## State Data

- Lesson

Students create graphs based on the characteristics of the names of the 50 States, and find mean, median, mode, and range of the data.

To begin the lesson, ask students to sort themselves into groups of four or five. Display a map of the United States. Ask each group to select ten states from the map and write the state names on index cards.

Ask each group to construct a bar graph (using grid paper) and a pictograph that displays the length of the names of the states.

Then have them use the graphs of the data and find the mean, median, and mode of the length of the names of the states.

When all the groups have had time to complete the task, identify one group and call on a volunteer from that group to tell the states they picked. Ask another to show the graphs, another to report the range, and others to inform the class of the mean, median, and mode of the data set. Repeat with each group.

As a comparison, students can view the State Data Map Applet and select "Letters in State Name" as the data set. This pictorial representation uses darker shades for longer state names and lighter shades for shorter state names. Allow students to compare and contrast the representations that they created with the one shown in the State Data Map, and ask, "Which one provides the most information?"

Remind students of the terms "measures of center and of spread" and what these terms mean.

*Teacher Note:* Alternatively, students may construct their bar graphs using the Bar Grapher Tool.

- Crayons
- Paper
- Index cards
- Grid Paper
- Computers with internet access

**Assessment Options**

- You may wish to make notes about student progress on the Class Notes.
- Students can provide written responses to the
*Questions for Students*, and you may collect these written responses to assess student learning.

**Extensions**

Students may repeat the activities in this lesson using the state capitals, in place of state names. This is a great link to social studies, for those curricula where students need to know the various state capitals.

**Questions for Students**

1. What measures of center did you find today? Were all of them the same?

[Mean, median, mode; Answers will depend upon student data.]

2. What was the range of your data set?

[Answers will depend upon student data.]

3. How would you show a younger child how to find the range? The median? The mode? The mean?

[Subtract the smallest number from the largest number; Order the numbers from least to greatest and find the middle number; Identify the number(s) which appear most often; Add all of the numbers and divide by the number of data items.]

4. How are the bar graph and the pictograph alike? How are they different?

[They both show the same data; The bar graph uses bars to count, whereas the pictograph uses pictures to stand for a number.]

**Teacher Reflection**

- Which students could construct bar graphs and pictographs with minimal supervision? What experiences are necessary for those who could not?
- Which students could create pictographs? What experiences are necessary for those who could not?
- Which students could find the range, mean, median, and mode of a set of data? What learning opportunities are needed for those who cannot?
- Which students could pose appropriate questions that could be answered from a data set?
- What adjustments will I make the next time I teach this lesson?

### Learning Objectives

Students will:

- Create a bar graph and a pictograph from a given set of data.
- Find the mean, median, and mode of a given set of data.
- Find the range of a given set of data.
- Construct a box plot.

### NCTM Standards and Expectations

- Represent data using tables and graphs such as line plots, bar graphs, and line graphs.

- Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

### Common Core State Standards – Mathematics

Grade 3, Measurement & Data

- CCSS.Math.Content.3.MD.B.3

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step ''how many more'' and ''how many less'' problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP4

Model with mathematics.

- CCSS.Math.Practice.MP5

Use appropriate tools strategically.

- CCSS.Math.Practice.MP7

Look for and make use of structure.