Students will measure various rectangles' lengths during this lesson. Students are going to:
- acknowledge the characteristics of length.
- sort and compare shapes based on these characteristics.
- utilize standard units when measuring.
- create common measure referents.

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

- Centimeter: A metric standard unit of measurement. 
- Estimate: A smart guess. 
- Inch: A standard unit of measurement.

- Rectangles of different sizes (1 per every 4 students or so) created by using masking tape on the floor in several spots throughout the classroom. Be sure to have some with lengths longer than one ruler. Be careful to make them exact whole-number measurements, not measurements involving ½ or ¼.
- inch rulers, one per student
- centimeter rulers, one per student
- 1-inch square tiles or 1-inch squares of paper; at least 1,000
- copies of the Lesson 2 Recording Page (M-2-7-2_Lesson 2 Recording Page)
- Lesson 2 Ticket Out the Door (M-2-7-2_Lesson 2 Ticket Out the Door)

- Gather the recording pages. Use the given standard units to verify accuracy. Assess which students are prepared for more challenging work and which ones require more experience with basic measurement activities.
- Give students Lesson 2 Ticket Out the Door (M-2-7-2_Lesson 2 Ticket Out the Door) to complete to gauge their comprehension of nonstandard and standard units of measurement.

Explicit instruction, modeling, scaffolding, and active engagement
W: Use masking tape to create rectangles on the floor in different sizes for a length-related exercise. Use a sticky note to mark them: Triangle A, Triangle B, Triangle C, Triangle D, and so forth.) 
H: Instruct students to measure the rectangles in centimeters and inches. Arrange the rectangle names on sticky notes in descending order of recorded measurement on a board. The length of the rectangles will increase the number of inches and centimeters. 
E: After talking about how they measured the length of larger shapes, students will move on to talk about other units of measurement, like yards and meters. They will then ascertain whether additional tools are needed to make the tasks more efficient. 
R: Assign students to locate items in the classroom that are comparable in length to their rectangle. 
E: Ask students to come to the group with their recording sheets. Assign students to groups or pairs to talk about rectangle measurements. Discuss which measurements were most useful in determining the proper rectangles. 
T: Students who are at risk for failure should practice with rectangles that are the same length as their ruler or other tools, or slightly shorter. Instead of leaving space between the end of the tools and the beginning of the 0—if at all possible—use rulers with ends that are 0. 
O: This lesson starts with measuring length, which the students are already familiar with. Next, it introduces them to selecting the appropriate measuring instruments. Students are asked to find relationships between both standard and nonstandard units, which serve as referents. 

Break up the class into smaller groups. "We're going to do a math discovery activity today, and each group will work with one rectangle. We are going to use our rectangles to learn about length." Assign student groups to their designated rectangles.

Remind the students of the definition of length and how to measure it. Distribute different nonstandard units to every group so they can measure. Give teams the option to select the nonstandard unit they want to use. Good options would be pencils, paper clips, erasers, coins, scissors, crayons, or sticky notes. "Each group will use the nonstandard unit to determine the length of the rectangle. Remember to measure from the end of the nonstandard unit. Do not forget to measure the rectangle lengthwise. To ensure there is no error, several individuals from each group should measure the rectangle. There will be a recording page for you to record your work." Distribute the lesson 2 recording page (M-2-7-2_Lesson 2 Recording Page). Look over students' measurements to make sure they are accurately recording them and measuring across the longest part of their rectangle. Encourage students to note the unit name on their recording sheet as they measure using the nonstandard unit.

Ask students to use a centimeter ruler to measure their rectangles again after they're done. "Everyone, get your rulers out. You will measure the rectangle's length for your group and enter the results in the table in number 2."

After the students have completed using the rulers, gather the class again and have a representative from each group stand in a line with a sticky note that has the group's rectangle name and length written on it. Encourage them to collaborate to line up the rectangles from shortest to longest.

"Now let's examine the numbers you entered, which indicate the length of your rectangles in centimeters. What do you notice about the numbers as you look at them, beginning with the smallest rectangle and working your way up to the largest rectangle? What is the difference between them and the nonstandard unit numbers you recorded?"

If you compare two rectangles using just inches or any other standard unit, you'll notice that the numbers go from smallest to largest. Talk about the recorded numbers for the nonstandard units. Here are some examples of discussion questions:

"Are these numbers in descending order? Why not?"
"Will a rectangle measuring two scissors be longer or shorter than a rectangle measuring three crayons?" (The length of the crayons and scissors would determine that.)
"Which is simpler to compare, inches or paperclips? Why ?"
"We're going to compare our rectangles now using an alternative measurement. We are going to utilize inches in our work. Flip your rulers (or distribute individual inch rulers). When comparing inches to centimeters, what differences do you observe? You're going to calculate the length of your rectangle in inches. Discuss the estimation process with your group, then write the estimate down on the recording page."

Assign students to speak in groups. Remind students that these are just estimates and that they shouldn't be using rulers just yet. Make sure every student records their estimate on the recording page by going around the room.

"You will have time to use the inch side of your ruler to determine the length now that you have made your estimates."

Give students enough time to complete their work. Walk around and watch how the students measure rectangles, paying particular attention to how they measure lengths greater than one ruler. Before putting the ruler down again, are they marking the spot where they previously had the end? When their ruler runs out, do they not know what to do? Help students learn how to stay on task by having them mark a spot on the rectangle and then using the ruler to continue from that point on. Which unit of measurement is more efficient, and why? Students should fill out the recording page with their measurements.

Ask students how they could determine the lengths of the other three sides of the rectangle using only one measurement to expand on this exercise and up the ante. (By measuring one of the shorter sides, they were able to use the rectangle's properties to determine that the other shorter side and the longer side would be equal to each other.)

Ask students to bring their completed recording pages to you after class. Use a sticky note or whiteout to cover the letter or label after selecting one for each rectangle.

"We're going to engage in a guessing game right now. Each of you will circle the room, examining the recording pages that are on display, and attempt to compare the dimensions with the new rectangle that I give you. Take the previous sticky note and hold it up while standing next to the matching rectangle when you believe you have found a match. We'll determine if someone's guess was accurate at the end, so don't tell anyone."

Give the students a few minutes to examine the rectangles and record pages while they move in groups around the room. For each rectangle they are assigned, students must make an educated guess as to which recording page best fits the description.

Ask each group individually if anyone correctly guessed their rectangle as you go around the room. He or she should hold up the sticky note (or recording sheet) if the group responds, "Yes." Proceed to the next group if the student responds negatively.

Discuss which measurements helped students make the best guesses. Did they search for measurements with more length and area if they were in a long, wide rectangle? Were the little rectangles harder or easier to guess?

Extension:

To meet your students' needs throughout the year, implement the strategies and activities listed below.

Routine: Hang pictures in the room that illustrate various rectangles measured in standard and nonstandard units to provide extra practice. Consider measuring a red rectangle with paper clips or macaroni, or a blue rectangle with coins or counters. Ask students to estimate the length of a picture you've chosen at random. Next, ask them to estimate how many square inches are inside the rectangle. As a result, students will become more adept at estimating and more at ease using a variety of measurement units to determine area.

Workstation: Set up stations where students can measure using a variety of nonstandard units, such as beans, index cards, and 1-inch color tiles. For instance, at one station, students could draw around their hand (all fingers together) and then measure the distance from palm to tallest finger using beans and a standard unit. Using paper clips or popsicle sticks, a workstation could hold five or six books of wildly different sizes for comparison.

Expansion: Give students the task of calculating rectangles' perimeters. Before letting the students work on their own, explain the perimeter-finding procedure and demonstrate it to them. Help students develop addition techniques so they can quickly determine the rectangles' perimeters.