At the beginning of the lesson, draw students’ attention to a completed graph. Review the various parts needed: title, x and y axis labels.
“Today we are going to make a graph using our names. What are some ways we can sort our names?” Ask students to share ideas (beginning letter, ending letter, syllables, number of letters, etc.) “Those are great ideas. Today we will count the number of letters in your first names. We will use the number of letters to create a graph. The goal of this activity is to find out how graphing information can tell us different things about the data we have collected.”
Show students the Name Graph Sample (M-1-6-3_Name Graph Sample.doc). Give each student a set of letter tiles (M-1-6-3_Letter Tiles.doc), and instruct students to spell their first names by gluing one letter in each square of the row next to their photographs on the large horizontal graph displayed in the classroom, without leaving spaces. Have students check that their first names have been correctly spelled and that no spaces have been left between the letters in their first names. When they are finished, have them cut off any remaining empty squares.
When everyone has added his/her name to the graph, ask,
- “What does this graph show?”
- “What can we learn from the graph we created?”
- “Whose name has the most letters? How do you know?”
- “Whose name has the fewest letters? How do you know?”
- “What other things do you notice about the information shown in the graph?”
- “Those are excellent observations. Let’s look first at how many letters long our names are. Whose name has the most letters? How many letters does it have?”
- “Whose name has the fewest letters? How many letters does it have?”
Have students first count the number of letters in each name to determine the name with the most letters. Then lead them to see that they can also determine the longest name by identifying the name that used the most squares in its row. Have students compare the lengths of the rows. Lead students to observe that the opposite is true when determining the shortest name.
Turn students’ attention toward finding out how many names are the same length. For example, count how many names have five letters. Begin by numbering the bottom row of the graph. Write one number beneath each box, starting with 1. Explain that these numbers indicate how many letters are used to spell each name. Draw students’ attention to the last letter in the name in the first row. Demonstrate tracing your finger downward to the number at the bottom of the graph. “This number tells us how many letters are in this name.”
Turn students’ attention to the vertical axis. Starting at the bottom with zero, number the side of the graph. Write one number next to each row. Explain that these numbers indicate how many students have a name with a certain number of letters. Demonstrate by tracing your finger up one column and stopping at the height of the column. “This number tells us how many students have a name this many letters long.”
Ask students to study the graph and find out how many letters are in their own names. Guide students in using their fingers to trace the last letters in their names down to the numbers at the bottom.
“Let’s use the data from our tally chart to create a new graph. How many people have names that are four letters long?” (Five people have names that are four letters long.)
“How many letters do the most people have? How can you tell?”
“There are seven people who have five letters in their names; that’s the most.” Lead students to see that they can tell by looking for the tallest bar in the graph. Explain that the taller the bar is, the more students there are who have that number of letters in their names.
“What else do you notice about our names?”
“There are only two people with eight or more letters in their names.”
Display the blank Name Length Graph (M-1-6-3_Name Length Graph.doc). Number the rows on the left from 0 to 10.
Explain to students that they will look at the information in the tally chart to determine how many names have the same number of letters and use that information to create a vertical bar graph.
“There are [X] students whose names are three letters long.” Draw students’ attention to the numbers at the bottom of the vertical graph. Explain that these numbers represent how many letters are in a name. “At the bottom of the graph we need to find the number 3 because these names all have three letters. Now color one square for each person who has three letters in his/her name just as I’m doing on the class graph.” Point out that you are making vertical bars. Explain how the numbers on the left side of the graph tell the number of students. Count the number of colored squares, then trace horizontally to the number. “There are [four] students whose names are exactly three letters long.”
Repeat this process for each number at the bottom of the graph. Choose students to color the squares in each column. Change colors for each column to create a visual distinction between them.
Use the Tally Chart here (M-1-6-3_Lesson 3 Tally Chart.doc). Each student should have a copy at his/her desk while the teacher uses an overhead copy.
“Let’s gather our data. Let’s look at the first name on our graph. How many letters are in it? Put a tally beside that number. Now let’s look at the next name…”
As you model the tallying for each name, the students tally on their chart. When all of the numbers have been tallied, have students count how many tallies are in each row and write that number at the end of each row.
Have students compare the heights of the bars to help them draw conclusions about the lengths of names.
Display both completed graphs and discuss what information each provides. Compare the horizontal format of the Name Lengths Graph with the vertical format of the Numbers of Names graph. Help students notice that the data in the horizontal bar graph starts at the left and is counted from left to right. The data in the vertical graph is counted from the bottom up.
Leave the graphs displayed for a few days so students can continue making observations.
Extension:
Use the activities and strategies listed below to tailor the lesson to meet the needs of students throughout the year.
- Routine: On select mornings, provide three read-aloud book choices from which students should vote for their favorite. Assign different color connecting cubes for each book. As part of the morning routine, have each student vote for his/her favorite book by placing a cube beside it. If there are already cubes beside the book, students should connect theirs, creating a train (column) of cubes.
When all students have voted, the class should discuss the data collected. Hold the columns side by side and guide students to make and express connections with number relationships. Encourage students to compare the cube trains visually.
“Which book received the most votes? How can we tell? Which book received the fewest votes? How many fewer? Can we tell how many students voted? How can we tell if there is a tie?”
When students are proficient at using the cubes to gather and explain their votes, have them use tally marks (M-1-6-1_Blank Tally Chart.doc) as a means to cast and record their votes. This would challenge students to look closely at the votes already cast to determine if their vote creates a group of five. Assign a reporter to count all of the votes and report the results to the class.
- Small Group: Remind students of the earlier activity where they created a horizontal bar graph by spelling their first names. Distribute letter squares. Direct students to repeat the activity, this time using their last names.
Direct students to arrange their names on the table or on the floor, creating a graph. Let students work for a few minutes without offering suggestions. If the group is having trouble, suggest that they put one name at the top, then place another underneath it, aligning the first letters on the left.
Point out that students have arranged the data in a horizontal graph. Give students time to make and share observations.
Bring out a set of connecting cubes and ask each student to take one cube for each letter of his/her last name and connect the cubes to make a train. Have students hold their cubes vertically so they stand up on the table or floor. Ask comparison questions such as,
- “Who has the most letters in his/her last name? The fewest? How can we determine this by looking at the cube trains?”
- “How many more letters does the longest name have than the shortest?”
- “Are there any names that are the same length? How do you know?”
Work with students to create a second name length graph (M-1-6-3_Name Length Graph.doc). Allow students to work together to interpret information from the horizontal graph and the cube trains and display it on the vertical graph. Have students discuss their observations.
- Expansion: Allow students who have mastered the standards to move on to create independently their own bar graphs using the vowels and consonants in the first names.
