson, students conduct and present the results of surveys in several ways. The process standards Communication and Representation are fundamental to this lesson.

Learning Objectives
 
Students will be able to do the following:
  • Determine the possible combinations given two variables.
  • Create a bar graph and a pictograph from data collected by a survey.
  • Find the mean, median, and mode of a given set of data.
  • Find the range of a given set of data.
  • Construct and describe a box plot.

Materials
 
Paper
Crayons
Calculators
The Bread Basket Activity Sheet
The Soup Spot Activity Sheet
The Clucking Chicken Activity Sheet
The Pizza Palace Activity Sheet

Instructional Plan

To successfully complete this lesson, students will need to apply what they have learned from the first five lessons in this unit. You may wish to assess this by presenting a bar graph, a box plot, and a pictograph completed earlier in the unit and asking students to pose questions that can be answered by looking at the graphical representations.

Display the four menus used in this unit, then put the students into pairs and ask each pair to select a menu from one food court establishment from which they will plan a party for eight people.

If they choose a menu without prices, inform them that they should estimate what those prices might be. Similarly, if they wish to order something that is not on the menu, they may wish to use the prices from a different menu or estimate the prices for the items.

When they are ready, ask them to write the price of the party on the board. Then have the pairs construct a box plot from the data, and to find the mean, median, and mode of the price of the party. When all have had time to complete the task, identify one pair and call on a volunteer from that pair to describe the menu and to exhibit their box plot. Repeat with each pair.

Next, put two pairs together, and ask them to make a box plot from their combined data. Allow the students a chance to share their work.

Now tell the students there will be a cake for dessert. Write four types of frosting and four flavors of cake on the board. Ask the students to report how many possible combinations there would be, and to explain how they got their answer.

Example:

Ask the pairs to list all the possible cake/frosting combinations, choose five of them and then survey 20 of their classmates (or students from another room) as to which of the choices they would be most likely to order. When all the pairs have reported in, ask each pair to construct a bar graph and a pictograph that displays the data they have collected. (You may wish to encourage them to use the Create a Graph Web site to construct the bar graph.)

If groups were constructing scale models or 3-D representations of the food court, you may wish to have them share these at this time.

Questions for Students
 
  1. What measures of center did you find today? Were all of them the same? Which best represented the "average" price of a party? (mean)
  2. What was the range of the data set you constructed as a pair? What would be the range if another party was planned for $14.95? Would the range be different? Why?
  3. What measure of center do you use when you make a box plot? (median) How do you show the range when you make a box plot?
  4. If you had four choices for cakes and six choices for frosting, how many different combinations can you make? (4 x 6 = 24)
  5. How were your bar graph and the pictograph alike? How are they different?
  6. What questions can you answer by looking at your bar graph? Are there any questions you cannot answer from it?
  7. Each pair had 20 pieces of data. Why aren't all the pictographs alike?

Assessment Options
 

At this stage of the unit, students should be able to do the following:

  • Determine the total number of combinations with two variables.
  • Create a bar graph and a pictograph from data collected from a survey.
  • Find the mean, median and mode of a given set of data.
  • Find the range of a given set of data.
  • Construct and describe a box plot.

Based on the comments you have made throughout the unit, you may wish to make remediation or enrichment plans for individual students. The comments may also help you plan appropriate instruction if you revisit this topic later in the year.

Teacher Reflection
 
  1. Which students were able to stay on task when they worked in pairs? What experiences would help those who could not develop this ability?
  2. Which students were able to stay on task when they worked with the whole class? What experiences do the others need to help them do this?
  3. Which students could construct bar graphs and pictographs with minimal supervision? What experiences are necessary for those who could not?
  4. Which students are able to use data to create a box plot?
  5. Which students could find the range, mean, median, and mode of a set of data? What learning opportunities are needed for those who could not?
  6. Which students could pose appropriate questions that could be answered from a graphic representation?
  7. What adjustments will I make the next time I teach this lesson?

Looking Back

  1. Which students met all the objectives of this unit? What extension activities are appropriate for those students?
  2. Which students are still having difficulty with the objectives of this unit? What additional instructional experiences do they need?
  3. Which students could compare different ways of data representation? What is your evidence for this?
  4. Were they able to create and explain the features of box plots?
  5. What were the greatest challenges for the students in this unit?
  6. Which activities were the students most motivated to complete? Why?

Moving Forward

  1. What experiences can I provide so that the students will remember how to construct and read bar graphs and pictographs?
  2. What experiences can I plan so that students have a genuine need to construct and read bar graphs and pictographs?
  3. What experiences can I provide so that the students will remember how to construct and read box plots?
  4. What experiences can I plan so that students have a genuine need to construct and read box plots?
  5. What learning experiences would help students not yet comfortable with the concepts in this unit?
  6. Where can students apply their understanding from this unit in other curricular areas?
  7. How will I teach this unit differently in the future?

NCTM Standards and Expectations
 
Data Analysis & Probability 3-5
  1. Design investigations to address a question and consider how data-collection methods affect the nature of the data set.
  2. Collect data using observations, surveys, and experiments.
  3. Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
  4. Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed.
  5. Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.
This lesson was developed by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

Web Sites
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