Alphabetical Statistics Day 2

Primary/Junior (Age 6 – 12)

Curriculum Goal

Primary: Data Management

  • Sort sets of data about people or things according to two and three attributes, using tables and logic diagrams, including Venn, Carroll, and tree diagrams, as appropriate.
  • Collect data through observations, experiments, and interviews to answer questions of interest that focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables.
  • Display sets of data, using many-to-one correspondence, in pictographs and bar graphs with proper sources, titles, and labels, and appropriate scales.
  • Analyse different sets of data presented in various ways, including in tally tables, concrete graphs, and pictographs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions.
  • Use mathematical language, including the terms “impossible”, “unlikely”, “equally likely”, “likely”, and “certain”, to describe the likelihood of events happening, and use that likelihood to make predictions and informed decisions.

Junior: Data Management

  • Collect data from different primary and secondary sources to answer questions of interest that involve comparing two or more sets of data, and organize the data in frequency tables and stem-and leaf plots.
  • Select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs.
  • Analyse different sets of data presented in various ways, including in stem-and-leaf plots and multiple-bar graphs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions.
  • Use mathematical language, including the terms “impossible”, “unlikely”, “equally likely”, “likely”, and “certain”, to describe the likelihood of events happening, represent this likelihood on a probability line, and use it to make predictions and informed decisions.

Context

  • Children are initially seated facing the teacher and chalkboard before working collaboratively in small groups.
  • Students will have completed Alphabetical Statistics: Part 1
Print Lesson
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Day 1 Lesson

Materials

  • Homework from Alphabetical Statistics: Part 1 completed by each student
  • One computer for each group
  • Live Excel chart (Appendix E)
  • Calculators
  • Scroll of wrapping or receipt paper prepared with letters of alphabet arranged from most used to least in the English language (Appendix A)

Lesson

  • Before continuing this activity, secure the rolled up scroll with tape or a magnet to a whiteboard or chalkboard. Ensure there is space on the whiteboard or chalkboard for the students’ collective data to be written beside it.
  • Ask students: What strategies did you use to count how many times each letter was used in the sentence you selected? Students may share that they used tally marks, charts or a cross-off as they go method.
  • Ask students to organize themselves in the same groups they were in for Part 1. These groups are located on Appendix B from Part 1.
  • Have one student from each group retrieve a computer for the group to use.
  • When students are settled in their groups, project Appendix E so that the entire class can see it. Announce: Compile your records to find the total number of times each letter appeared for each member of your group. On the board, you will see that a live class chart is displayed. Input your group’s totals into the chart. For example, if I was in Group 1 which is red, we would add up or find the sum of the number of times the letter “a” was recorded by everyone in the group then input that number beside Group 1 and so on with the rest of the letters. I’m going to reiterated that you should be entering the number of times each letter of the alphabet appeared in all of your sentences combined.
    • If technology is unavailable, print a copy of Appendix A for each group. When each group has found the sum of the number of times each letter was used, have one member from each group input their data into Appendix A on the teacher’s computer or onto a prepared piece of chart paper that reflects Appendix A.
  • Tell students: When you are done entering your group’s data, I have a fun game for you to play while we wait for the other groups to finish. In your groups you will play the game “You Can’t Say L”. The game begins by the group selecting one person to be designated as the talker and the others as the listeners. The talker talks for as long as they can without using the letter “L”. The listeners role is to make sure that the talker does not use the letter L. When the identified talker uses the letter “L” a listener becomes the new talker and the original talker becomes a listener. By the end of the game everyone should have the opportunity to be the talker at least once.
    • The objective of this game is to isolate the letter “L” and challenge students to become aware of how difficult it is to not use certain letters.
  • The completed table will be projected on the board with the total number of times each letter was used amongst all the students’ selected works.
  • Tell students: Let’s determine a list of the top 10 letters in their order of frequency from our samples.
  • Write the top 10 letters near where the rolled-up scroll with the letters of the alphabet arranged from most used to least used in the English language (Appendix A) is hanging so it can be easily compared to the class’ data once revealed.
  • Before unrolling, tell students the following: Remember when I told you that I prepared a list of all 26 letters of the alphabet in order of their usage in the English language? We are now going to compare our class data to a larger data set.
  • Ask your students: Will these lists be identical? How many letters do you think will match? How much of the order would have to match for you to be satisfied with our statistical sample? Ask for a drumroll and unroll the tape for the big reveal! Pause to allow students time to compare the tables.
  • Ask students: What would happen if we had done a larger sample? How might the results differ if we used first-grade reading materials instead of advanced? What if we used sentences from a Spanish or French book? If we tried the sampling experiment again, would we be likely to produce results that would match exactly the order on the receipt paper? Why do mathematicians say that larger samples will more closely resemble what really happens? Do they think a larger sample would produce results closer to the actual order?

Previous: See Alphabetical Statistics: Day 1

Look Fors

  • What strategies did students use to tally the usage of letters?
  • Do students recognize the margin of error?
  • What do students know about samples and populations?

Adapted by Hannah Genich from A Collection of Math Lessons from Grades 3 Through 6 by Marilyn Burns

Print Lesson
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Day 1 Lesson

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