Lesson 15

This warm-up prompts students to carefully analyze and compare length measurements given in different units, reminding about the relationships between yards, feet, and inches. In making comparisons, students need to attend to both the meaning of each unit and its relationships to other units.

• Groups of 2
• Display the four measurements.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “All four quantities measure lengths. What do you notice about these lengths?” (They are in different units. Three of them are equivalent to 1 yard, and one of them is 3 yards.)
• “If we convert the quantities that are equivalent to 1 yard into feet, what will they all be?” (3 feet)
• “What if we convert them into inches?” (36 inches)

In this activity, students analyze length measurements, perform multiplication, and convert distances from yards to feet in order to compare and order them. The quantities in yards involve only whole numbers while those feet involve fractional amounts, to encourage students to convert from the larger unit to the smaller one.

• Groups of 2
• Consider asking students if they have played frisbee or another game that involves tossing an object. Alternatively, display a video clip of a frisbee game or a frisbee being tossed, or display a frisbee.
• Display the table. “What do you notice? What do you wonder?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Read the opening paragraph and the bulleted information in the activity statement.
• “Let’s find out who the top frisbee throwers are in this group of friends.”
• Display a yardstick and a foot-long ruler, if available.

• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who convert all the given distances into feet before finding the missing distances and ordering the measurements.

Students may be unsure how to find Elena’s throwing distance because it requires multiplying a mixed number by a whole number (\(3 \times21 \frac{1}{3}\)). Ask them if it’d help to consider the whole number (21) and the fraction (\(\frac{1}{3}\)) separately (and multiply them separately).

Students may rewrite \(21\frac{1}{3}\) as \(\frac{64}{3}\) and multiply it by 3 to get \(\frac{192}{3}\), but may not know how this number compares to other distances because of its fraction form. Encourage them to think about what whole number this fraction approximates, or reason using smaller fractions with denominator 3. For instance, ask, “How much is \(\frac{30}{3}\)? \(\frac{60}{3}\)? \(\frac{150}{3}\)?”

• Display the tables from the activity.
• Select students to complete the first table and share their reasoning.
• Then, select students to share their strategies for putting the distances in order. For each strategy, ask if others in the class reasoned the same way.
• “Tyler’s throw was 17 feet and Han’s was 17 yards. Can we tell who threw the frisbee farther without converting one unit to the other? If so, how? If not, why not?” (Yes. We know that 1 yard is greater than 1 foot, so 17 yards must be greater than 17 feet.)
• “How many times as far as Tyler’s distance was Han’s distance?” (3 times as far) “How do you know?” (A yard is 3 times as long as a foot, so 17 yards is 3 times as long as 17 feet.)

In this activity, students apply their knowledge of multiplicative comparison and ability to convert feet and inches to solve a logic puzzle. They use several given clues to determine the heights of four objects. As they use the clues to reason about the heights of the towers and who built them, students reason abstractly and quantitatively (MP2).

This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing

• Groups of 4

MLR5 Co-Craft Questions

• Display only the opening paragraph.
• “Write a list of mathematical questions that could be asked about this situation.”
• 2 minutes: independent work time
• 2–3 minutes: partner discussion
• Invite several students to share one question with the class. Record responses.
• “What do these questions have in common? How are they different?”
• Reveal the task (students open books), and invite additional connections.

• “Work with your group to complete the first problem. Then, work on the last problem on your own before discussing it with your group.”
• 8–10 minutes: group work time
• 3–5 minutes: independent work time

Students may conclude that Andre’s tower is 117 inches (or \(39 \times 3\)), not realizing that this contradicts the second clue about Tyler having the tallest tower. Encourage students to check that their responses satisfy all the clues.

• See lesson synthesis.