Category Archives: Graphing

Barbie Bungee 2014

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What a difference a year makes!  My current students saw all of the Barbie Bungee action from the sidelines as 6th graders last year.  They have been asking me ALL YEAR LONG when we were going to do Barbie Bungee.  This build up was terrific!  Once they knew Barbie Bungee had arrived, they were begging for math class.

After all of the build up, my students took Barbie Bungee very seriously this year.  I make it a competition, and they all wanted to WIN.  They did multiple test drops, they measured carefully, and they drew beautiful graphs.  I did not teach them about the line of best fit, but had them read about it here instead.  I told them whoever had the most accurate data and the best line would win the competition!  They were inspired to learn all about the line of best fit!

Again, I let them adjust their graph after the 90″ test jumps.  This year I was tougher on them, and would not let them test jump again until they fixed their graphs.

The big jump day was so exciting!  Students were yelling and screaming.  One group had a rubber band disagreement.  They calculated the number of rubber bands and wanted to put a half of a rubber band on so their estimate would be perfect.  They wanted to win.  However, we don’t do half rubber bands, so the great rubber band debate ensued. They  only agreed to put the last rubber band on seconds before the jump.  It was a deadly mistake, and their Barbie was the only one to crash.  It was a tragic (read great) learning lesson!

Please enjoy the pictures and the video.  I have so much fun with this project and making the video each year.  It is the best project I have ever done with my students!

My Procedure:

  1. Day 1
    1. Show students Bungee Jump videos on YouTube.
    2. Group students and have them come up with a company name, slogan, goals, and logo for their Barbie Bungee company.  Have them read about the line of best fit for homework.
  2. Day 2
    Give students the handout and let them do the test jumps and the graph.
  3. Day 3
    1. TEST DROP day from 90″.  Students adjust their graphs if needed, and get to add a data point to their graph and adjust their line of best fit if needed.
    2. Re-drop if needed once graph is completed.
    3. Estimate how many rubber bands they will need to drop from 160″ and then attach those rubber bands to Barbie.
  4. Day 4
    1. JUMP DAY – Finish putting rubber bands on Barbie and then JUMP!
    2. Go to Alcula, enter their points, and see the linear regression equation, as well as how many rubber bands they SHOULD have used.  Screaming ensues on this day as well.
  5. Day 5
    Talk about the equation of a line.  Have them speculate what slope means, what the y-intercept means.  Blow their minds!  🙂

Life Sized Human Graphing

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Today I did a lesson with 6th grade called Linear Graphs:  Life-Sized Coordinate Pairs  that I found on the Teaching Channel.  Definitely go there and watch the video.  It explains it in great detail!

To do Life Sized Human Graphing put a giant coordinate graph on the floor and then give the kids a rule.  They must come up with an ordered pair that fits the rule and then go and stand on their ordered pair.

I taped a coordinate plane on the floor with painters tape.  I also had each student wear a dry-erase necklace to write the ordered pair on so everyone could see their ordered pair.  They kept saying, “Does my ordered pair work?”   I kept saying, “Go graph yourself and see!”.  The class stayed engaged the entire time, and were even “overly engaged” arguing about the math at points.  I love that. After the first few examples I let them ALL come up and get in line instead of just four or five.  I did this mostly because they begged me.  They couldn’t wait to get up and see if their point fell on the line!

Whole Body Graphing ispeakmath

I used Max’s “noticings” in this as well.  They first noticed that they were all in a line.  Then they noticed that the line was steeper when it was 2x or 3x.  They noticed that 2x made the y-value go up by 2, 3x by 3, and so on.  The connections that were made today were amazing and I hope that they carry over tomorrow when I introduce slope (aka rate of change)!

I also made a powerpoint so that the game would be easy to manage.  Just click to follow the link and download the file from the Math Wiki.  After we start graphing linear equations I want to try Graphing Full Body Style!

Life Sized Graphing ppt

 

Equation of a Line Song!

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I used the Y in the song YMCA to help my students remember that the y-axis was vertical.  So, what could be the next step except for a song and dance about the equation of a line using the YMCA!  My students really enjoyed singing about fractions, so I wanted to sing and even dance this time!  I know that I am not breaking any new ground here, but my students are fabulous so I wanted to share our version!  We just learned it today so it’s a little rough, but I rarely have both 6th grades together for class so I had to video them today.

I downloaded a karaoke version of the YMCA from iTunes for accompaniment.  We only sang our song to the chorus of the YMCA so luckily, I found a version that started with the chorus!  Of course when we went outside to practice (and video) I couldn’t get the music to play.  But, we’ll do this again for sure!

Equation of a Line Song
(Sung to the chorus of YMCA)
Edited to add a new verse, 2014

y = mx + b, Equation of a line!
y = mx + b…
Puff, puff positive. Nice negative,
0 slope, And undefined

y = mx + b,  Equation of a line!
y = mx + b…
Begin at the B.  Rise and then run.
Connect the points, to graph the line!

That’s all!  Enjoy!  🙂

Ski Slopes – Day 5

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Day 5 – Slope

I always use the ski analogy to teach students slope.  This year, I added some Powerpoint visuals and a very fun Teacher Tube video to spice up my lesson.  There are two things that I focus on when teaching slope:

  1. Read a graph from left to right, just like you read a book.
  2. When you think slopes, think about skiing!

I picked where I left off in the previous lesson, and had a “reminder” discussion about M. The students got out their graphing worksheets to review.  We talked again about how M determined the steepness of the line and which direction the line went.  I told them that M was a pretty pathetic name, and that we needed to come up with a better name for M.  As a 6th grade teacher, at this point I had kids yell out crazy random names.  BUT, I told them that we would have to give M not only an interesting name, but also a descriptive name so that M would not easily be forgotten.

Since I’m a Powerpoint fan now, I made a Powerpoint full of ski slopes and put a big ski slope on the screen just as I finished this talk.  Instantly, many kids said, “Slope!” like they had discovered it all by themselves.  Some kids were disappointed that we decided not to use their more creative names, but most students were very happy with good old “Slope”.

I then presented them with animated skiers going up, down, and off of the sides of mountains!  I love using Powerpoint, as I can make it much more fun than my usual little stick guy falling off an undefined slope drawn on the whiteboard.  It was great for a laugh as usual.  Next year I need to add more positive and negative slopes with the corresponding equations.  While most students did get the connection between the graph of a negative slope and -M in the equation, I need to be more explicit to increase comprehension for all of my students.  I believe that adding the equation to each slide will fill in this gap.

After my slope lesson I introduced my students to my best slope discovery of all  – a fantastic “Slope Dude” video that I found on Teacher Tube.  It is cheesy and fun – just up my math video alley.  The kids LOVED it.  It is actually so catchy that I now say, “Puff, puff positive” and “Nice negative” every day.  It also defined the word “undefined” a “cuss word” in mathematics, which really entertained my 6th graders (hopefully enough so that they will actually remember it long term)!

I really love the online PLN!  Thanks Slope Dude!  : )

y=Mx+B Discovery Lesson using an Online Graphing Calculator – Day 4

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Day 4 – An Introduction to Slope and y-intercept

What does y = Mx + B mean?  I didn’t want my students to just memorize what M and B meant, I wanted them to understand it.  So, instead of just telling (or showing) them what M and B stood for, this year I let them discover it for themselves!  And since seeing is believing, I decided to use an online graphing calculator.

First, I taught them how to use a basic graphing calculator that I found online.  Then, they graphed a series of graphs on the online calculator.   I had them answer questions for each graph on a Discovering M and B worksheet.  I had shown them the equation y=Mx+B the day before.  I did this very briefly, just to show them how to pick out the M and the B from an equation.  I did not tell them what M and B meant.

After graphing a series of graphs, they had to answer questions at the bottom of their worksheet.  Side one focused on slope, and side two focused on the y-intercept.  I taught this lesson two classes in a row.  In the first class, I had never used this lesson before and wasn’t sure how easy it would be since they had not used the online graphing calculator before.  Plus,  I was being observed so I was a little nervous.  However, I realized in the first class that my students were trying to “zip” through the questions in order to get to the other side.  They weren’t thinking enough about the questions.  And, when I told them that their answers weren’t correct, they wanted me to tell them the answer right away without further thought.  So, in the next class, I decided to try to get the students to really focus on the questions at the bottom of each page by making it kind of a “challenge”.

** Note:  As the teacher, you MUST make your students focus on the questions at the bottom of each page.  Do NOT give them the answers until they try to figure it out themselves.  This is the key to this entire lesson. **

I told the students that in order to answer the questions,  they would have to look through their worksheet to try to figure out the pattern.  To make it more dramatic, I called the pattern a “puzzle” and made a huge deal about “figuring out” what B meant.  I was tough on them, looking for great descriptions for slope and insisting on an accurate description for B.  I told kids when they were close!  But, I wouldn’t say, “You GOT it!” until I saw the word intersection.  A few kids got it early, and after my, “Yes!!” I put my finger to my lips in a shhhh, don’t tell the secret!  It drove the other kids crazy!  I told them, I am looking for one special word!  After a few failed attempts, some students were even googling, “linear equations and B” to try to find out what word I was looking for!  It was so much fun for me, and you could feel the excitement in the room!

All of my students were able to figure out that M indicated the steepness of the line and which way the line went (positive or negative).  Most of them were also able to figure out that B was the point where the line intersected the y-axis.  Quite a few of them even came up with the word intersection.  It was a great day!  Worksheet included.

Discovering M and B

Reading Graphs and Functions – Days 2 and 3

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Day 2 – Reading Graphs

My goal today was for students to be able to interpret line graphs.  We discussed what it meant when the line on graphs go up, straight, and down.  I started out with an unlabled line graph that we made our own story for to illustrate them the basics.  Then, I moved on to fun!  I used plenty of line graphs from Jessica Hagy’s hilarious site Indexed.  I showed them a few completed graphs as examples.  I then gave them the axes only and let them figure out how the graph should go.  When they drew the line incorrectly I would ask them questions.

 

 

For example, when I gave them axes labeled education level and poverty, several students drew the line y=x.  I asked them,  “So, you are telling me that you have ZERO years of education, but also have ZERO poverty?  Does this EVER happen in real life?”  After thinking for a minute an insightful student got the “light bulb” expression and said, “YES! Paris Hilton”!   (This entertaining but pretty accurate comment led to the discussion of outliers.)  I then explained that they needed to consider the average situation (or even the expected situation), not the exceptions.

 

Day 3 – FUNCTIONS

What math teacher does NOT like the function machine?  I introduced my students to the fabulous function machine.  I named my function machine Fred the Function Machine, and then gave the students inputs and outputs (with dramatic illustrations for each one).  I put the inputs and outputs into a table.  It was up to them to guess what Fred was doing inside of his box!  Once they figured out what Fred was doing, we then wrote Fred as a mathematical expression.  For the first one, Fred was doubling all of the numbers.   My kids answers were, “Times two!” and “Fred is multiplying by two!”   2(input) = output.  I talked about x and y as input and output at this point, using my table as my example.  And Fred became y = 2x.  I explained that a function was a rule and that Fred had to do this rule every time an input went in.  This led to great discussions about how different numbers produced different outputs, and that if you put the same number in you had to get the same output.

Their Own Function:

We did a few more examples and then I had them draw their own function machine.  I let them name their own function anything they wanted (they loved this), make up their own function, and only write down the inputs and outputs in an x|y table.  They, they switched with their neighbor to see if their neighbor could guess what their function was.

Function Table (Table of Values):

Next we drew and completed a table of values with four columns.  The columns were input (x), our function (rule), output, and ordered pairs.  They completed several function tables and plotted lots of points.  I am not sure about this “function table”.  As a former high school teacher, all I ever drew for the kids were the old two-column x|y tables.  However, I wasn’t sure that this was enough information for them to understand what was happening “between the lines”.  So, I decided to instruct them with all four columns because it really leads them along the way with the input, rule, output, ordered pairs idea.  BUT, I was worried because this table very large (and thus probably impossible to remember).  This prophecy came true several nights later when I instructed them to create a function table for homework and they were all lost.  I am hoping it is just lack of experience, as this is the first time they have tackled the table of values.

Overall not very original, but the Hagy graphs were fun!  Next year I would love to do something more engagine with these two days…ideas welcome.  : )

The Coordinate Plane: Graphing Day 1

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This is a very exciting time for me, as the majority of my 6th graders are not intimately familiar with all of the wonders of graphing!  I can’t wait to introduce them to this world of mathematical modeling, especially since it will be all new for them!  I especially can’t wait for them to see all of the data that we have collected taking shape and making sense.  I plan on posting a series of blogs for most of the lesson in this unit.

We have been working closely with data all year through the use of Google Spreadsheets.  We have mostly analyzed the data they have collected through pie charts and bar graphs.  But finally, it is time to take it to the next level – linear functions and predictions!

The first day I taught them all about Coordinate Plane.  I assumed that most of my students knew this as it is on the 5th grade NC EOG tests.  However, I wanted to review the terminology and clear up any graphing confusion.  (Over Christmas I gave them a fun “plot the Christmas tree” sheet one day and heard a lot of, “is it in the elevator and then up the elevator?  or up the elevator and out of the elevator?”)  There is nothing I love less in the teaching of mathematics than ineffective analogies.

I gave them rulers, colored pencils and graph paper.  They drew the y-axis in yellow and the x-axis in blue.  They numbered the axes in colored pencil (red pencil for negative numbers).  We talked about what the word origin meant.  We then added a big dot for the origin and also added the quadrant names.  I had them stand up and do the YMCA to remember that the Y-axis was vertical.  We discussed the fact that x comes first in the alphabet so the x-coordinate gets to go first when graphing.  A Twitter colleague  Dan mentioned that the x-axis comes first because it is the original number line.  Then, you go up or down the new line, the y-axis.  I love that and will definitely use it in the very near future (tomorrow).  I like for my students to think logically when trying to assimilate mathematic information.  No elevators for us!

We plotted a few points together and then moved onto Battlegraph!  I found a great game complete with Powerpoint presentation online that I used. I did the Racetrack graphing game with 7th grade, but the 6th grade really seemed to enjoy Battlegraph!  I played music while they played and some groups really got into sinking each other ships!  It was a very fun day of teaching.

Up Next…Functions!