Scale Drawings and Maps

5 min

Narrative

This Warm-up serves two purposes. It refreshes the concept of distance, rate, and time of travel from grade 6, preparing students to use scale drawings to solve speed-related problems. It also allows students to estimate decimal calculations.

Students are likely to approach the question in a few different ways. Monitor for students who:

  • Estimate the speed of the train in miles per hour and compare this to the speed of the car.
  • Find the distance the car travels in 4 hr and compare this to the distance the train travels.

Launch

Give students 3 minutes of quiet think time. Ask students to give a signal when they have an answer and explanation. Follow with a whole-class discussion. 

Student Task

Two cities are 243 miles apart.

  • It takes a train 4 hours to travel between the two cities at a constant speed.

  • A car travels between the two cities at a constant speed of 65 miles per hour.

Which is traveling faster, the car or the train? Be prepared to explain your reasoning.

Sample Response

The car is traveling faster. Sample reasoning: The speed of the train in miles per hour is 243 ÷4243 \div 4. This is (240÷4)+(3÷4)=6034(240\div4)+(3\div4)=60\frac34, and that's slower than the car. Alternatively, in 4 hr, the car would travel 4⋅654 \boldcdot 65 or 260 mi, and that's farther than the distance between the cities. So again, the conclusion is that the car is traveling faster. 

Synthesis

Invite students to share their strategies. Make sure to highlight different strategies, such as calculating the train's speed and calculating how far the car would travel in 4 hr.

Record and display student explanations for all to see. To involve more students in the conversation, consider asking:

  • "Did anyone solve the problem in a different way?"
  • "Does anyone want to add on to _____’s strategy?"
  • "Do you agree or disagree? Why?"
Standards
Building On
  • 6.NS.2·Fluently divide multi-digit numbers using the standard algorithm.
  • 6.NS.B.2·Fluently divide multi-digit numbers using the standard algorithm.
  • 6.RP.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <em>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</em>
  • 6.RP.A.3.b·Solve unit rate problems including those involving unit pricing and constant speed. <span>For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?</span>

10 min

15 min