Who Will Get There First? Using the Rate Time and Distance Formula

This has been my favorite lesson of the year so far. I gave it to my Intro to Algebra Students during the Solving Equations unit. It just uses the simple rate*time=distance formula. The students have a lot of choices for the project. It took them 2-3 class days. The most important part of the project was explaining what the variable represented. You can see from the student examples below that they did not all do it correctly. However, overall I really was pleased with the engagement level and the end product. (See student examples below) I have given the directions to the project below as well.  
Positives: Student Choice, Engagement Level, Problem Solving Skills, Messy Numbers, Differentiated learning, Real World problem, Outrageous, 

To Work On: Find a way to access at the halfway point of the project. Some students don't get on track early enough.

Who Will Get There First?
You get to chose a destination.  You and a friend are going to race to a destination.  Your friend gets the faster transportation choice.   You get a 6 day head start.  Do all the calculations and see who will get there first.  

Here are your modes of transportation choices.

Bike:  3.5 miles per hour average*

Scooter:  1.1 miles per hour average*

Skateboard:  1.3 miles per hour average*

Walk:  .9 miles per hour average*

Pogo Stick:  .5 miles per hour average*

Big Big Wheel:  2 miles per hour average*

Roller Blades:  2.5 miles per hour average*

Run:  1.8 miles per hour average*

*All average speeds are accounting for sleep and eating.

You may pick your own mode of transportation, but you must get it approved first.  It may not be motorized.

                     

Destination Restrictions:  Between 500-1000 miles away from here.  Pick a city.    

Equation 1:  You must have a variable in your equation to figure out how much time it will take you to get to your destination.  

Equation 2:  You must have a variable in your equation to figure out how much time it will take your friend to get to your destination.

Conclusion:  You must justify who arrived first and by how much time.  Your answer MUST BE GIVEN IN DAYS and HOURS, not just hours.  

You must give your results in a video link or digital document link with all information given.

Padlet, Google Document, Video, Presentation

Rubric

Chosen City with mileage by 10 minutes in.  5 points

Equation 1.  5 points

Equation 2.  5 points

Conclusion:   5 points

Resources:

https://padlet.com/

https://awwapp.com/  

https://sketch.io/sketchpad/

HERE ARE THE STUDENT RESULTS

Created with Padlet

Give Meaning to Numbers with Technology

A colleague and I were talking about math problems a few days ago.  He told me that he really likes to give meaning to numbers because it helps the students put the numbers in context.  I completely agree. We were working on percents at the time in my Introduction to Algebra class so I decided to give a little more meaning to my percentages.  Here is what I did.



Since my students have laptops,  I had them go to Kohls.com and pick out an item that they liked. They got to choose a 15% off, 20% off, or 30% off coupon.  (I thought they all would pick the 30% coupon too, but they didn't)  Take the price of that item and reduce it by the coupon amount.  Then they were asked to add on 8% tax.  Lastly they had to post their work to a padlet.com site where all could see their work.  You can see their work too: http://padlet.com/dsladkey/kohls  Padlet is a great tool for student collaboration.  www.padlet.com   

Here is the progression of the assignment

1.  Find an item at Khols.com  Find the price.  (even if it is already discounted)

2.  Choose a 15% or 20% or 30% off coupon.

3.  Reduce the price by the amount on the coupon.

4.  Take the new price and add 8% tax to it.  

5.  Show your picture and all your work on a common padlet site for all to see.  http://padlet.com/dsladkey/kohls





What were the big takeaways?

1.  They learned the material without a bunch of problems without meaning.
2.  Choice.  It gave students a choice for what they wanted to work on.
3.  Pride.  When we shared these out, there was a lot of pride happening.
4.  Recall.  A student asked a question on the test and I just said "Do you remember what you did with the Kohl's activity" and they said, "Oh yeah"
5.  Engagement.  This activity took about one 50 minute period. They were diligently working the whole time.
6.  Accountability.  All students could see all the posts.

Dave
@dsladkey

Which is the best deal? Gatorade Introduction to Algebra Problem

Here is a Grocery Store problem.  I went to the store and video taped all the different Gatorade options.  (And yes, I did get some looks at the store)  My student's will have to decide which is the best deal.  I want my students to try to use problem solving skills to get at the best deal.  I want them to struggle a little bit with the complexity of the problem.  They will somehow need to get all of the 5 different options on the same unit measure playing field.   I have given a couple of answers below.  I was looking for students to justify their work with equations, diagrams or graphs.  They are not bound by any particular method.  However, they must show their work and give their answer in complete sentences.  In the video their is an example of what kind of work I expect.  I debated on whether to include this.  My end thinking was that I wanted them to see that their needed to be some work shown and a complete sentence answer. So I showed them a couple of solutions in the video.  But the exemplar solutions are NOT in the worksheet.

Click Here to Get the PDF Worksheet  (see below)

Of course I loved the traditional approach of figuring out the price per oz.  However, if you notice she also write that the Large Can was equal to 3 of the Smaller cans.  (24qts = 3(8qrts))  I love it.

This was a different student's paper.  This was another favorite answer because she wrote a diagram of two of the smaller bottles equaling the larger bottle.



All this really makes me realize how different we think.  I have to get myself out of teaching a certain method and saying that is the only way to do it.  It just is not right.  Think of your choice of cars.  Why are there so many cars choices out there?  It is because we all are different and like different things.  In math, it is the same way.  The plain and simple truth is that understanding our method of choice thoroughly first, then branching out to understanding other answer methods will benefit us.  I know I will forever be learning how to teach better.  This is exciting and daunting at the same time.  I will keep on trying to get better.

Let me know your thoughts?
Dave

Sum of Three

I got this activity from my brother-in-law and really like it.  It is called "Sum of Three".   In essence you have students in groups of three each doing a different problem.  Then you have them add the answers together to be the sum of the three answers.  They will bring this number up to you and ask if this is correct.  If they are correct, then they get to move on to the next problem set.  If they are incorrect, then they must decide how to go about getting the correct answer.  This is the best part of the activity.  When the students get the problem wrong, they automatically think it is somebody elses mistake.  They then will systematically go through the process of how to do the problem with everyone.  It is a great group activity.  Here are my directions.  I have given a couple examples as well. 
1.  Get your class into groups of three.   I always do this on a random basis.  Let's say you had 26 people in your class.  Take 26 kids divided by 3 and you get 8 full groups of three.  Count students one, two, three, and so on till eight, then start back at one, two, three and keep doing this until you run out of people.  In this case, you will have 6 groups that have 3 in it and 2 groups that have 4 in it.  Now the ones get together and the twos get together and so on.
2.  Hand out a problem set A in paper form to each group.   This will have three problems in it.  A1, A2, and A3.  Each student will work on a different problem.  The group will then add the sum of all three answers. 
3.  When a group thinks it has a sum, they bring up THEIR PAPER to show you their answer.  Don't have the students SAY the sum.  This might give it away for the other students.  If they are correct, give them the problem set B in paper form.  If they are incorrect, then they must go back and find out where they made a mistake.
4.  I have my students do all their work on a separate piece of paper to be turned in.  This creates a little accountability as well as a place for them to work.
5.  You will have to decide how many sets of problems you will want.  I typically have 3 to 4 sets.  I have the last set as extra difficult.

Here are a couple of examples of the "Sum of Three" activity.



This is a problem set for multiplying fractions in Intro to Algebra



This is the answer sheet that I use when the students come up to give me their SUM.



This is an Algebra "Sum of Three" problem set.  I have the students add the y-intercepts of the line.


PDF of the FRACTIONS "SUM OF THREE" ACTIVITY

PDF of the EQUATION OF A LINE "SUM OF THREE" ACTIVITY