GO IN DEPTH

#### Materials

• Tape measures (and other measuring devices, such as rulers and yardsticks)

### Purpose

To gather and analyze data. To review measurement and graphing.

### Context

Before doing this lesson, students should have had many opportunities to experiment with the process of measuring. They should have explored various materials with different kinds of measuring tools without any focus on particular units of measurement, measuring accurately, or understanding differences between kinds of measurement (length versus weight, for example). This exposure to measuring in an exploratory environment familiarizes children with the concept and tools of measurement.

Once students have this familiarity, they are ready to be introduced to the idea of units of measurement. Students should measure with the idea of units in mind and then be challenged to consider why it is important to have standardized units of measurement. From here, students will measure with standardized units and compare conclusions with one another, beginning to more formally analyze data.

In this lesson, students will build on previous experiences and measure each other’s wingspan, and record and analyze the data.

### Motivation

To review measurement and estimation skills with your students, see Cool to Rule: A Game of Prediction and Measurement. Lead your students through the activity.

After students complete the activity, ask questions such as:

• What helps you guess (predict) the size of something?
• What tools did you use for measuring?
• What else in the classroom could you use for measuring?
• If you had to measure the length of the classroom, what would be a good unit to use?
• What if you had to measure the length of a pencil? What would be a good unit to use?

### Development

Ask students to define the term, "wingspan."

They will likely use a bird as an example, defining wingspan as the measurement from the tip of one wing to the tip of the other when the bird is flying, or when the wings are outstretched from the body.

Ask students how wingspan relates to humans. Explain that human wingspan (armspan) can be determined by measuring between the tips of the longest fingers when the arms are outstretched from the body at the shoulder. Have students model their own wingspan.

Ask students what units they think would be good to measure wingspan. Why? Tell them that for the remainder of the lesson they should measure in inches.

Distribute the What’s Your Wingspan? student sheet. Have students work with a partner, following the instructions to measure each other’s wingspan and height (in inches). When students finish collecting the data, record the class set of data at the front of the room.

After the class data is recorded, ask questions such as:

• Why is it important to indicate the units used?
• What is the range of wingspans? Of heights?
• What do you notice about the differences between wingspan and height? Is there typically a big difference? A small difference?
• How many people have the same wingspan and height measurement?
• How many people have a wingspan measurement that is one inch different from their height measurement? Two inches?
• What conclusions, if any, can you draw from the data collected?
• Can you make generalizations based on a small amount of data?
• What errors did you possibly make while measuring and recording the data? How could you take more accurate measurements next time?

There are many different ways of looking at the data, and each will give you slightly different information about it. If you have a large enough group (roughly 10 or more) to analyze, you will usually find that the greatest number of students have wingspans equal to their heights. Measurements that differ by one or two inches are also very common.

Ask students how graphing the information would make it easier to answer questions about it (questions such as those above), including supporting the claim that for most students in the class, wingspan is nearly identical to height.

Now, depending on your students, either have students independently develop a graph to depict the relationship (the difference) between wingspan and height, or use the Class Data: Wingspan and Height teacher sheet to create a class graph of the data. (You could print this ahead of time and make a transparency of the graph.)

To use Class Data: Wingspan and Height, have each student add his or her own data by marking an X in the column describing the difference in his or her wingspan and height.

### Assessment

Have students analyze the graph, focusing on the central idea of the relationship between wingspan and height for students in this class.

Ask questions such as these questions:

• Why was it important to use the same units for measuring wingspan and height?
• Why was it important for the entire class to use the same units?
• What conclusions can you draw about the data?
• Does the graph support the conclusion that for most people in the class, wingspan is nearly identical to height? Why or why not?
• How was the data easier to analyze when depicted in a graph?
• What other graphs could you create in order to answer other questions about the data? What if you wanted to easily find out the average wingspan for girls? For boys? Or the average wingspan for people of a certain age?
• What could you do to make a more general conclusion about the relationship between wingspan and height?

Students could make different graphs to answer different questions about the data. They could compare various graphs and decide which was the best representation of the data, and why.

### Extensions

Patterns in Mathematics is a website from Annenberg/CPB Math and Science Project that explores patterns as they occur in language and numbers.