As a warm-up for this part of the service project, I post a question on the board to Prompt student thinking. Students are encouraged to work independently or with peers to think about the problems that is posed.
1. How long will it take to ride 100 miles if we ride at a pace of 10 mph? 20 mph?
2. Write an expression to show how you solved these problems.
Students are called together as a class to share the various strategies used to answer these questions. After strategies are shared, we work together to write a formula (distance/speed = time).
Next, students are prompted to use what they have learned to determine how long it would take to ride 100 miles in 15 minutes.
This problem is more rigorous than the first two in the warm-up, because a remainder must be interpreted. It is important to allow students freedom when solving this problem, because there are diverse entry points. We can learn a lot about our students by the way they approach a problem.
When looking at a picture from the lesson("use what you know resource" , you can see that students had to interpret the remainder 10. Some students incorrectly thought of this 10 as 10 minutes. Be careful of this common error, help students understand how to make sense of the remainder at this point in the lesson, so the error is not repeated throughout.
Students use what they have learned from the warm-up to determine the length of time it will take to ride each multiple of 10 miles. They use repeated reasoning and structure after determining how long 10 miles will take.
MP8: Students look for and make use of structure when completing this task. Mathematically proficient students recognize this problem can be solved using the structure of elapsed time. Rather than using division for each problem, students build off their original discovery that 36 minutes = 10 miles. Note: 10/15 when divided equals the repeating decimal .666. Some students converted .6 to 6/10 then changed that into minutes using the equivalent fraction 36/60. It takes 36 minutes to ride 100 miles at 15 mph.
Other students found the fraction 10/15 in simplest from is 2/3. 2/3 of 60 minutes is 20 + 20 = 40 minutes. I accepted each of these answers as reasonable if students could explain their reasoning.
Students are called back together at the end of class for an opportunity to check in, share, and then make revisions. This part of the lesson emphasizes the significance of precision, perseverance, and mathematical arguments.
Since there are two reasonable approaches, and two different answers, this is an example of a high quality task - the math isn't always nice and neat but it's "real". To correct this piece of the lesson together is crucial. Students need to understand why two different answers are acceptable (because we have rounded .666666666 to .6 and although these numbers are similar, they are not exactly the same. So somewhere between 2/3 (40 mins) and 6/10 (36 mins) are acceptable answers. When using a calculator, or a spread sheet, the decimals are accounted for.
Most importantly, students need to attend to precision (MP6). Once a choice is made, they should use the same reasoning to solve the rest of the problems.
Students may need time to revise their work after the group share.