Calculating Speed Day 2

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Objective

SWBAT: • Make conversions to determine my speed using different units • Use multiplication and division to calculate rates • Use data to plot points on a line graph. • Compare speeds.

Big Idea

Who’s faster? During the second day of this investigation, students use conversions and rates to calculate and compare their speeds. Students also use their data to plot points on a line graph.

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 be able to compare speeds to determine who is faster.  A common mistake is for students to think that the person with the lower speed is faster.  They may be thinking of a finishing time, rather than a speed.  I remind students that the faster person goes further in the same amount of time.  Therefore Morgan is faster because she goes further than Jamie in the same amount of time.

Students participate in a Think Pair ShareI call on students to share their ideas.  If needed I get two volunteers to model Morgan and Jamie’s speeds.  Students may notice that Morgan’s speed is twice as fast as Jamie’s speed.  I am interested to see what students think about question (c).  It is okay if they are unsure about (c), we can return to this question during the closure.

Who's Faster?

10 minutes

I want students to be able to take a speed and translate it into a graph.  I want students to recognize that if Agedel travels at a speed of 9 feet per second, then after two seconds he will go 18 feet.  Students sometimes struggle with what happens at 0 seconds.  I tell students that 0 seconds is before they start moving, so they have traveled 0 feet.

We complete the first table together and students work on the other tables independently.  I call on students to share out their answers.

On the next page, we plot the data onto a graph.  I model how we can use the data in our table to plot each point. Students finish the other two graphs on their own. Students are engaging in MP4: Model with Mathematics.

 I ask, “What do you notice?”  Some students may notice that the points create a straight line.  Some students may notice that the lines do not have the same steepness.  I want the students to be able to see that the graphs also show that N’Yshma is the fastest, since she travels farther in the same amount of time.

To Do List

3 minutes

Notes:

  • Students will work in the groups they worked in during the previous lesson.  I used the data from the previous lesson’s TTG to Create Homogeneous Groups  of 3-4 students.
  • I use the data from “Calculating Speed Day 1” TTG to prioritize which groups I need to check in with first.
  • Each group receives a Group Work RubricI use this data to give each student a citizenship grade for the day.
  • I have colored pencils, markers, and rulers available for students to use.
  • My goal is for students to at least complete the questions in part 1 and create a graph comparing the speeds of their group members.

I read over the to do list with students.  I tell students to get out their previous day’s packet.  Each group needs to check in with me before they move onto the next item on the to do list.

Work Time

25 minutes

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?
  • What information do you need to make the graph?
  • What did we do with the class example before we made the graph?
  • When we look at the graph, how can we tell who is faster?

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 does your speed in mph compare to your estimate?
  • How long do you think you could keep up this speed?

If students successfully complete steps 1-3 on the to do list, they can move onto the challenge problems.  

Closure and Ticket to Go

5 minutes

I re-read problem 1c from the do now and ask students to share their ideas.  I want students to recognize that since we are just converting the measurements from feet per second to miles per hour, that Morgan’s speed will be double Jamie’s speed.

I tell students that Morgan’s speed is 9.54 miles per hour and I ask them to figure out what Jamie’s speed in miles per hour is.  Students participate in a Think Pair Share.  I call on students to share their ideas.  Students are engaging in MP8: Look for and express regularity in repeated reasoning. 

Instead of giving a Ticket to Go I collect student work to look at and I pass out the HW Calculating Speed Day 2.