Andrea Palmer PROSPECT HILL ACADEMY CHARTER SCHOOL, SOMERVILLE, MA
6th Grade Math : Unit #5 - Proportional Reasoning: Ratios and Rates : Lesson #11

Calculating Speed Day 1

Objective: SWBAT: • Make conversions to determine my speed using different units • Use multiplication and division to calculate rates
Standards: 6.RP.A.3 6.RP.A.3b 6.RP.A.3d MP1 MP2 MP3 MP5 MP6
Subject(s): Math
60 minutes
1 Do Now - 7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to start thinking about what speed really means.

I ask students, “What does it mean for Usain Bolt to run at a speed of 23 miles per hour?”  I want students to set up the rate, recognizing that “per hour” means their denominator needs to be 1 hour.  Just because he was traveling at a speed of 23 mph does not mean that he could maintain that speed for an hour.

2 Setting Expectations - 5 minutes

I tell students that today they will be working to figure out their sprinting and walking speeds.  I tell students to copy their data from the previous day’s packet.  I tell them that by the end they should know their speed in miles per hour.  I ask students what conversion facts they think they will need.  I copy them on the board and students put them in their packet to refer to later.

I tell students that this task is complex.  They have skills and strategies for working with rates and measurements and all of these skills will help them to work through the task.

3 Part 1: What was your sprinting speed? - 28 minutes

Notes:

• Before this class, I use the data from the previous lesson’s TTG to Create Homogeneous Groups of 3-4 students.
• Each group receives a Group Work RubricI use this data to give each student a citizenship grade for the day.
• My goal is for students to at least complete the questions in part 1 today.  We will be working on extending this task during the next lesson, so students will have some time to work on part 2.

I tell students about the groups they are working in.  Students move into groups and begin working.  Each student has unique data, but they will be able to ask each other questions about how to change their rates and measurements.  I walk around to monitor student progress and behavior.  Students are engaging in MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, MP5: Use appropriate tools strategically, and MP6: Attend to precision.

If students are struggling, I may ask the following questions:

• How long did it take you to sprint 40 feet?  How can we figure out how many feet you traveled in 1 second?
• How far did you travel in one second?  At this rate, how far would you travel in 2 seconds?  In 3 seconds?
• How can you use what you have to create a rate showing how far you would travel in one minute?  What units do you have?  What units do you need to have in your answer?
• If you know how far you travel in a minute, how far will you travel in one hour?
• How far would you travel in one hour?  What units do you have?  What units do you need to have?

If students are struggling with the actual calculations, I have calculators for students to use.  If a student uses a calculator, I still require them to set up the rates and show the calculations he/she is making to get the answer.

If students need extension, I may ask them the following questions:

• What if your walking speed is 1 meter per 1.5 seconds, what is your speed in feet per second?
• How long do you think you could keep up this speed?

If students successfully complete part 1, they move onto part 2.  I took away the scaffolding in part 2 so students need to complete multiple steps to answer the questions.  If they struggle, I have them look at their process in the part 1 problems as a reference.

If students successfully complete part 2, they move on to the challenge questions.  If students ask me how many kilometers are in a mile, I will give them the conversion.  I want students to figure out on their own what information they need to know to complete the problem.

Student Work: Converting measures of speed
Real World Applications

Students really enjoyed using their data to calculate their speed.  By breaking down the more complex question of “How fast were you running in miles per hour?” into smaller questions, more students were able to access and solve the problems.  I ended up passing out calculators to each group during this part of the lesson.  Some students used them and some students did not.  I collected students’ work at the end of the lesson and here are some of my observations.

Unit 5.10 Accurate Calculation.jpg

Most students who used a calculator to were able to accurately calculate their speed in miles per hour.  This student had a speed of 27,720 feet per hour.  She was able to use the conversion fact of 1 mile = 5280 feet to set up a proportion.  Using the calculator she was able to find that 27,720 feet is equivalent to 5.25 miles.

Unit 5.10 Labeling Mistake.jpg

Some students were able to find the correct speed, but made mistakes in labeling their answers.  This student used the calculator to divide 28,800 feet by 5280 feet.  She found her sprinting speed was about 5.45 miles per hour.  She mistakenly wrote 28,800 miles/1 hour as part of her answer.

Unit 5.10 Conversion Trouble.jpg

Other students made mistakes converting their speed from one unit to another.  This student accurately calculated his sprinting speed as 41,040 feet/ hour.  In trying to change his speed into miles per hour he starts adding groups of 5280 feet.  He ends up adding 3 groups of 10,560 feet and gets 42,240 feet.  Since his amount is more than his total of 41,040 feet, he estimates to about 3 miles per hour.  He counted each group of 10,560 feet as one mile, instead of two miles.  He did not stop to make an estimate or use the calculator and ended up with a speed that was much lower than his actual speed of 7.77 miles per hour.

At the beginning of the next lesson I gave students their work back.  I asked how students could estimate to make a reasonable guess of their sprinting speed.  I also asked students how they could use a calculator to find a more precise measure of their speed.

4 Closure and Ticket to Go - 10 minutes

I ask students to share out how they found their speed in feet per second.  I have a student come up to the front to show and explain their thinking under the document camera.  I ask students to come up to show and explain their work for problem 3 and 4. Students are engaging with MP3: Construct viable arguments and critique the reasoning of others.  I ask students to show me with their hands if they have completed the problems in part 1.

I ask students to share out what obstacles they encountered and whether/how they overcame them.  I remind students that they will be working on a task using this data in the next lesson.

With a few minutes left, I pass out the Ticket to Go and the HW Calculating Speed Day 1.