Lesson 7

This warm-up helps students develop strategies to find multiples of 12 mentally using place value strategies and the distributive property. This prepares students for converting measurements in feet to measurements in inches.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How are the values of the products \(45 \times 12\) and \(46 \times 12\) related?” (There is one more 12 in \(46 \times 12\).)

The goal of this activity is to compare measurements in the customary length units of inches, feet, and yards. Students first sort the measurements in a way that makes sense to them. Monitor for students who:

• sort by the unit of measure
• sort by the way the quantity is written (whole number, mixed number, fraction)

Then, students find the equivalent lengths and list the sets of equivalent lengths in increasing order. Four different lengths have been chosen and each one is presented in inches, feet, and yards. The activity synthesis highlights why expressing all the measurements using one unit is a convenient way to identify common measures and list them in increasing order. Give students access to yard sticks. 

• Create a set of cards from the blackline master for each group of 2.

• Groups of 2
• Give each group of students one set of pre-cut cards.
• Display a yardstick.
• “What do you notice? What do you wonder?” (It shows feet and inches. It shows 36 inches. I wonder if it’s the same length as a meterstick.)

• “In this activity, you will sort some cards into categories of your choosing. When you sort the measurements, you should work with your partner to come up with categories.”
• 4 minutes: partner work time
• Select groups to share their categories and how they sorted their cards.
• Choose as many different types of categories as time allows, but ensure that one set of categories identifies the way the quantity is written (whole number, mixed number, fraction).
• “Now work with your partner to match the cards with equal measurements. Then, list the groups of matching measurements in increasing order.”
• 3 minutes: partner work time

• Invite students to share the matches they made and how they know those cards go together.
• Attend to the language that students use to describe their matches, giving them opportunities to describe how they know the measurements are equal.
• Highlight the use of phrases, such as:
  • There are 12 inches in one foot.
  • There are 3 feet in one yard.
  • To find (a fraction) of a foot, I multiplied 12 by the fraction.
• “How did you compare the sets of measurements? Why?” (I chose one of the units, feet, and compared all of the measurements in that unit.)
• “Why was it important for all of the measurements to be in the same unit in order to compare?” (That way I can just compare the numbers because they all have the same unit of measure.)

The goal of this activity is to solve multi-step conversion problems using customary length units. The given information for both problems is in fraction form. Students need to find the perimeter of the different fields and then investigate how many times around each field is a given number of miles. The first problem involves 3 steps:

• find the perimeter of the rectangular field
• find the total distance of 6 laps around the field
• convert from yards to feet or feet to yards

The second problem has only two steps, but the number of laps is unknown and students need to find how many laps make at least 2 miles.

When students critically analyze Priya's claim that six laps of the soccer field is more than a mile, they critique the reasoning of others (MP3).

• Before the lesson, figure out a location that students would be familiar with that is about 1 mile away from the school. You will share this location in the launch to help students understand how far 1 mile is.

• “About how far is a mile?”
• 1–2 minutes: quiet think time
• Record responses for all to see.
• Describe to students a location that is about a mile away from the school.
• “About how many feet are in a mile?”
• “What is an estimate that is too low? Too high? About right?”
• Record student responses in a table like this one:

  too low	about right	too high

• Display: There are 5,280 feet in one mile.
• Leave the display up throughout the lesson.
• “We are going to solve some problems about miles.”

• 7-10 minutes: partner work time
• Monitor for students who:
  • find the number of yards in a mile
  • convert yards to feet for the first problem

If students don’t have a strategy to solve the first problem, consider asking:

• “Can you represent a person running one lap around the field?”
• “How can you figure out the distance of one lap around the field?”

• Invite students to share their solutions to the first problem.
• “How did you find how far 1 lap around the field is?” (I multiplied the length and width by 2 and added them.)
• “How far is one lap?” (\(264\frac{1}{2}\) yards)
• “How far is 6 laps? How do you know?” (1,587 yards, I multiplied \(264\frac{1}{2}\) by 6.)
• “How did you find the product \(6 \times 264\frac{1}{2}\)?” (I multiplied 264 by 6. I know that \(6 \times \frac{1}{2}\) is 3 so I added that.)
• “Is 6 laps more or less than a mile?” (Less, because it’s less than 5,000 feet. Less, because a mile is more than 1,700 yards.)