## Body Measurements

• Lesson
3-5
2

People come in all different sizes and can be measured in lots of different ways. In this lesson, students can make their own fascinating discoveries and become aware of the concepts of ratio and proportion as they relate to measuring features of their own bodies.

As a whole group, introduce the idea of body measurements. This can be done in ONE of the following ways:

• Quickly review one the two other Illuminations lessons, Sizing Up or How Long? How Wide? How Tall? How Deep?, with questions such as "What did you notice about the measurements of (your arm) and (your leg)?" Be sure to pick two measurements that are equal or very close. Ask, "Do you think this is always true for every person?"
• Give a simple art lesson (or invite an art teacher) on how to draw a human body that is in proportion.
• Visit goldennumber.net. This web site has color-coded lines of measurement for the human body, face, and hand that provide a nice visual description of the mathematical task of this lesson.

The purpose of this introduction is to grab student interest in doing an investigation of body measurement ratios, so pick the "hook" that best fits your class and your skills. The introduction should only take 5‑10 minutes.

Then tell the students that they will be taking lots of different measurements to find out whether lengths and/or circumferences of body parts such as arms, legs, and necks are just random lengths or if they are related somehow. They will work independently but will sometimes need to request help from a partner. The measurements will be written on the Student Recording Sheet.

Before students get started, explain the My Measure activity sheet and model how to take the measurements accurately. Give special attention to the circumference measures, as many students may not be familiar with this. The teacher should model one of the tasks before students get started.

 My Measure Activity Sheet

Thinking out loud as you show an example will help students understand what to do. For instance, say, "Okay, I’m going to put the end of the measuring strip right here, at my wrist. Now, I’m going to lay the strip in a straight path along my forearm. I’m going to fold the paper strip at the end of my forearm so I know where to cut the strip. There, I cut the strip. Now I’ll measure it with a centimeter ruler. Let’s see, it’s about 27 cm. I’ll record that data on the chart."

• Use the paper strips to measure a body part. Cut the strip to fit as accurately as possible. (Measurements are never absolutely exact.) Paper strips can be taped together for longer measurements. Tape first and then use the longer strip for measuring; this avoids the problem of errors caused by overlapping strips.
• Use the ruler to measure the paper strip. Label the strip with the body part and the measurement (for later use).
• Record the measurement on the My Measure activity sheet.

To aid with classroom management, consider these suggestions.

• There are a lot of measurements to be taken. To save class time, have students get started during class and then complete their measurements as homework; or divide the class into three groups and assign the questions on the My Measure activity sheet as follows: Group 1, Questions 1‑3; Group 2, Questions 4‑5; Group 3, Questions 6‑7.
• For measuring faces, consider using close-up photos of the students. These will need to be taken and developed in advance of the lesson. Students can measure the photos rather than their faces.

Allow the students to get started and work for about 5-10 minutes. At that point, pull the class together to discuss what is going well and what problems the students are encountering. It’s better to address these concerns before too much class time has passed. This is also a good time to demonstrate the following relationships, which the students need to understand for the analysis portion of the lesson:

• "equal" – Show two paper strips, A and B. Have the students say, "A equals B in length."
• "half" – Show two paper strips, A and B. Fold B in half, cut on the fold line. Compare the whole strip (A) to the half strip (the new B). Have the students say, "A is twice the length of B" and "B is half the length of A."
• "one and a half times" – Show three paper strips, A, B, and C. Fold C in half, cut on the fold line. Tape C (half) to B. Compare B‑C to A. Have the students say, "B‑C is the same and half again as long as A" and "B‑C is one and a half times as long as A."

The teacher should model how this information applies in the actual measurement tasks. She could measure her forearm and upper arm, find that the measurements are "close enough" to conclude that they are roughly equal in length. That is, measurements of 26 cm and 27 cm are roughly equal since measurements are always a little imprecise.

• Construction Paper (cut into long 1" strips, about 20 per student), or Measuring Tapes
(Note that the numbers on a measuring tape may distract a student from the idea of finding a relationship among measurements. The use of construction paper strips is therefore preferred.)
Scotch tape
• Centimeter rulers, meter sticks
• Mirrors (enough for about a third of the class)
• My Measure Activity Sheet

Assessments

1. Collect the My Measure activity sheets. Note whether data is complete and reasonable.

• During the investigation, were students measuring accurately?
• During the investigation and analysis of the data, were students able to see the equal, double, half, and one and a half times relationships?

Note any students who were not able to easily see the first three relationships. Also note any students who were able to see the one and a half times relationship.

Extensions

1. Investigate the golden rectangle in art and architecture.
2. Research the Fibonacci number sequence and how it applies to body ratios.
3. Take digital pictures of pets (or other animals). Investigate to see whether animals have measurement relationships.
4. Visit http://goldennumber.net/body.htm. Go to "Do It Yourself." Experiment with the Golden Section Gauge, the Golden Grid, and the hand measurer.
5. Draw pictures of people using information learned in this lesson.

Questions for Students

1. These questions (and others) can be asked as the teacher circulates the room, during the sharing portion of the lesson, or at the end of the lesson as a writing prompt for math logs. What did you learn, notice, or wonder about when you were measuring?

• It was easier to do measuring with a partner.
• It was hard to measure things that aren’t flat or straight.
• I wonder if every measurement will change when I grow.]

2. Can you ever get an exact measurement of length or circumference? Why or why not?

[Possible answers for why you can never get an exact measurement are:
• It’s hard to know exactly where "the top of your head" is.
• Things like hair, jewelry, bandaids can change your measurements.
• Pulling the measuring strips tighter changes the measurement.]

Teacher Reflection

• How did your lesson address auditory, tactile and visual learning styles?
• Were concepts presented too abstractly? Too concretely? How would you change them?
• Did you set clear expectations so that students knew what was expected of them? If not, how can you make them clearer?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments, and were the adjustments effective?

### Learning Objectives

Students will:

• Use strips of paper or measuring tapes to measure length and/or circumference of various parts of their own bodies.
• Analyze the measurements for relationships such as equal to, twice the length, half the length, and one and a half times the length.
• Compare measurement data with other students’ data.