Both standard and nonstandard units are used to measure length in this lesson. Students are going to:
- find out which measurement units best convey length by comparing solutions to a problem.
- assess the appropriateness of using nonstandard units and the necessity of using standard units.

- What qualifies a tool or strategy as suitable for a particular task? 
- How accurate must calculations and measurements be?

- Equation: A number sentence where two expressions are equal. 
- Estimate: A smart guess.

- yarn cut into 3-foot pieces, one for each group of students and one for you
- extra uncut yarn
- scissors, one pair for you
- nonstandard measuring units, different sets of units for each group (large paper clips, small sticky notes, jumbo clothespins, regular-sized unsharpened pencils, long straws, etc.)
- nonstandard measuring units for you that are similar to those given to each group but are of different sizes (small paper clips, large sticky notes, tiny clothespins, short pencils, stirring straws, etc.)
- paper and writing pencils for each group
- various uniform sets of play money (such as 8 pennies, 8 nickels, 8 dimes, 8 quarters), one set of 8 coins per student
- Murphy, S. J. (1998). Super Sand Castle Saturday. HarperCollins.

- Watch the students make sure they are laying their units out end to end without any overlaps or gaps when they measure. Ask groups to double-check their measurements if you see them committing these mistakes. Please help them understand the significance of the yarn being pulled straight and the necessity of touching units. Direct control over student work will make it easier to identify those students who might benefit from additional guidance or practice.

Modeling, explicit instruction, scaffolding, and active engagement 
W: Tell the class that you have a piece of yarn cut to the desired length that you want to use to build a bookshelf. Instruct pupils to measure the yarn and then "call" a lumberyard to make an order for a board that is the right size for the shelf. 
H: Split the class up into groups and give each group a piece of yarn and an unconventional measuring device. After measuring the yarn, have each group share the resultant length. Take a similar-looking but different-sized yarn length measurement and observe the discrepancy. 
E: Repeat the exercise using different measuring tools and groups. Change the size of the tool you use; it can be longer, shorter, or the same. Ask students to predict if the yarn you cut will match theirs exactly, be longer, or shorter. 
R: Ask students to recommend alternate measuring devices that can guarantee a precise size match and be uniform for all users. Give out tape measures, rulers, and other tools, and take another measurement of the yarn. Use standard measurements to communicate the findings of their research. 
E: Talk about the observations that the students made using this exercise. Determine when using nonstandard units of measurement is permissible and when using standard units is required. 
T: Give students an unconventional measuring tool to use in estimating the length of an object in the classroom. Ask students to decide whether to measure an object using a standard or nonstandard measuring unit. 
O: This lesson aims to give a practical problem that establishes a reason for measuring length, which is commonly represented by height. After experimenting with nonstandard units of measurement, students learn that standard units are required. They understand that everyone must be able to convey their message using the same referents—in this case, standard units of measurement—as they update their measurements using these units. 

"Today, I need your help. I made the decision last night that I needed a new shelf to store some books. I measured the length of this yarn to match the desired shelf and determined the ideal location for the shelf. To construct the shelf, I must now call Home Depot and ask someone to cut a board. To let the retailer know how long the board should be, I need your help measuring the length of the yarn. I'll cut a piece of yarn the same length as the one I cut last night for each group. Using the tools I give you, you'll measure the length of the yarn. Before beginning to measure, remember to pull the yarn straight and tight."

Assign students to groups of three or four. Provide a length of yarn, a set of nonstandard units, a sheet of paper, and a pencil for recording results for every group. Give the groups enough time to work. Groups should move around to check if they are pulling the yarn straight, placing the units end to end, and estimating if they don't reach exactly from one end to the other.

Regroup the students into a single, sizable group. "Let's make sure that when I call, the lumberyard clerk will comprehend my directions. Assume that I am a store employee and that you are going to advise me on the ideal length of the shelf. I'll attempt to precisely cut a length of yarn to symbolize the board."

Invite a single group to present its measurement.

"Could you pretend to call me Ava? Tell me you'd like to build a shelf and that you'll need a precisely sized board. Next, based on your most recent yarn measurement, tell me how long it should be." Turn your hand into a "phone" and strike up a discussion with Ava.

Teacher: "Hey, Home Depot. How may I assist you?

Student: "Hello. I need a piece of wood to build a shelf. It should be 25 paper clips long."

Teacher: "All right, I'll chop that up and get it ready for you. Good-bye."

Take out a small paper clip box. Cut a 25-clip length of yarn after measuring it. To check if you made it to the proper length, compare your piece to the student's. Pretend to be confused about the discrepancy and suggest that maybe you should try using something else. 

"Wow. I need a much longer shelf than that board would provide. Let's give the store employees a different measurement when we give them another call. Perhaps this time will be correct."

Use "phone calls" from various student groups to repeat the exercise. Use longer units for some demonstrations and shorter ones for others, depending on which ones the student utilized. If the group was using regular-sized, unsharpened pencils, for instance, take out a much shorter, previously sharpened pencil. Additionally, make equal lengths of yarn using a few units that are the same as the group.

Discuss the observations students make as you cut such a wide range of yarn sizes. As soon as students realize that you are not using the same units as they were, ask them to predict if your yarn piece will be the same as theirs, shorter, or longer.

"Now, I'm at a loss for what to do. I can't guarantee that the store will use a pencil the same size as mine if I call and ask for a board that is eight pencils long. So, what should we do?"

Students may suggest alternative units or measurement tools. Ask them to carefully evaluate each to see if there is a possibility that someone is using a different measuring tool or different-sized units. Give the common units that students use—inches, feet, and centimeters—the majority of your attention since they are universally understood. Show that the markings on the ruler, yardstick, and tape measure are the same (an inch on the ruler is an inch on the tape measure), if you have any of these tools. Make sure the object to be measured is properly positioned with the tool, and emphasize the significance of using the tools correctly.

Another thing you could mention is that quarters are about an inch wide, and US dollar bills are always six inches long, so two of them put end to end would make a foot. Therefore, in the absence of a ruler, we could even measure things with money.

"Let's try measuring our yarn once more so I can get a board that fits the shelf precisely. I'm positive the lumberyard clerk will have the same tools, so let's use these this time (referring to the standard units)."

As you divide the class into groups, give each group a new standard unit (a ruler, tape measure, model dollar bills or coins that are life-sized, etc.) along with their piece of yarn. Give time for fresh measurements, then report the findings. Select a small number of groups to receive "phone calls" from, each with a different unit. This time, you will cut each piece of yarn the same size as the pieces in the groups, with a tiny allowance for any stretching of the yarn. Additionally, students will start to understand that identical-sized yarn pieces can be produced by utilizing various but consistent units. (A yarn piece that measures three feet in length is equal to six dollar bills in length.) After completing these exercises, students should talk about what they saw. Find out if it's acceptable to take approximate measurements using nonstandard units like paper clips, shoes, or fingers. The majority of students have observed adults using their hands or strides to measure distances. Students must comprehend when using nonstandard units is acceptable and when using standard units is required.

Extension:

Throughout the year, adapt the strategies and activities listed below to your students' needs.

Routine: Pick a piece of equipment, like a table or whiteboard, that has a length that is simple to measure in the classroom. When students enter the classroom on one or two mornings a week, present them with a nonstandard unit. Place a stack of tiny papers—one for each student—beside the item. Give students a length measurement of the object and ask them to estimate how many nonstandard units would fit across it. They should then write their estimate on paper. If more than one student has the same estimate, count the marks beneath the number and write the estimates on a whiteboard from least to greatest. Select a student or two to use the measuring device to determine the true length. Students will learn that the size of the measuring unit dictates how many units will be required by conducting measurements with the same assigned object but a different unit of measurement.

Small group: Some students may benefit from additional learning opportunities. Assign these students some objects to work with, like books, desks, flags, rugs, markers, pointer sticks, etc., and then arrange some standard and nonstandard units like paper clips, pennies, rulers, yardsticks, and 1-inch tiles.

Students should decide which unit of measurement would be most appropriate. Is it sensible to measure a large whiteboard with pennies? Do they have to measure the marker with a yardstick? Ask each student to select a unit of measurement and an object to measure. Help students understand that the measurement units we use must have a logical and practical meaning. Although we wouldn't use paper clips to measure the length of our classroom, we could use them, for instance, to measure the length of our shoes.

Expansion: To complete this exercise, give each student a uniform set of the following coins (play money): eight pennies, eight nickels, eight dimes, and eight quarters.

Check out Stuart Murphy's book Super Sand Castle Saturday if it's available. This book serves as an example of why it is crucial to compare the sizes of sandcastles kids have constructed for a contest using uniform measurement units. Make note of the requirement for the measuring units to be in contact with each other for accuracy.

Provide each student with an 8.5" x 11" piece of plain paper and a set of eight play money coins after they have discussed the book or a scenario similar to it. Have them each draw an eight-coin-tall tree. Work for a while, then compare the drawings. Do trees vary in size among individuals? Which ones are higher up, and why? Which ones are shorter, and why?