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.

• “What do you need to do to find Elena's throwing distance?”
• “How could you decompose and multiply each part by 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 disc 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.

• See the Lesson Synthesis.