Lesson 8
What is an Inch?
Warmup: Notice and Wonder: Inches and Centimeters (10 minutes)
Narrative
The purpose of this warmup is to elicit the idea that there is a unit of measure that is longer than a centimeter but is still small—an inch. This will be useful when students are introduced to customary units beginning with the inch tile and the inch ruler. While students may notice and wonder many things about these images, the difference in the length between tick marks on the rulers (the lengthunit) is an important discussion point.
Launch
 Groups of 2
 Display the image.
 “What do you notice? What do you wonder?”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Share and record responses.
Student Facing
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
 “How are these images the same? How are they different?” (They both look like rulers. They both start with 0 and count up. One of the rulers lines up with the square from 0–1, but the other ruler does not show the same length unit.)
 “We have learned that there are different length units we can use to measure. We have measured with standard units from the metric system like centimeters and meters. In the next activity, we will learn more about a new standard unit that is longer than a centimeter, but much shorter than a meter.”
Activity 1: What is an Inch? (25 minutes)
Narrative
The purpose of this activity is to introduce the inch as a length unit in the U.S. customary system. In the launch, students use inch tiles and classroom objects that are “about an inch” to help them develop a benchmark for an inch. They may continue to use the inch tile to measure lengths in inches or as a tool for checking their measurements with a ruler throughout the lesson.
Although students have measured objects that are not a whole number of length units long in previous lessons, it will be more likely that students will measure lengths that are clearly not a whole number of inches long. Students should not record measurements to the half inch, but should instead discuss the reasoning they use to decide which whole number to use and the language they use to express that their measurement is not exactly that number of inches long (MP3, MP6).
Supports accessibility for: Attention, Memory
Required Materials
Materials to Gather
Required Preparation
 Each group of 4 needs access to several objects between 1–11 inches long. Consider using classroom objects such as markers, colored pencils, 11 connecting cubes, books, or any other object with a length shorter than 12 inches.
Launch
 Groups of 4
 Give students access to inch tiles and 12inch rulers.
 Display image of an inch tile and a ruler.
 “What do you notice about this image? What do you wonder?” (The square fits between the 0 and the 1 on the ruler. The length of the side is the same as the length from 0 to 1 on the ruler. What is the name of the length unit? Does the square have a special name like the centimeter cube did?)
 1 minute: partner discussion
 Monitor for students who say the units don’t look like centimeters or who wonder if it’s an inch.
 Share responses.
 “You have learned how important it is to have standard units of measure.”
 “We have been working with metric units—centimeters and meters—that are used around the world.”
 “In the U.S., our measurement system is called the customary system. An inch is the smallest unit for measuring length in our system.”
 Hold up an inch tile.
 “This is an inch tile. The length of each side of the square face is 1 inch.”
 As needed, invite students to use their rulers to verify that each side of the square face of the tile is 1 inch long.
 "What are some things you can think of that are about an inch?”
 1 minute: quiet think time
Activity
 “Use your tile to find 2 things around the classroom that are about an inch long and write them down.”
 3 minutes: independent work time
 Share and record responses.
 “Now you are going to measure a few objects around the room using an inch ruler. For each item, record the length in inches.”
 5 minutes: smallgroup work time
 Monitor for a student who measures an object that is not a whole number of inches.
Student Facing

Find 2 items that are about an inch long.

________________________________________
 ________________________________________

 Measure the length of each object.
object to measure  length in inches 

marker  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
colored pencil  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
11 connecting cubes  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
a book  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
your choice objects:  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
\(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)  \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) 
Student Response
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Advancing Student Thinking
Students may measure the correct number of length units, but record the length in centimeters or meters. Consider asking:
 “How long is the ___? How do you know?”
 “If I used the inch tiles to measure the __, would I find the same measurement?”
 “If I used centimeter cubes to measure the __, would I find the same measurement?”
 “How could you revise your measurement to show the accurate length?”
Activity Synthesis
 Share a student’s object that is not a whole number of inches long.
 “How can we describe the length of the _____ when its end doesn’t line up with one of the inch marks on the ruler?” (If it is close to 3 inches, I can write “about 3 inches.”)
 1 minute: quiet think time
 Share responses.
Activity 2: Measure the Sides of Shapes (10 minutes)
Narrative
The purpose of this activity is for students to estimate and measure in inches. Students first estimate the length of given sides of shapes and then measure the sides using inch rulers. In the activity synthesis, students share how they measured the different sides and continue to discuss how to communicate the measurement of lengths that are not clearly a whole number of units long (MP6). They also make sure to indicate that their measurements are in inches since students now have both centimeters and inches they can use to measure lengths.
In the lesson synthesis, students discuss how they might measure longer lengths in inches. The discussion is designed to elicit their experiences with centimeters and meters and build curiosity for the next lesson in which students measure in feet.
Advances: Speaking
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to inch tiles and 12inch rulers.
Activity
 “Now you will get a chance to practice measuring the sides of shapes.”
 “First, estimate the length of the side and record your estimate. Then, measure each side, and record your responses. Don’t forget to include the unit, inches.”
 6 minutes: independent work time
 “Now compare your measurements with your partner’s.”
 2 minutes: partner discussion
 Monitor for students who recognize that the third problem has a measurement that is more than 5, but not quite 6 inches.
Student Facing

Here is a rectangle.
How long is the long side of the rectangle in inches?
Estimate: ____________
Measure the long side of the rectangle.
Actual length: ____________

Here is a square.
How long is a side of the square in inches?
Estimate: ____________
Measure one side of the square.
Actual length: ____________

Here is a triangle.
How long is the longest side of the triangle in inches?
Estimate: ____________
Measure the longest side of the triangle.
Actual length: ____________
Student Response
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Activity Synthesis
 “I noticed that some students had different measurements for the longest side of the triangle. Why do you think that is?” (It was less than 6, but more than 5. It was in between 5 and 6 inches.)
 Invite previously identified students to share their reasoning for 6 inches.
 “Sometimes, the object we are measuring will have a length that falls between 2 measurements on the ruler. Choose the number that is closest to the end of the object. Sometimes the length of the object in inches may be longer or shorter than the actual length.”
Lesson Synthesis
Lesson Synthesis
“Today, we used inch tiles and rulers to measure the length of objects and sides of shapes in inches.”
“How was measuring in inches the same as measuring with centimeters? How was it different?” (It was the same as measuring with other units. We used our rulers the same way. If you used inch tiles, you lined them up from one end of the other with no gaps or overlaps like other units. It was different because an inch is longer than a centimeter. An inch tile is longer than a centimeter cube. Our measurements were smaller. It doesn't take as many units to measure some of the same things we measured before.)
“About how long do you estimate the bookshelf will be in inches?” (It would be a lot of inches—maybe 100.)
Choose a bookshelf or whiteboard in your classroom for students to base their estimates on. Student estimates will vary based on the furniture available in your classroom.
Cooldown: Measure a Rectangle (5 minutes)
CoolDown
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