Workout

Personal Reflection:
I'm going to be honest right up front.  I'm not a runner.  So when I workout on a treadmill, it's a pretty slow jog.  The beauty of this post is that if you choose to use it with your students, they can laugh and criticize the person on the treadmill and you can promise left and right it isn't you, and you can agree, the person here is one step above a sloth!  :)

That being said, I can't be the only "numbers nerd" out there that is constantly doing mental math while working out.  Maybe you count your reps when lifting weights and calculate the total pounds you've lifted?  Maybe you set a swimming goal and are finding the fractional portion of your workout completed with each length or lap?  Maybe you figure out how many hours you'll have to stay on the treadmill to burn that milkshake you enjoyed last night?  I know I'm constantly looking at the numbers and doing a variety of calculations.  I couldn't help but take a few photos today thinking that the wealth of information included on the screen is invaluable.

Grade Level: 7-9

Course: Pre-Algebra, Algebra

Standards:  8.EE.5, 8.EE.6, 8.F.2, 8.F.3, 8.F.4, 8.F.5, 8.SP.1, 8.SP.2, 8.SP.3, N-Q.1, A-CED.2, A-CED.3, A-REI.10, F-IF.4, F-IF.5, F-IF.6, F-BF.1, F-LE.1, 
SMP: SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8

Skills: Algebra, Functions, Lines of best fit, slope, rate of change, real life application, computation, extrapolating data


How to use this as a mad minute:
You have 60 seconds. List all of the questions you could answer given the four photos provided.

How to use this as a warm up:
You could ask the students to consider one of the following:
1.  Write down three reactions you have looking at these photos.
2.  What information is provided in these photos?
3.  Is this person moving at a constant rate?  (Consider vertical movement as well as speed.)
4.  Is this person burning calories at a constant rate?
5.  Can you write an equation given the information above?  (Try it!) 

How to use this as a mini-lesson:
To use this as a mini-lesson, expand on the warm up questions above.  You can ask students to make data tables, graph the data provided, and to compare rates of change and determine if a line of best fit is appropriate.  Students can show the data in multiple ways and can then evaluate the graph, equations and tables to identify real-life meanings (What does the slope mean in the graph?  What does the intercept represent?)  A copy of all four photos on a single page is available here.

Note:  I didn't provide my 20 minute script because I feel this is best used as an EQUATE lesson, below.

How to use this as a full lesson?
I feel this situation is IDEAL for the EQUATE lesson routine.  As you may already know, this relies heavily on letting students explore what is most meaningful to them and then asking questions to guide their exploration and results.  I can only outline what "might" happen, but students have ways of amazing us!

EXPLORE--Provide a photo copy of all four photos on a single page.  Give them a few minutes to look at the photos and discuss them with their teammates.  You may structure this conversation and provide guidelines as your classroom expectations dictate.

QUESTION--Ask the students to brainstorm the types of questions they could explore given these photos.  What do they "wonder" about mathematically?  Is there enough information to answer those questions?  Remember to push your students to think mathematically and to ask questions appropriate for their grade level.  Asking if it is linear is a great start, but asking if they can use information to tell MORE than that is key.  Challenge them to ask and answer challenging questions.  Questions I might expect or encourage:

• Is the rate of linear (and/or) vertical movement constant? What about the rate of calories burned?
• How fast is this person moving?  
• Based on the information I can see, were they always moving at this rate?  
• How long will it take to "climb" a mile?
• How long will it take to "run" a marathon?  What about burning off my favorite meal?

 Note:  Some questions are much more basic than others.  The last few questions require analysis offered in the first two or three questions, but students could easily get "stuck" with having too much information or too many steps to explore.

Additionally, this is where students get to ask you for more information.  If you can provide it, great!  If not, push them to answer their question given the information provided or to do the research needed to answer the question.  For example, I would NOT tell them whether or not the person was moving at a constant rate.  I would, however, allow them to look up the number of feet in a mile or the length of a marathon.  (I wouldn't tell them, but I'd help them access appropriate resources!)

APPLY--Remember to encourage your students to apply their learning!  If students know how to write equations from a table of data, they should do so!  If students know how to make accurate graphs, they should do so!  This is a great time to reflect on the units you have worked on and what skills students have obtained.  This will encourage students to apply those skills to their problem solving process.

TRY SOMETHING--Encourage the kids to get working!  They may feel "stuck" or that they dont' know what to do.  Try anyway!  That's the goal.  Get going, try something and see what happens.  Of course, kids need guidance, but it is their job to take their exploration, their questions, their previous knowledge and apply it to work on finding solutions.

EXPLAIN--Students need to wrap up their exploration by explaining not only what they did, but why they did it, how their previous knowledge related to the problem, and what inferences they drew.  They need to be able to justify their answers and how they know that their solution is both reasonable and accurate.

How to use this as an assessment?
If your students have experience with looking a real life data to explore questions like the ones above, let them go!  Give them a challenge question and the data and make sure they don't just find a numeric answer but also that they explain their process and thinking!

Please feel free to use any of these ideas and modify them to meet your needs.  However, please acknowledge the original source of the items and my own lesson outlines.  ©NatalieRSprigg 2013