Pass It On! Linear Modeling Activity

Do you want your students to be engaged?  Do you want them to make predictions?  Do you want them to Move and Learn?  Are you working with linear equations?  Try this activity in Algebra 1.

Pass It On Book Passing Activity
Students will be passing 4 textbooks around the room in a established pattern. (see picture)  The number of students that pass the books will be determined and then the length of time will be noted.    (number of students passing the books, time to pass books) = (x,y)    Predictions will be made for the x and y unknowns.


Explain the outline of the activity.
Assign a timer.
Assign a note taker to record the data. (in a google sheet with a common link preferably)
Establish a pattern for passing the books.

Establish a short (approximate 10 second) routine for BEFORE the books are passed.  (jumping jacks, twirls, stacking books one by one, etc. This is to establish some type of y-intercept for the problem) See the video.

Practice passing the books around the path to make before timing the events.

Now time your class doing 3 people, 8 people, 14 people and 21 people.  

Record the data in a Google Sheet.  Here is our data from our class:  http://tinyurl.com/racingthetime 

The data is below: these coordinates are in (# of people moving the books, time) = (x,y)

(3 people , 11.17 seconds)

(8 people, 17.4 seconds)

(14 people, 25.4 seconds)

(21 people, 34.67 seconds)

MAKE PREDICTIONS

Get your class into groups of three and ask these two questions.  

How long will it take for the books be moved by 30 people?  

(30 people, ? seconds)

If it took 73 seconds to move the books, how many students did the moving? 

(? people, 73 seconds)

I had the groups put their predictions in the google sheet that was created for the data.  

Lastly have your class actually test the predictions by measuring for 30 people and 73 seconds.  It was a lot of fun to find out the actual time for 30 people and the actual amount of people for 73 seconds.  The students were really into it.  

Good questions to ask 

What does the slope mean?

What does the y-intercept mean?

What methods could be used to predict your answers?

Hope you can give this a try.

My Best,

Dave

World Record Distance for Throwing a Fish at a Stop Sign

What is the world record distance for throwing a fish at a stop sign?   Hey, I don't think this stuff up.  But one of my students did.  Try to imagine a competition where everyone was seeing how far they could throw a fish to actually hit a stop sign.  One of my students was searching the internet to see if there were any sites that would have some data on this.   Unfortunately he couldn't find any data on this.  He moved on to a new idea.

Letting my students choose their own rates of change brought a huge amount of buy in.  The used their Chromebooks to search for data.  It was a blast. The students came up with many different ideas. For instance one student picked McDonald's hamburgers.  Did you know that from 1990 to 2013 the price of a hamburger has gone up 14 cents every year?  They OWNED IT.  They also took the time to figure out exactly what the rate of change meant.  I have always had a hard time teaching this.  But because they tried to find the data themselves the could communicate the idea of rate of change and what what happening over time.

White Sox Tickets anyone?   The ticket prices went up $1.02 each year from 1991 to 2003.



One student chose this.  (1950 year,  0 people living in Antarctica)   (1990 year, 0 people living in Antarctica)   0 people over 40 years.   Rate of change is 0 people per year.  Very Clever.  However, I told him he needed to find some information that gave a rate of change OTHER THAN ZERO.


So what did this lesson do?
Differentiation?   Yep
Student Choice?  Yep
Engagement and buy in?  Yep
Crazy Ideas?  Yep
Messy Numbers?   Yep
Fun for the teacher?  Yep


 Here was the original assignment.  https://docs.google.com/document/d/1cygX8-EKqVdvGu-1IX-cthodUHeBVTGrrSA4cGsYS-4/edit?usp=sharing

Rate of Change Ideas for class

World Records Over time     

100 meter dash   

High Jump  

Hot Dog Eating go to History for info.     

Common household items

Here are the other postings.  We posted them to Padlet.

Created with Padlet

Measuring to find the Slope of a Line

Slope is so cool.  But I have made it so boring in the past.  I don't want SLOPE to be boring.  So this is what I tried.  I took some blue tape and made a big line across the front of the room on the wall.

Starting the Lesson (we have not covered anything to do with slope yet)

Ask the question:  What is your guess for the slope of this line?  I had the students think about the question and talk with their partner.  Then I picked a few students at random.  Here are a few of their guesses.

The most interesting thing that came out of this was that some students wanted to know the rule before they guessed.  I then asked if anyone would like to share what they know about slope.  The rule of slope is the rise of the line over the run of the line came out.  Also the word steepness came out.  We did some discussing regarding the fact that the rise "looked" smaller than the run and how that might look with numbers and decimals.

Refine your guess:  I told them that all of their guesses were too high.   Someone also noted that the slope was positive.  So we talked about the fact that it had to be greater than zero.  Then I told them that since all the guesses were too high that m=1 was too much.  I asked them to talk with their partner and come up with a new guess.  Here is the second round of guesses.


Measure Yourself: We were definitely getting closer.  The discussion shifted to the equivalent numbers of 0.13 and 13/100.  Also 0.7 and 7/10.  I told them about the fact that you could measure the rise by starting at any point on the line and going straight up to any other point, and measure that.  Then the rise would be from that end point all the way across horizontally to the line, and measure that.  Now I asked that they come up to the line and actually measure the slope.  I only had half the class to this because of space.  The rest of the class were asked to be thinking of how and where they wanted to measure the line.

This first round of measurements came on with some amazing accuracy.  The slopes came in at 0.269 as the lowest and 0.3125 as the highest.  I thought this was spectacular.  

Also, I had one group that measured in wrist width.  They measured 4 wrists high and 13 wrists long.  This was an answer that was very close to the middle answers.   We used inches, cm, and wrists as our measurements.  I never told them what to use before the activity.   

By the way, I measured the whole triangle height over the width and got 67 inches over 210 inches.  So the actual slope turned out to be approximately 0.319.

The homework for the tomorrow is to measure the slope of 5 things.  Give all the measurements.  Take a picture if you need to.  We will see what they bring to class tomorrow.

Take Aways
Here are some reasons that I was excited about today's lesson.

1. Taking a guess at the answer helps students to try without the fear of failure.  It is only a guess.
2. Refining the guess helped them to continue to think about what exactly slope is.
3. They had to measure something.
4. They used different unit measures.
5. Today students were Active and Participating in learning Slope
6. We also compared multiple equivalencies.   0.5 was the same as 1/2 or 5/10
7. Learning a math concept always takes more time than I think.  This took 25-30 minutes.