To assess prior knowledge, display a bar graph and ask students to describe values graphed and to tell the number of data points for each. For example, you may use one of the bar graphs completed in the previous lesson.
Ask students what they might find out by comparing the names in the class. Record their answers. Have each student write his or her first and last name on an index card, then write on the card the number of letters in each name.
| Sample Names |
| Valerie Bertinelli | Paul Newman |
| Nicholas Cage | Jack Nicholson |
| Michael Caine | Christopher Reeve |
| Katherine Hepburn | Diana Rigg |
| Anthony Hopkins | Susan Sarandon |
| Meryl Streep | Ben Kingsley |
Ask students to line up the cards from shortest last name to longest last name. Tell them that the difference from the smallest value to the largest is called the range. Have them find the range for the number of letters in last names in the class. [In the sample above, the range is 10 – 4, or 6.]
Ask students to determine which name length occurs most often. Identify that number as the mode. Tell them that the mode is one of three measures of central tendency. If two lengths occur more than the others, the data set is called bimodal, but if there are several values with equally high occurrences, as in this sample, there is no mode.
Repeat with lengths of first names. Ask students to compare the range and the mode of the data sets.
Tell students to group themselves according to whether they had two to three, four to five, six to seven, or more than seven letters in their last name. Write the categories one under the other on the board.
Ask students in each group to tape their file cards end to end in a line after the number that tells how many letters are in their last name. Record how many students are in each category. Then elicit from them a possible name for the bar graph.
| Letters in Our Last Names |
| 2-3 | | | | |
| 4-5 | Cage | Caine | Rigg | Reeve |
| 6-7 | Hepburn | Hopkins | Newman | Streep |
| 8-9 | Kingsley | Nicholson | Sarandon | |
| 9+ | Bertinelli | | | |
Ask students to copy the bar graph onto grid paper.
Repeat with first names, using the same categories. When students have finished, ask them what they can tell about the names in the class from looking at the bar graphs.
After students have offered several statements about a single bar graph, encourage them to use numbers to compare the two bar graphs.
Next, have students use a computer to generate a circle, or pie, graph. Students should use the NCTM Circle Grapher tool.
Have students enter their last-name as data in the space provided. Then generate the graph.
You may wish to ask students to write fractions to compare each section with the whole.
Print out the graph. Ask students to compare the pie chart with the bar graph, telling how they are alike and how they are different. Repeat with the first-name data.
