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

Blue Tape Math

What is Blue Tape Math?  

Simply put, it is having your students use blue masking tape to represent math on the wall, floor desk or windows.  

Why use Blue Tape in Math?

MATH:  Students are using ratios, scale models, fractions, decimals and graphs ALL THE TIME.  Blue masking tape also 'slows' the math down a little bit so all can jump in and be engaged.
MOVEMENT:  Students are moving while learning which helps our kinesthetic learners.
MEASURING:  Students are using rulers, protractors, tape measures.
AND NO MESS with painters masking tape.  It comes right off of walls, glass, desks and floors.

Math Skills

Ratios
Scale Models
Measuring an angle
Measuring a side length
Fractions (While measuring distances)
Graphing
Areas

Where can students create their shapes?

Walls, Windows, Floors or on the Desks.

Ideas for when to use blue tape

Create a figure with a specified area.
Create a regular hexagon or pentagon.
Create parallel lines, or parallel lines by using a traversal
Create a parabola from a quadratic function.
Create a kite.
Create a triangle with Blue Tape.  Find the area of this triangle in multiple ways.
Create a shape (triangle, quadrilateral, etc. ) .  Create a different shape with the same area or perimeter.
Create a circle using blue tape.  Now guess how many diameters will be needed to make the circle?  Test your guess by creating diameters to go all the way around the circle.
Quadratic expressions and equations.  Click to get to the activity we did in class.

This project students created their own non-right triangle and then found the area of it using 3 different formulas.  #precalculus 

This group had a "random triangle that turned out to be an equilateral triangle.  They called the PERFECT triangle.  They were proud.

In this project students are making shapes to understand quadratics. This was in Algebra 1.  A colleague @rachelfruin and I wrote this  if you are interested, here is the progression.   

Try Blue Tape Math with your colleagues in the office.  We did.  It was a great experience.  @rachelfruin  @smiller229 and @mthor_  all have been working on blue tape math together.  The best way to describe what happens when you are using blue tape to get at a solution is that the process is 'slowed down'.  It helps everyone collaborate together at the same pace.  Try it in your office, and then try it in your classroom.  

Take the Blue Tape Math Challenge 

Find one or two colleagues that are up for an adventure, and create a regular pentagon with only a ruler, protractor, and some blue masking tape.  You can create the regular pentagon on the floor, desk or wall.  At the end of your creation reflect on the things you needed to accomplish the task.  Then discuss how you might use blue tape math in your class.  If you have time, let us know what you think @rachelfruin  @smiller229 and @mthor_ @dsladkey

A Word of Caution.  

Your lesson is going to take a lot longer.  This was something that was frustrating at first, but I realized that sometimes when a problem takes longer, the students understand it more thoroughly.   Another word of caution is that I always measure the figure on the INSIDE.  It has much crisper lines.  Also, I have my students use 1/4  inch blue tape.  See below.

#bluetapemath  

Try quarter inch blue tape at ZORO.  Under $3 for 1/4 inch 6o yards of blue painters tape.

The Ups and Downs of Blended Learning

I feel like a first year teacher again.  Do you remember that?  The roller coaster you were on emotionally?  Well welcome to my world this semester.  I have taken the Blended Learning Plunge. See my first post about blended learning here.   I have my students for "In Class" days 3 times a week.  Then for two days a week they have "Independent Days".  These are days in which they do not have to attend class unless they have a grade below a 70%.

The Ups
The independent days have been spectacular.  There has been some "ah hah" moments for my students that could never have happened in a traditional setting.  Let me share a story.  I gave a visual pattern assignment to my class on an "Independent Day".  (this is where only a few of students are in my class)   So I only had a handful of students doing this problem in class.

We actually followed Michael Fenton's steps through this visual pattern with a piece of typing paper.  Click here to check that out.  So a student and I were working on a problem together.  Although she is very slow at processing arithmetic, she is very good at seeing patterns and growth of patterns.  For this problem we progressed by giving steps 1, 2 and 3.  (see picture)
Then she was asked to draw step 4.  No problem.
Then she was asked to draw step 10 with relative ease.
Then I asked her to tell me about step x.  (This was the key moment I had been waiting for.)
She said do you mean step 11.
I said no, step x.
She said I don't know what you mean by step x.
This girl has taken 8th grade algebra, Intro to Algebra and now Algebra 1.   Now she was finally able to ask  about what x means.  It was a breakthrough. We continued to work together.   She put together the expression that represented the xth step.  Yes it took a while, but that was an amazing day of teaching.  I felt like it was a day that I live for when a student "gets" it.  A student finally figuring out what x is in an algebra class. Thank you Fawn Nguyen for visual patterns and Micheal Fenton for a format to teach visual patterns.

Here is another girl explaining the problem.  She did her work OUT of class on her own.  This is amazing work on Independent Day.

The Downs

So not all things can work perfectly.  That is certainly the case for me.  I had two students email me this past week with frustrations about the Blended Learning process.  They don't feel like they are getting enough practice.  These are strong students too.  I need to listen to them and try to improve the way that we are doing things.    

Planning:  Am I giving the students enough resources?  Am I providing the structure for the students working outside of class?  I'm not very confident right now.

Getting Enough Math?  I continue to struggle with the idea that the students are not getting enough math.  I don't see it happening (because they are not in my sight two days a week) so it is not as easy for me.  The balance is trying to give enough resources for students who are out of class and also make them appropriate for where their learning is.  If it is too tough, they can't complete it.  If it is too easy, then they tend not to do it.  We must keep our ideas and our routines fluid to see if we can improve them.  I certainly do. 

Refining

Since we are always learning we must always refine our teaching.  That is certainly what I'm doing now.  I am trying to provide the right balance of digital resources and practice.   I'm now working on a document for the chapter that we are working on.  I wouldn't call my document a Hyper-Doc.  However it is similar.  Below is the document I'm working on right now for the chapter we are in. Note:  this document  Always learning.

Visual Patterns: Concrete Results

I would encourage you to use visual patterns in your class as soon as possible.  There is an excellent website to get yourself started at http://www.visualpatterns.org/ 

I gave this problem to my students in the middle of the quadratics unit for Algebra 1.  Any student has a chance at this.  That is what makes this so wonderful.  The playing field is leveled.  This particular problem is very cool because there are so many ways to view it.  So the beauty of visual patterns is that each student can look at the problem differently and still get the same answer.  The key is having them JUSTIFY their work.  You might want to try it yourself before looking below.

Here is my original problem 

Some things that I try to do when using this kind of problem.

1.  Have students work on their own first.  Then after some alone time, give time for collaboration.

2.  Have students try to work multiple solutions if they finish with one.

3.  Push students to visualize the problem in some way.  (manipulatives or drawing or sketch or computer based image...)

4.  Push students to give some meaning to the problem with algebraic symbols.

5.  I try to remember that this problem might take 20 or more minutes to work out.

Here are a few examples of what my students created with this problem.

This one saw the perfect squares involved and then just subtracted the two missing pieces off at the end.  

This group saw the smaller perfect square in the pattern.  Then dealt with the rest in a linear way.

  

I love this one because it incorporated a graph to make sure of their answer

This one is detailed.  The recognized the perfect square in the middle and then dealt with the other stuff as linear.  

I made these visualizations for the problem.  However, many of the students had these types of things on their papers before they wrote up the equations.  You can also see by the video below how the students were visualizing this problem.  Also, next year I'm planning on having the students do this type of visualization with a spreadsheet that @alicekeeler made.  http://alicekeeler.com/pixelart I found it in her blog post:  http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/ 

(x+2)(x+2)-2

(x+1)(x+1)+2x+1

(x)(x)+4x+2

More questions were asked for this problem.

Are the algebraic results all the same?

How do we know that the algebraic results are all the same?

Can we use DESMOS to see if they are the same?

Can we simplify to see if the algebraic results are the same?

Can you imagine your students wanting to know these questions?  It was so much fun.  

Here is the reward of the day.  One student who has trouble with the algebraic concepts and who almost never wants to talk about it got up and did this....magical.

Lastly, I'm thinking about taking the @saravwerf Number Talks challenge.  See her blog post at https://saravanderwerf.com/2016/06/27/secondary-number-talks-ill-convince-you-with-ducks/