My Sixth Grade Class Sings the Fraction Song

Posted on November 3, 2010 by I Speak Math

I think that singing is an amazing way to remember something. My students can do each section of the fractions lesson. However, when we put it all together, they get it mixed up. They want to add the denominators when adding because you multiply them together when multiplying. I wanted to make a fractions song that incorporated addition/subtraction as well as multiplication and division.

There are many fraction songs on the internet that are amazing. I especially like the “I Will Divide” one that is played to guitar. It is very creative! I even found some fraction rap songs online. However, I did not want an entire fraction “ballad”, just a few short catchy stanzas that would (hopefully) stick in the kids heads.

I have not been my most creative self lately as being a “first year” teacher is taking it’s toll on me this year. However, I was able to pull together some words to my own fraction song once I decided on a melody. I used the classic, “Skip To My Lou”. I like to use the simple melodies that they learned when they were little. And I like to have repetition.

The Fraction Song
Sung to “Skip To My Lou”

Adding fractions LCD
Equivalent fractions each will be
Denominators stay the same
Numerators add some fame!

Simplify then multiply,
Simplify then multiply.
Times the bottom and the top,
It’s so fun that you can’t stop!

Dividing fractions is so fun!
Keep, Change, Flip the second one.
Simplify THEN mulitiply
Simplify THEN mulitiply

After learning it they wanted to do a “Fraction Parade” around campus, but we were really loud so I had them just parade around the room. I found a tamborine in the office at school and that just added to the fun!

I made a foldable to go along with the song (Fraction Song Foldable). I do an example problem on the inside.
Enjoy!

Skype + NC = NYC! Stop-Motion Movies and Technology in the Classroom

Posted on October 28, 2010 by I Speak Math

The 7th grade class at my school is currently working on a cross-curricular Japanese Anime project where they creating their own stop-motion animated films based upon environmental themes. The students work in groups and come up with their own idea relating to the theme, the characters they would like to use, and how they would like to present their message. Then, in the classic stop-motion animation style, they take a series of pictures that they edit in imovie to create an animated film.

The project, The Animated Classroom: Using Japanese Anime to Engage and Motivate Students, was recently written up in the September edition of the English Journal. For the math aspect of this project, the students read and timed their entire movie, and then read and timed each scene. The art teacher and her previous students had determined that they would need 2-3 pictures per second to make the animation appear “smooth”. So I had my students calculate the range for the number of pictures they would need for their total movie and for each scene based on this estimate. It is important that the students take enough pictures as it is often difficult to go back and take more pictures once the shooting is over.

The students take all of the shots and do their own editing. The characters in their movies can be anything from lego figures to barbies and paper dolls, or they can draw on a whiteboard. An interesting part of the project for students is determining the angles to take the shots from, and how much they should pan or zoom. Since the characters aren’t alive, it would be very boring (and not very animated) for the characters to be just standing facing each other during the talking.

Fortunately, I am friends with Matt Clark, the two-time Emmy nominated Director of Photography of the NBC hit show 30Rock. With this project looming, and all of these camera angle questions in mind, who else better to ask than an extremely talented and exceptionally good-natured cinematographer?

Thanks to Skype, we were able to live stream Matt into my NC classroom directly from 30Rock’s NYC set! Thanks to a overhead projector, we were able to put his face on the BIG screen! However, for him to see the students, they had to sit in front of the computer when they asked their questions. We also hooked into the sound system in the room, and it was great hearing his voice overhead! But there was too feedback, so we had to go back to computer audio.

Each group collaborated before the interview and came up with the questions they wanted to ask him. The students came up with some fabulous questions and I was impressed by their professionalism. It is so hard to believe that they are only 12 and 13 years old sometimes. They are an amazing group of students! Some of the questions the groups asked about were camera angles, panning, zooming and the amount of hours it took to film a 30 minute episode (the answer is 60 hours!). Thanks Matt for the math lead there – we are going to find that rate tomorrow in class and see how their filming hours and finished film time compare to 30Rock.

When they were finished asking their group questions we had a couple more minutes so Matt gave them more great tips about filming. Then, I let them ask their fun questions. They were most interested in the number of re-takes Matt had to take (especially of Tracy Jordan)! At the end, they thanked Matt and then all at once said, “Who Dat Ninja?”. That gave Matt a laugh. My students had obviously been planning that one. ; )

Click here to watch a video segment of our Skype call!

The video is on YouTube now but will be embedded once Zamzar is finished converting it!

Tomorrow the art teacher is going to have the students chose two of Matt’s suggestions to incorporate into their film. It should be another exciting day!

I Just Cannot Get Over Google Docs!

Posted on October 25, 2010 by I Speak Math

I really cannot get over Google Docs. I just CAN’T! It is so amazing! I am having my 6th graders finish up their “How I Spend My Time” Google Spreadsheet project this weekend. All they had to do was enter in their decimals, insert a chart, and then print it out at home. Many students finished entering all of the information during class, so they just had to insert the chart and print at home.

There are two things that I love about Google Spreadsheets. One, as a student types, I can WATCH them type! Two, if they have questions, they can ask me i in the chat box. Then, I can give them suggestions and even look at their sheets to see what is going on.

So, it’s Sunday night and I am working now that the kids are in bed. I open the Google Docs to see how my students are doing. I pop into the chat box to ask them if they have any questions. I look at their work and help a few of them.

Here is a screen shot from my computer of all of the action (click on the picture to see everything including the chat box and the pie chart)! It’s amazing, and I love it! Everyone should try this!

Google Docs in Action!

Solving for Y with Cups and Kisses!

Posted on October 24, 2010 by I Speak Math

My students beautifully tackled two step equations with ease, showing all of their steps along the way and solving to perfection! So, when it was time to graph, I decided that we would spend a day solving for y before learning all of the different forms of the equation of a line. Sometimes as a teacher, you assume a new concept will be easy for your students. However, my students are treading through the new waters of Algebra, and what seems obvious to me is not always obvious to them. After I spent hours making a fun “Solving for Y” Jeopardy game so that would could spend an hour solving equations for y with glee, we instead spent an hour of misery. The kids were tortured by the problems that they thought were “way too hard” simply because they did not understand what they were supposed to be doing.

My mistake was that I assumed since they could solve for x in two-step equations so beautifully, that throwing a y in there would be no problem. What I missed was that unlike students I teach in high school, these students had never solved equations with two variables before and simply did not know what to do with them. Can you add them, subtract them, put them together? Solve for y? THAT is not an answer! We are used to seeing x=12 as an answer, not y = 2x – 5. Ohhhh….. Finally my light bulb went on.

I felt so bad. I wasted a day of learning (for them, as I had learned a GREAT deal). I was desperate for them to see how easy it was to solve for y, and let them get lots of practice at solving for y at the same time. But, I had already lost a day, and some of their trust. They did NOT like this “solving for y”. I had messed up.

So, what do you do when you mess up and want to make it right? Well, give them candy of course! ; ) Thanks to an amazing brainstorming session with the wonderful, brilliant teachers on Twitter a new plan was devised. We would solve for y in the style of “Hands On Equations” with small Solo cups, Hershey kisses, and integer counters.

I used two colors of Kisses (one for +x, one for -x), solo cups for y (sorry, no -y’s), yellow and red integer circles for the numbers, and my “Hands On Equations” equation mats. I made a worksheet (at end) and modeled the equations with my new best friend, Elmo. I had them model EACH equation, and write exactly what they modeled (in equation solving form) on their worksheet. THEN, we moved on to solving without cups and kisses.

** The BEST part of this activity was by far the cups! **

When I had 3y = 6x + 3, I asked them, if 3 cups equals 6 Kisses and 3 chips, then how much does EACH cup (or y) have? By using cups they could actually put 2 Kisses and 1 chip in each cup. An unexpected plus of the cups was that the students did not once forget to divide BOTH the coefficient of x AND the constant by the coefficient of y!

Solving for Y with Kisses and Cups

Another highlight of the activity was the last problem. It came down to 4y = x + 4. I was so excited to see the students realize that each cup got 1/4 of a Kiss! They discovered that they had to split the Kiss into fourths to put an equal amount of Kiss into each cup. So, the answer was y = (1/4)x + 1. My HS students in the past have always had trouble extracting the slope when they come up with y = x/4 +1. I am really hoping Kisses help them greatly with this! We will see this week as we delve into finding slope! : )

My favorite part of the whole day was hearing kids say, “Wow, this is so easy!”. Their favorite part was eating the 6 Kisses I allotted per student at the end of class.

Solving For Y with Cups and Kisses Activity Sheet

Fractions in Action…Free-Throw Fractions!

Posted on October 24, 2010 by I Speak Math

I am used to teaching precalculus, not fractions. I was not really looking forward to teaching fractions to my 6th graders this year. In the high school setting, most students have severe adverse reactions to fractions. So, I decided that I had to do something FUN to save everyone’s sanity. I wanted an activity where they would want (or at least get) to practice tons of operations on fractions. Luckily, I am at a project based school and they highly encourage “thinking outside of the box”. So, I decided to take them “outside”!

We met outside on the basketball court, and each student could volunteer to shoot free-throws. They drew to see if they would throw 6, 8, or 10 shots. Then, we kept track of their shots on the “Free Throw Stats Sheet”.

FreeThrowFractions

After all of the kids had gone, we sat down at the picnic tables and …

Wrote the fraction “shots made / shots attempted”.
Simplified the fraction
Wrote the simplified fraction as a decimal (dividing by hand)
Found what our shot percentages were (decimal x 100).
Found the LCM of all shots attempted.
Wrote equivalent fractions using the LCM.
Compared all players using the equivalent fractions.
Compared ourselves to our local college basketball teams.

After the first 4 steps, I had them just look at the players and estimate the top five shooters. Then, after we did the equivalent fractions, we actually ordered all of the players to see how close our estimates were. With the number of shots that we took, the kids were pretty accurate in their estimates before making the fractions equivalent. Ah, if I only had more class time in a day!

Back in the classroom the next day we compared ourselves to the local college team. The GREAT thing was that the percentages were listed in decimal form! That was such a bonus for me and really made them think about it more. (ie – The highest women’s free throw percentage was 0.806 – what is this percentage? Not 8.06 or 806 but 80.6 % – ahhh!!!)

Davidson College Women’s Basketball Stats

Davidson College Men’s Basketball Stats

Instead of all around groans when we did fractions, the kids seemed to really enjoy it. As we were shooting, the kids were doing much of the math in their heads and then saying things like, “I’m at 100%!” or “Two out of four – I’m at 50%. Hey! I’m as good as Shaq!!” Plus, sometimes it is just great to get outside on a beautiful fall day! : )

As always, suggestions welcome for improvement of this activity for next year!

Suggestions Needed for Seating Arrangement in GDocs Group Project

Posted on October 23, 2010 by I Speak Math

My 7th grade class is doing an group project involving Google Docs. They are creating a presentation in Google Docs where they insert movies they made and a graph they created in Google Spreadsheets. We are down to the “putting it all together” stage, where they will need to simultaneously add pages to and edit the presentation on their individual computers. There are groups of four students each. The last day we worked on it they sat at tables with two students on each side. However, with the computers open, the four members were completely “disconnected” from each other. The two students on each side were able to work together and see what the other was doing, but they were not interacting well “across the table” for mainly spatial reasons.

I am at a very open school and we can go anywhere on campus, outside, in the grass, on the patio, on picnic tables… But, I would love suggestions of HOW I should have them sit to best facilitate working together as a group of four with open computers. I have several ideas listed below, but would love to know if anyone has done this before and if so, what worked best for you?

Ideas:

Four kids in a row on a picnic table – laptops all in a row. Everyone can see everyone else’s computer, but the end kids seem far away.

Four kids in a circle, with open laptops almost touching. I don’t have large enough round tables to facilitate this however, so could they have the laptops on the ground and be “hunched” over them? It’s not very ergonomic, BUT the kids could actually SEE their group members over the computer screens.

Three kids working on computers in a row and one “reader” who makes sure their group includes all aspects of this detailed project. I would have the reader be my most proficient computer user so (s)he could help the others instead of just doing most of it on (her)his own.

That’s all I’ve got! Please help! : )

Concept Based Blank Study Guides

Posted on October 8, 2010 by I Speak Math

I am using a “mini-SBG” system with my classes this year. They have a list of concepts and a Concept Checklist where they keep track of their progress on each concept. I give them a pretest before each set of concepts where they can earn a score of B (beginning), D (developing), P (proficient) and E (Exemplary) for each concept. As we move through the unit, I quiz them on certain concepts, and then they update their Concept Checklist. (More detail here).

Students always have a hard time studying for chapter / unit tests. I have them make index cards as we move through the chapter so they will have those to study from. However, I also want them working extra problems to study before a test. However, in a large unit it can be difficult for them to pinpoint exactly which problems they need to focus on. So, I created a blank study guide.

The Blank Study Guide has three sections. The first section is CONCEPTS and has the students list the concept number and name of any concept that they do not currently have an E on. I believe I may change this to to however since I grade the concepts very hard and it takes perfection to get an E.

The second section is NOTE CARDS and asks them to list any index cards that they are having trouble remembering, or any vocab words that would like extra work on from the index cards.

The third section is called EXAMPLES and is for working problems. I tell them to refer to section one and to find at least one example problem from their books or their notes for EACH concept that they listed in section one.

Blank Study Guide
Most of the students who did the study sheet really liked it. They told me that it helped them know what to study. Some of the students did not do it, or were confused by it. But, that is all part of the learning process. As we do a study guide for each chapter I believe they will become more proficient at completing them.

Making Middle School Magic – Powerpoint Jeopardy!

Posted on October 6, 2010 by I Speak Math

Yes. Today was simply magical in my 6th grade classes! They came into class with Weird Al’s “I Lost On Jeopardy” rocking the classroom at full blast! I had them dancing like crazy before class began. I even had a few guess, “Are we going to play JEOPARDY?!?!?”

I put them in six groups (two to three students in a group) and gave them whiteboards. The rules were that ALL group members had to agree on the same answer and ALL members had to have all of the correct work on their boards. I went i order around the room and let each group pick a category/point value. However, if they MISSED the question then another group got to try to answer it. I picked this group by rolling a dice.

I used a PowerPoint Jeopardy game that I found online and tweaked. I found a Jeopardy theme song midi online and added it to all of the question slides. Although the music got really old for me by the middle of the second class, it added a bit of fun and even excitement to the game. The music made the kids try to “beat the clock”.

This game went so well! The kids worked harder than I have ever seen them work! Most importantly, they worked together better than I have ever seen! They were all intensely engaged and at the end of class they even BEGGED for just one more math problem! (Which I of course could not help but give them – to the detriment of their next class, sorry JuRu.)

I need to work on this game some more as several of the links were corrupt. Also, you could not tell which questions had been selected. I am actually going to create my own game with all of the bells and whistles and then post it here so please check back!

Walking the Walk: Teaching Math Vocabulary

Posted on October 2, 2010 by I Speak Math

I speak math is my blog title. I feel I am a translator of math into english. However, what I would really love is for my students to speak math as well. When I started this summer, all I has was, “One vocab page for each chapter”. However, thanks to Twitter and the wonderful world of the internet, I have come up with a few more strategies. I have dismissed the “one vocab page for each chapter” for now because of the Index Card Flip Chart that we are making in class. What I am currently doing is called, “Vocabulary Illustration”. I did not come up with this fabulous idea, I got it from Bill’s blog here and then tweaked it a bit. I assigned the project to my 7th grade class and got some really neat illustrations! However, they weren’t as “fine tuned” as I would have liked so I created a rubric to guide them on their illustrations. Vocabulary Illustration Rubric.

Now, I randomly assigned each student a word from each chapter before we start that chapter and hand out the rubric. On the day they are due, each person presents their illustration to the class. I grade their illustration while they are presenting so they get immediate feedback.

After they turn them in, I have the other classes vote on them (names omitted). The next day, I award the winning illustrations with a prize from the prize pail. I also hang up all of their illustrations in the room.

I believe that I may go one more step this chapter. After hanging the illustrations up, I am going to give each student a blank sheet of white copy paper and have them copy their favorite illustration for each vocabulary word to keep in their folder. I am hoping that the visual vocabulary will reinforce their understanding (and recall) of the words. When they are studying for the test, they can study their index cards and their vocabulary sheets. I will post a picture of one after we make the sheet.

The Math Wiki is full of more vocabulary ideas that I have yet to try! And I am always looking for great ideas to help students attain a working math vocabulary! So, if you have them, please let me know. : )

Negative Numbers!

Posted on October 2, 2010 by I Speak Math

I am teaching negative numbers to my 6th grade class. Most of them have either never worked with operations on signed numbers or have only worked with them briefly. As soon as I brought it up, many students groaned. When I inquired about the groans they told me, “Oh – I HATE those!” and “I just don’t GET them.” A few students however were happy to offer up the “rules” that they had memorized. Unfortunately, the pretest I had given showed that even those students were not computing the signed numbers correctly.

I basically had a blank slate. So, I decided to start from scratch and introduce signed numbers using red and yellow integer circles. I made a worksheet where they progressed through the following problems.

addition of numbers
addition of negative numbers
SUMMARY
subtraction of numbers
zero pairs
subtraction of negative numbers
SUMMARY

: Integer Circles and Worksheet

I had them draw the circles on their papers and even encouraged them to use red and yellow markers. The loved it and understood it all! Until we came to subtraction of negative numbers like 4 – (-3). For some reason, this concept really gets kids. Even with the circles in front of them, they want to make this problem 4 + (-3). It happens over and over again. In my past experience it is misunderstood by so many that I honestly thought about teaching multiplication and division of signed numbers first and then just saying, “You are just distributing a -1!” But, my conscience would not let me. I wanted them to really SEE it! So, I plugged on, showing them how if you have four yellow circle (+) and you put three red circle (-) down to cancel and get 1 circle then you DON’T have 4 – ( -3), you have 4 + (-3). At this point, I heard many “lightbulb” moments throughout the room.

We also went outside and drew number lines with chalk on the sidewalk and then “walked” the problems. They actually walked out how a subtraction of a negative ends up adding. They really seemed to get it.

Before class was over I did a three question “quick check” and did not let them use the circles (but they could draw them). The questions were…

1. -3 + (-4)

2. 5 – 7

3. 5 – (-6)

Everyone in the entire class got number one right. Only two kids missed number two. But, over half of the class missed number 3! The most common incorrect answer was -11 !!

In summary, I think that the chips were almost a success as they now get everything but “subtraction” of negative numbers. Almost isn’t good enough however. And, I don’t want to just tell them the rule and have them compute it. I want them to understand it and to know it. But, I feel like they have done so much work with this (two days) and are still lost on this concept.

Maybe I am expecting too much too soon. I have not taught this grade level before. Is this such a new and foreign concept to them that it just takes a while to absorb and a lot of practice to be able to calculate this sort of problem? Will they eventually get it or must I insist on them getting it now.

UPDATE: FOR NEXT YEAR:

I don’t know about you guys, but my brains works fiendishly at night while I sleep. I wake up in the morning refreshed and with new ideas churning (especially if I am thinking of an issue (or blog about it) right before I go to bed. So, here is what I am going to try next year.

Day One – Addition and subtraction of numbers, excluding subtraction of negative numbers. I am going to use three models.

circles
money (thanks Cathy!)
“walking” the numberline

I want them to be very secure in this concept and to UNDERSTAND that 3 + (-4) is the SAME thing as 3 – 4. To strengthen this I am going to draw the circles on the board and have THEM make up the equations, then have different people write their equations on the board. The kids will see how the different equations mean the same thing. I may have them make up money stories as well for this.

DAY TWO: Subtraction of Negatives

For the warm-up I will review yesterday and introduce zero pairs. Then, I am going to START with the number line (or the money), or both. I will then move to modeling with the circles. THEN I am going to have them write the equations for the ones that I model. Finally, I am going to insist that they re-write 8 – (-2) = 8 + 2, over and over again. I want to spend an entire day on this because they seem to really get everything else, but this throws them!

If you have any comments, suggestions, or great ways you conveyed this to students I would really appreciate it!

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