Sunday, June 14, 2015

8 Things I'll Take Away from the GafeSummit 2015

GAFE SUMMIT June 11 and 12, 2015 in Homer Glen IL

Here is the link to all of the sessions

1.  FAILURE IS A PART OF LEARNING.  We need to incorporate this idea into all we do as teachers.  We need to create activities that students don't feel like they have to get it perfect the first time.  We need to be honest and show our own mistakes and failures.
INSPIRED TO TRY:  Give my math students a chance to fail (try and try again) every day by these types of warm ups.    Estimation  Questions  Would you Rather... Thanks  @jamestsanders  presentation
MY FAVORITE:  Scroll down and see a few sites that students love.
The Dung Beetle helps us remember that out of the bad comes the good.

2.  GOOGLE FORMS   This is a must in my classroom.  It is easy.  It is fast.  All the responses are nested into a spreadsheet.  Here a  couple of new things I have taken away.  You can put conditional formatting into your response spreadsheet.  For instance:  when you have a survey of how students are doing and you ask them to rank it 0 to 5.  Then you can conditional format any cells color to be lets say RED.  That would alert you to students who have a hard time with the material.  TUTORIAL 
INSPIRED TO TRY:  Exit slips and consistent communication through Google Forms.  Also, I want to look into Move Note.  Thanks @JasonMMarkey

3.  GOOGLE DOC and GOOGLE SLIDE   If you are trying to give a document to someone else so they can use it on their own, in the url at the top of the document just change the /edit to /copy.   Tutorial   I also learned how to make a pictorial table of contents in Google.  Here is an example. Slides Thanks @jheil65

4.  PADLET.COM  Padlet is my all time favorite student interactive site.  This session confirmed that Padlet is the BEST.  Padlet is simply a public posting board that the technology doesn't get in the way.  Go to and sign up today.  I have my students all have accounts too.  Thanks @HollyClarkEdu

5.  QUESTIONS.  We don't allow students to ask enough questions.  I learned a structure that will help my students to ask questions without fear.  I'm really excited to use this.  In essence, as a group of four have our students ask a lot of questions and just write them down without judgement.  Then we ranked the questions for relevance and importance independently (however, it was digitally collaborated through google docs)  Then have them rank them as a group of four.   It was an excellent process.
INSPIRED TO TRY:  I would like to begin a unit with this structure.  This will help my students to ask questions before we know anything, thus give more freedom in asking any that are coming to mind.  Presentation   Thanks @HollyClarkEdu 

6.  GOOGLE +    I signed up for google plus professionally.  It has a lot of features that are really nice.  I have more to learn.  Thanks for helping me get started @cchausis

7.  GOOGLE HANGOUTS    I learned a lot of hangout etiquette .  Most importantly, I learned how to mute when some else is talking.  I learned that Hangouts are not longer tied to Google +.  You can screen capture something for all to see for the hangout.  You can give a link from your hangout for others to join you.  Use this link to go straight to a hangout.  And tons more.  More Info here. Thanks @AmplifiedIT 

8.  CHROMEBOOK SHORTCUTS:  I love shortcuts.  This one was fun.  I'm just learning my way around my new Chromebook so this was perfect timing.  Here are a few of my favorite Short-Cuts.
Screen Capture

Turn the screen 90 degrees.  This one is most helpful for teachers for when students are playing tricks on their friends.  

This opens up all the Short-Cuts.  

I took all of these shortcut images from the presentation from Adad Ocampo which was great!

Monday, May 4, 2015

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.
save image
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.  

save image
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.    

Wednesday, April 22, 2015

Which Word is Most Important: Practice, Explore, Concept, or Procedure?


Put yourself in the mode of teaching a Math Lesson. Which Word is Most Important: Practice, Explore, Concept, or Procedure?

Submit your response here
See summary of responses here 

When you are teaching a Math Lesson which word do you give the LEAST time to:  Practice, Concept, Procedure, or Explore?
Submit your response here
See Summary of responses here

My answer to both questions was EXPLORE. However, here is my typical lesson:  Concept first, then Procedure, then Practice, and if we have time I have my students Explore.   What am I thinking?  I need to have my students Explore More

I have been adjusting the order of my lessons lately to have EXPLORE first.     I have been finding that when students explore first, then they understand the concept faster later.  So Explore is not a waste of time but an important step in the process of learning of a math concept.  Explore is a word that frees students to make mistakes in their work and still learn. Another word that I see as synonymous with Explore is PLAY.   Do we let our students PLAY with MATH?   How can we EXPLORE first?   We need to find great explorations so that our students are not too frustrated, but yet not be bored with it.  Here are a couple examples of an exploration to start a lesson.
POLYGRAPH PARABOLAS  This is a Dan Meyer/Desmos Activity
Search 3-act Math Problems
Who will get there first?  A previous blog post on rate time and distance

I know I am going to try to Explore more FIRST!!!  I hope you will EXPLORE this idea more.


Tuesday, March 17, 2015

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.

Image result for runner

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

Chosen City with mileage by 10 minutes in.  5 points
Equation 1.  5 points
Equation 2.  5 points
Conclusion:   5 points



Tuesday, March 3, 2015

DOC and the Magic Straw: A Story about the Benefits of Collaboration

This is a very short story about DOC who is the inventor of a magic straw.  The story carries symbolism to show how easy it is to share your work with others and also have them contribute with you.  

Book titled 'Drago and the Magic Pen'


DOC is named after GOOGLE Doc 

MAGIC STRAW:  The link that is created when you share a Google Document in VIEW mode.

MAGIC PEN:  The link that is created when you share a Google Document in EDIT mode.

I use Google Docs almost every day.  I love the ease of use.  If you haven't used a Google Doc, please take the time to try it out.  Most of all I love Google Docs because you never have to click on SAVE again.  So give it a try, and create a Google Doc and then SHARE your document for all to see.  Directions on how to share are below.

Here are some directions for sharing a link for a document.  This is directly from  a Google Help Page on Sharing

1.  Sign in to Google Drive or a Docs, Sheets, or Slides home screen.
2.  Open the file you want to get a link for.
3.  Click Share for files or the share icon for folders in the top-right corner of the screen .
4.  Click Get shareable link in the top-right corner of the sharing box. A link to the file will be copied to your clipboard.
5.  Paste the link into an email or chat to share it.
6.  To stop allowing people to access the file using the link, open the sharing box > click the dropdown menu below "Link sharing on" > choose OFF > click Done.
7.  By default, the link you share will be view only for others. To allow people with the link to comment on or edit the file, click the dropdown menu under "Link sharing on" and change the setting from "People with the link can view" to "People with the link can comment (or can edit)".
8.  To allow anyone to be able to open the file or folder using the link, make sure to change your sharing settings to “Anyone with the link” or “Public on the web”. Click Change… when you’re in the sharing box to change this setting.

Saturday, February 28, 2015

Sometimes UN-Simplified is Better

To Simplify or Not to Simplify, that is a good question.

Recently, I have not been simplifying my work.  Let me explain.  We have been working on finding the equations of sine graphs in Precalculus.  I have found that when I type out my work in Desmos it doesn't automatically simplify it.  It still graphs it.  You can see the changes as you type them in.
This is really cool.  It leaves it so that the students can think about how the numbers came to be.  It is almost formula like.   See below.

Then, I asked my students to simplify the equation so that we can gain meaning out of the numbers.

Here is the project we just finished with if you are interested in taking a look. It is a project where we look at the vertical height of a person on a swing.  There is data involved and then we have to find the correct sine wave.

Here is another place that I see non-simplification as a perfect fit.  In linear equations using slope. You can see here it fits right into the slope formula.  This also shows equivalencies of linear equations.   So if you make a mistake on one simplification step, you will see it right away because it will not match up with the first one.

Actually, I think that when we show our steps in this way we are "digitally showing our work."  Hope you can give it a try.


Thursday, January 29, 2015

Math is always better when you do more than just WATCH

It is easy to think that when students watch us do problems that they get it.  They are usually concentrating and thinking about what we are saying, but it often does not sink in.  I am trying to get my students to DO MORE themselves.  This time it has to do with making a Ferris Wheel and using it to help solve Trigonometry problems.   Yes, it does take time out of class to do this.  I think it is well worth it to invest the time now, so that they can recall it later.

This unit we are covering the beginnings of Trigonometry.  Working with the Trig fundamentals is tricky.  Students often get confused.  So a few years ago we introduced the unit called "High Dive" where a fictitious scenario of a person being released from a Ferris Wheel into a moving tub of water.  (Key Curriculum Press)  Most importantly it gives the students a visual handle on the basic Trig ideas.  This year I extended this to include a physical handle on Trig.  We made Ferris Wheels out of pipe cleaners.  It turned out really well.  Seeing the test scores from this year, I'm confident that the students did even better than last year.  Here is what we did.

There is a Ferris Wheel whose center is 65 feet off the ground.  The Ferris Wheel has a radius of 50 feet.  The Ferris Wheel is moving at a rate of 1 revolution per 40 seconds. The diver is on the Ferris Wheel which always moves in a clockwise direction and will start from the 3 o'clock position. Here are some questions we explored.
1.  When will the Diver be at the highest position?  What is that height?
2.  What is the angular speed of the diver?  What is the linear speed of the diver?
3.  Map the divers height for 1 revolution of the Ferris Wheel.
4.  What height will the Diver be after 14 seconds?
5.  If there was a 30 fence hiding the front of the Ferris Wheel, what percent of the time is the Diver ABOVE the fence?
6.  How long does it take to go from the 3 o'clock position to the 8 o'clock position?

So with our Ferris Wheels IN OUR HANDS, we went through many of these questions while moving the wheel to match our questions.  The students made the Ferris Wheel with their own hands.  It was a homework assignment.  I gave them 8 pipe cleaners and 2 Popsicle sticks and they had to make a working Ferris Wheel.  They also had to make a place where the diver was on the Ferris Wheel.  Kind of like a marker.

Here is one of my students talking about her experience with the Ferris Wheel.

One Student made an unbelievable Ferris Wheel.  He got his own piper cleaners.

I know I learn better when I can touch it, feel it, manipulate it and visualize it.