Measure with Nonstandard Units

Est. Class Sessions: 2–3

Developing the Lesson

Part 1: Measuring with Palms

Make a Unit Palm. Read aloud the book Actual Size by Steve Jenkins. As you read, discuss the sizes of various animals and their body parts. Upon finishing the book, tell students that they will be using their body parts to measure different objects.

Show students your hand with your fingers closed and your thumb open or perpendicular to your fingers. See Figure 1. Ask students to show you their hand in the same fashion. Show students the distance across the palm, or the width of the fingers. Tell them that this distance is called a palm. Show students the gorilla palm on the cover of the Actual Size book.

Ask:

Look at the gorilla's hand. How would you measure this gorilla's palm? (I would measure across the palm, just like on my hand.)
Who would like to trace my palm?

Ask a student volunteer to trace your palm onto the sheet of paper you have displayed. Cut out the tracing of your hand and use a ruler or straightedge to draw a line across your palm. Write your name on your palm tracing. See Figure 1.

Give each student a sheet of drawing paper and a ruler. Ask them to work with a partner to trace their palm and cut it out. Students should then label their palm unit with their names and draw a directional line. Then ask students to repeat this process two more times so they have three unit palms. Ask students to put two palms away and keep one out on their desks.

Find a Distance of One Palm. Show students one of your unit palms again and walk around the room comparing distances to your one palm unit.

Ask:

Is this distance more or less than one of my palms?
What do you think I should do about the thumb? (It is not included in the measurement.)
Look at my palm unit. What distance might be one of my palm units?

Eventually compare your palm unit to one of the distances equal to your palm unit that you identified prior to the lesson. See Materials Preparation. Attach your palm to that distance. For example, the width of the doorframe is equal to one palm unit.

Now ask students to find a distance in the room equal to one of their palm units.

As students wander the classroom looking for distances, ask:

Is the distance exactly one palm?
Is the distance larger than one palm?
Is the distance smaller than one palm?
Show me how you are using the palm unit to measure the distance.
Do you think all of us will find the same things? (Possible response: Your palm is larger than mine, so I have to try distances that are shorter.)

Once students have identified a distance equal to one of their palm units, ask them to attach the unit to the distance with a piece of tape. When students are finished they should return to their seats. Ask students to look around the room searching for palm units.

Ask:

What distance did you find that was one palm unit?
Did anyone else find that distance to be one of his or her palm units?
Did everyone find that distance to be one of his or her palm units? (Possible response: No, mine did not work there. My palm was too small.)
Are all the palm units the same? (No, because we are not the same size and our hands are different sizes.)
Tell your neighbor about something in the room that is shorter than one of your palms.
Tell your neighbor about something in the room that is longer than one of your palms.
How would I measure a distance a lot longer than one of your palms? (Possible response: I would line up several of my palm units.)

Measure with Palm Units. Ask students to place the two palm units they prepared earlier on their desks. Give each student a sheet of drawing paper and ask him or her to use the two palm units to measure the length of the long side of the paper. Give students a few minutes to experiment with this task.

As students are working, ask:

What are you doing about the thumb? (Possible response: I'm ignoring the thumb.)
How did you decide if the length is closer to [3 or 4] palms? (Possible response: I think less than half of my palm covers the paper so the length is closer to 3 palms.)

Removing the thumb from the palm unit may help some students focus on the palm.

After students have finished measuring the length of the paper in palms, ask a student to show other students how they found their measurement. See Figure 5.

Ask:

Did you measure the length of the paper the same way [student name] did?
Do you think you all have to measure the same way?

Line up your palm units on the display. Place the heel of one of the palm units above the tip of the fingers on the other palm unit to measure the length of the drawing paper. See Figure 6.

Ask:

I saw someone measure the length of the paper this way. Did they measure the length in palms? (No, they did not. The palm unit is across the hand not the length of the hand.)
What advice would you give this person? (Be sure the units are lined up in the correct direction.)

Line up your palms on the display, but overlap the palms some. See Figure 7.

I saw someone measure the length of the paper this way. What advice would you give this person? (Possible response: Be sure the units do not overlap.)

Record these and any other initial ideas students have on a sheet of chart paper titled "Measurement Advice." See Figure 8. Additional ideas will be added later in the lesson. Display this chart for the remainder of the unit as it will be referred to in later lessons.

Direct students' attention to the Measure with Palms pages in the Student Activity Book. Review the list of distances to be sure all students know which distances are being referenced. For example, students must be clear about which board length they are to measure. It is important all students measure the same distances so comparisons can be made.

When students are ready, ask them to measure the distances listed in Question 1 using the two palm units they cut out earlier.

After students are done collecting their measurements, ask:

Do you have any other measurement advice to add to the chart?
Do you think everyone got the same measurement for the length of the board? (no)
Why or why not? (Possible response: Everyone does not have the same size palm.)

Measure with Gorilla Palm Units.

Show students the gorilla palm on the cover of the Actual Size book.

Imagine a gorilla came to our class to measure the distances with her palms. What would her measurements be like? (Possible answers: She will get smaller numbers. She will have to do it fewer times.)

The gorilla palm on the cover of the Actual Size book is larger than Gloria's palm. To make this activity easier to manage, a similar and smaller image was made as a Master. If you wish to use the actual size of the gorilla palm, trace and make copies of the image from the book cover.

Distribute copies of the Gloria the Gorilla's Palm Master and ask students to cut it out. Tell students they are going to measure the same distances with Gloria's palm.

Ask:

Compare your palm to the gorilla's palm. How are they the same? (Possible response: They are the same shape. They each have four fingers and a thumb.)
How are they different? (Possible response: The gorilla's palms are larger.)
I measured the length of a sheet of paper to be [4] of my palms. About how many gorilla palms will equal the length of the paper? (Possible response: 2 or 3; less than mine)

Ask students to measure the previously measured distances but this time with gorilla palms. Students should work with a partner to place one palm next to the other repeatedly for each length. Students will record these measurements on the Measure with Palms page in the Student Activity Book.

Approximate Measurements. As students measure, many times their measurements will not end exactly at a whole unit. At this age level, it is acceptable for them to report their measurements rounded to the nearest whole unit, half unit, or even quarter unit depending on their level of expertise with both measurement and describing parts of a whole. However, for data analysis purposes, students are asked to record their measurements to the nearest whole unit. Students will need to decide if it makes sense to describe the measurement in terms of another whole unit. These decisions are typically made in an authentic situation (e.g., Do I have enough ribbon? How much ribbon do I need?). Guide students to understand whether the measurement should be rounded up or down. In this less-than-authentic situation, students can either say the measurement is closer to the larger number of units or closer to the smaller number of units.

Compare Palm Measurements. Once students have finished collecting their measurements, ask them to work with a partner to complete Questions 2–5 while they wait for others to finish.

Once everyone has collected his or her measurements, ask:

Do you think we all found the same measurement for the length of board using gorilla palms? (Possible response: They all should be about the same since everyone used the same unit.)
Look at the gorilla palm measurements. How do they compare to your palm measurements? Why? (The measurements all have smaller numbers because the unit is larger.)

Ask students to complete Questions 2–5 with their partner, then ask:

Which unit did you use to answer Question 2? (Possible response: my palms; gorilla palms)
If you did not use [my palms] for Question 2, did it change the length? (Possible response: No, it just changed the measurement.)

Continue to discuss student responses to Questions 3–5. Ask students to share their reasoning to the "could be" or "crazy" statements in Question 5.

Adventure Book:

Student Activity Book: 173 174

Answers