- 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.

- 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.

- Children and the teacher work together for the first part of the lesson before students engage in independent and collaborative tasks.

- Scroll of wrapping or receipt paper prepared with letters of alphabet arranged from most used to least in the English language (Appendix A)
- One sheet of blank paper for each student
- Slips of paper with group color and names (Appendix B)
- Pencils
- One computer or tablet per group
- Live Excel Chart (Appendix C)
- Sticker Sheet Example (Appendix D)

- Introduce the lesson to your students:
*For the next two days we will be studying the English Language alphabet. Together, we will explore the alphabet and investigate ideas about probability and statistics. Before breaking into small groups, I want you each to make an individual prediction. Without discussing or sharing your thoughts with the group, please predict what you think the five most used letters in the English language are. In other words, the letters that occur the most often when authors write books, newspaper articles and when we practice our writing skills! Write the five letters you think are used the most often and draw a star beside the letter you think is used the most.* - Distribute a blank piece of paper and pencil to each student. Provide students with roughly two minutes to record their responses.
- While students independently work, create groups of three or four using your preferred method of grouping. Use Appendix B to create and organize groups by colour. Provide this slip of paper to each group once announced. This step ensures that students input data into their group’s designated rows.
- When everyone has ranked their top five letters, announce the assigned groups. Have groups organize themselves on the carpet, at tables or desks. Have one student per group secure their computer or tablet and load Appendix C.
- If technology is unavailable, print a copy of Appendix C for each group. Once each group has completed their predictions, have one member from each group input their data into Appendix C on the teacher’s computer or onto a prepared piece of chart paper that reflects Appendix C.
- Inform your students that you’d like them to work together:
*Share your predictions and determine which letters as a group are the five most commonly used letters. Input your group’s top five most used letters into the chart. The teacher is to project the live chart onto the board then circulate and listen to interactions.* - When all groups’ predictions are inputted on the board, ask:
*What method did your group use to determine your top five letters?*- There will likely be more vowels than consonants on their list. Ask:
*Why are there more vowels than consonants? Students may suggest that all words have vowels.* - Now ask:
*Who in the world would care about the order of the usage of the letters of the alphabet? Can you think of anyone who needs to know or would benefit from knowing?* - If someone says that no one would care, respond with:
*I know several instances where this information would be very useful. Any other ideas?* - If there is no response, prompt students by suggesting games such as Scrabble. Ask students:
*In the game Scrabble, there are nine As and one Z. Why are there more As than Zs? Which letters do you think are worth more points, the letters that occur more or less frequently? (A is worth 1 and Z is worth 10) Which letter would you prefer to receive?*

- There will likely be more vowels than consonants on their list. Ask:
- After responses have been shared, tell students the following: I
*have another use that doesn’t have to do with a game.* - Project Appendix D and say: L
*etter stickers are often used by artists and designers to communicate meaning. Ask students: What do you notice about the frequency or the number of times different letters are used?*If this question does not prompt discussion, ask students:*What do you notice about the number of times the letter A is used compared to the letter Z?*They should respond by saying that there are more A’s than Z’s. - Follow up:
*The number of each letter differs depending on how often they are used. These sheets would not sell if artists ran out of certain letters after a sentence of two.* - Tell students:
*I already know which letter is the most common and I have prepared a list of all 26 letters of the alphabet in order of their usage in the English language. I’ve written this sequence on a secret scroll. Show students the scroll rolled up but do not share the data. Continue: Before we unroll the results, we are going to conduct a mathematical investigation. You will be collecting statistical samples and we will be using the information you gather to predict the order of usage of all 26 letters of the alphabet. Then we will compare our predictions with what is on the secret scroll.* - Continue:
*It would be very difficult and unreasonable to count every letter ever used in all the works of writing ever done in the English language. I’d like each of you to do the following for homework tonight: Select a sentence with at least five words in it from any book. Copy the sentence onto the back of the piece of paper where you wrote your individual top five predictions. With this sentence find out and record how many times each letter of the alphabet appears in your sentence. Bring your recording sheet tomorrow to use in your group.* - Allow students to decide how they will approach counting the letters in the sentence they selected. Students may decide to use a tally chart to record their work.
- Provide an example to students if they are confused.

Follow Up Lesson: Alphabetical Statistics: Day 2

- Can the child identify that some letters are used more frequently than others?
- How do children work collaboratively to pool their rankings?
- Can learners relate and/or find value in knowing this information in everyday life?

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

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