Students will compile and arrange data to construct a bar graph. They will analyze the information depicted in their graphs. Students will be able to: 
- collect and arrange data. 
- display data on a graph as horizontal and vertical bars. 
- analyze and interpret information displayed on a graph. 
- respond to comparative questions using data from a graph.

- How can the arrangement and visualization of data help reveal the relationship between quantities? 
- How do predictions come from the combination of probability and data analysis? 
- What impact does data type have on display selection? 
- What does it mean to evaluate or estimate a numerical quantity? 
- What qualifies a tool or approach as suitable for a particular task? 
- Why does "how" we measure differ depending on "what" we measure?

- Bar Graph: A graph is a pictorial device used to show a numerical relationship. A bar graph uses the length of solid bars to represent numbers and compare data. 
- Data: Information, especially numerical information, usually organized for analysis. 
- Pictograph: A graph that uses pictures to show and compare information. 
- Survey: A collection of information. 
- Tally Chart: A table that uses tally marks to record data. 
- Tally Mark: A mark used to keep track of items when counting.

- a completed graph to use as a model 
- large horizontal graph with one-inch gridlines. The number of rows should be the same as the number of students in the class (use a chart or grid paper). The y-axis is labeled “Number of Students,” and the x-axis is labeled “Number of Letters in First Name.” 
- large vertical graph with one-inch gridlines (about eight columns) 
- 1" x 1" photo of each student or 1" x 1" piece of paper, each with a student’s name on it 
- letter tiles made from construction paper or use paper tiles provided (M-1-6-3_Letter Tiles). Print/photocopy enough so that each student can spell out his/her name. 
- scissors, one per student 
- one glue stick (or roll of double-sided tape) 
- Prepare a large graph in advance with enough horizontal rows (one inch apart) for each student to be included. Attach a photograph of a student (or a small piece of paper with the student’s name) at the beginning of each row (M-1-6-3_Name Graph Sample). 
Tally Chart (M-1-6-3_Lesson 3 Tally Chart) 
- Name Length Graph (M-1-6-3_Name Length Graph) 
- Name Graph Sample (M-1-6-3_Name Graph Sample) 
- Blank Tally Chart (M-1-6-1_Blank Tally Chart) 
- Observation Checklist (M-1-6-3_Observation Checklist) 
- connecting cubes 
- three read-aloud books

- During this exercise, formative assessment could come from teacher observation. Split the class up into pairs. Divide the connecting cubes into red, green, yellow, and blue colors. Students should connect cubes with similar colors to make trains. Give the students instructions to arrange the cube trains horizontally and observe the data they represent. Ask the pairs to make a bar graph that shows how many cubes are in each color train. Encourage students to comment on their graphs.
- You can document student progress using the Observation Checklist (M-1-6-3_Observation Checklist)

Explicit instruction, modeling, scaffolding, and active engagement 
W: Explain how to use graphs and observe the information gathered. 
H: Use the provided tiles to have students spell their first names. Have them adhere the tiles to a picture of themselves. 
E: Compare how long their names are based on how many letters they have and how long the tiles are next to them. Determine which names are the longest, the shortest, how many are of the same length, etc. 
R: Make a vertical graph based on how frequently students' names contain a given number of letters. 
E: Comment on the changes to the graph's format. Inform students that in the next lessons, they will work with vertical and horizontal graphs. 
T: Use connecting cubes to have students vote on different topics throughout the year, or have them tally marks. With their last names this time, have students make a graph that looks like the one with their first names. 
O: This lesson aims to introduce students to the creation and analysis of bar graphs. 

Start the class by pointing out a finished graph to the students. Check the various components required, including the title, and x and y-axis labels.

"Today, we will use our names to create a graph. How can we organize our names?" Invite students to share their thoughts about letters (beginning, ending, syllables, number of letters, etc.). "I think those are fantastic ideas. We'll count how many letters are in your first names today. We're going to make a graph using the number of letters. This exercise aims to investigate the various ways that graphing data can provide insights into the collected data."

Present the Name Graph Sample (M-1-6-3_Name Graph Sample) to the students. Provide a set of letter tiles (M-1-6-3_Letter Tiles) to every student, and tell them to use the large horizontal graph that is displayed in the classroom to spell their first names. Students are to glue one letter in each square of the row next to their photographs without leaving spaces. Ask students to verify that the spelling of their first names is accurate and that there are no spaces between the letters. Once they're done, ask them to cut off any blank squares that remain.

Once everyone has signed their name on the graph, ask,

"What does the graph display?"
"What can we infer from our graph?"
"Which person's name contains the most letters? How are you aware?"
"Which name contains the fewest letters? How are you aware?"
"What other observations about the data displayed in the graph do you have?"
"Those are great observations. First, let's examine the length of each letter in our names. Whose name has the most letters? How many letters are there?"
"Which name contains the fewest letters? How many letters are there?"

First, students should count how many letters are in each name to determine which has the most. Then show them that by identifying the name that makes use of the greatest number of squares in its row, they can also determine which is the longest. Ask students to compare the row lengths. As you determine which name is the shortest, help your students notice that the opposite is true.

Assign the task of determining the number of names that have the same length to your students. Count the number of names that contain five letters, for instance. Number the graph's bottom row first. Under each box, write a single number, starting with 1. Describe how each name's number represents the number of letters needed to spell it. Point out to the students the final letter in the first row's name. Show how to trace the number at the bottom of the graph with your finger. "We can determine the number of letters in this name with this number."

Draw your student's attention to the vertical axis. Number the graph's sides, beginning at zero at the bottom. Next to each row, write a single number. Explain that the numbers show the proportion of students whose names contain a particular number of letters. To illustrate, trace your finger up one column, stopping at the column's height. "This figure reveals the proportion of students whose names consist of this many letters."

Ask students to count the number of letters in their names by examining the graph. Assist students in tracing the final letters of their names with their fingers down to the bottom numbers.

"Let's make a new graph using the data from our tally chart. What proportion of people have four-letter names?" (The names of five individuals consist of four letters.)

"What is the average person's letter count? What allows you to know?"

"The maximum number of people with five letters in their names is seven." Show students how to find the graph's tallest bar to determine the answer. Describe how many students with that many letters in their names there are, the taller the bar.

"Aside from our names, what else do you notice?"

"Only two individuals possess names with eight or more letters."

Show the Name Length Graph (M-1-6-3_Name Length Graph) in blank format. From 0 to 10, assign numbers to the rows on the left.

Inform the students that they will utilize the data in the tally chart to count the number of names that have the same number of letters to construct a vertical bar graph.

"There are students [X] whose names consist of three letters." Bring the students' attention to the vertical graph's bottom numbers. Describe how these figures indicate the number of letters in a name. "Since all of these names consist of three letters, we must locate the number three at the bottom of the graph. Now, just as I am doing on the class graph, color one square for each person whose name contains three letters." Make note of the fact that you are creating vertical bars. Describe how the graph's left-hand numbers indicate the number of students. After determining how many colored squares there are, trace horizontally to the number. "The names of [four] students are precisely three letters long."

Perform the same steps for every figure at the graph's base. Select students to add color to each column's squares. To make a visual difference between each column, change the color of each one.

Use the lesson 3 tally chart by clicking here (M-1-6-3_Tally Chart). When using an overhead copy, each student should have a copy at their desk.

"Let's collect the information. On our graph, let's examine the first name. How many letters does it contain? Make a tally next to that number. Let's now examine the following name..."

The students count on their chart as you demonstrate how to tally each name. Ask students to count the number of tallies in each row after all the numbers have been tallied and write that number at the end of each row.

Ask students to conclude the lengths of names by comparing the bar heights.

Present the two finished graphs and talk about the details they each offer. Draw a comparison between the Name Lengths graph's horizontal and the Numbers of Names graph's vertical formats. Assist students in realizing that the horizontal bar graph's data is counted from left to right, starting at left. From bottom to top, the data in the vertical graph is counted.

Allow students to continue making observations by leaving the graphs up for a few days.

Extension:

Throughout the year, modify the lesson to fit the needs of the students by utilizing the strategies and activities listed below.

Routine: Give students three options for read-aloud books on certain mornings, and they should vote for their favorite. Allocate distinct colored connecting cubes to every book. Every student should vote for their favorite book by setting a cube next to it as part of the morning routine. The students should join their cubes with those that are already next to the book so that a train (column) of cubes is formed.

After everyone has cast their vote, the class should talk about the information gathered. Place the columns next to each other and assist the students in drawing and articulating connections between numbers. Motivate students to make a visual comparison of the cube trains.

"Which book got the most votes? How are we able to know? What was the least voted-upon book? For how many fewer? What is the number of students who cast ballots? If there is a tie, how can we determine it?"

Once students are comfortable gathering and interpreting their votes using the cubes, have them cast and record their votes using tally marks (M-1-6-1_Blank Tally Chart). This would put students to the test of carefully examining the previous votes to see if their vote results in a group of five. Assign a reporter to tabulate all of the votes and present the findings to the class.

Small Group: Bring up the previous exercise in which the students spelled their first names to create a horizontal bar graph. Assemble the letter squares. Give the students instructions to repeat the exercise using their last names this time.

Give the students instructions to arrange their names in a graph on the floor or table. Give students a short period to work without making any suggestions. Suggest that if the group is having problems, they write one name at the top and another underneath it with the first letters aligned to the left.

Make note of the fact that the pupils have created a horizontal graph with the data. Permit students to jot down and discuss their observations.

Present a set of connecting cubes to the class, instructing each student to select a cube representing each letter in their last name and join the cubes to form a train. To make them stand up on the table or floor, have students hold their cubes vertically. Pose comparison queries like these:

"Which person's last name contains the most letters? The fewest? How can the cube trains be used to help us determine this?
"What is the difference in number of letters between the longest and shortest names?"
"Does the length of any names match? How are you aware?"

Collaborate with students to produce a second name length graph (M-1-6-3_Name Length Graph). Let students collaborate to analyze the data from the cube trains and the horizontal graph, then present it on the vertical graph. Ask students to share what they noticed.

Extension: Permit students who have grasped the standards to proceed to independently make bar graphs using the first names' vowels and consonants.