Friday, August 23, 2013

NEW JOB!!! and some fraction ideas

I recently accepted a new teaching position with a middle school where I'll be teaching 6th and 7th grade math. I was fortunate to be at my last school for about 10 years exploring 7th and 8th grade math: Pre-Algebra, Algebra 1, Algebra 1A, Algebra Honors, and Geometry. I'm extremely grateful for the opportunities, experiences, friendships, and professional growth opportunities the school afforded me. As I advance in my teaching career, I'm very excited about my new position, new school, new students, and new everything. There are many differences between my previous school and my future school... and I welcome them wholeheartedly.

As my future school transitions to Common Core, I'm giddy at the thought of exploring so many wonderful concepts in 6th and 7th grade math. However, I will be working with students that have typically struggled when it comes to understanding math. Therefore, I had a few ideas about fractions I thought I'd like to explore with you.

I'll include all the visuals here, but feel free to go to my "fractions test page" at Estimation 180 to get the full experience. Please offer me some feedback. I'd like to pursue these "fraction" ideas with other items; some easier, some more difficult. Is this something you could use? Is this something worth pursuing?

Question: Where would the cylinder be one-third full?
(Image 1)

We're estimating here. I did not provide any choices because I want students to formulate ideas on their own. Look at their screen and move their finger up and down the screen to find one-third. Come up to the board at the front of the classroom and put a post-it note on the board.

Offer some choices: When ready, click on the image for choices.

Notice I said, "when ready"? Did you have students discuss? point with their fingers? place a few sticky notes on the screen at the front of the room? or something else to get students invested? Because of the restrictions at Estimation 180, this image will currently serve as the next viable step. Now students have a choice. I'm not the biggest fan of this, but it's something. Were there students who were way off because their sticky or initial guess didn't even fall within the given range?

Make a choice and demand reasoning: Why did a student choose "C" instead of "D"? Have students try and convince each other. Argue! Egg them on a little bit. Have students choose a line in which they think the cylinder will reach one-third its capacity.

Do some math? I provide you with the capacity of the glass: 1,170 milliliters. Find one-third of that. Encourage different strategies in your class. Doing the math won't tell students if the answer is choice A, B, C, D, or E, but it might help with later parts of this activity.

Reveal the answer: a really short video.

I have additional video for two-thirds, fourths, and a full cylinder (when using thirds or fourths). I haven't inserted the choices, added a counter, or other after effects. Would this be something you'd be interested in? Please let me know.

Two things:

  1. I also set this up as Red Dot (Active Prompt) activity and it'd be fun to see how students would approach this activity without multiple choice. Then, show the class their results before watching the answer (video).
  2. I'd love to see Dave Major make a slider so students could slide a bar up and down the cylinder. Using a computer or tablet, students could place the bar where they want and without a given range of choices. Then we could see who was actually correct.

What feedback do you have for me? Again, is this something you could use? Should I prepare more at Estimation 180? Would you like to see the remaining fractions and other ideas?



  1. Love the fraction activity. The lines are close enough together that it may be hard for them to choose between but the debate will be great. I am not clear on how giving them the volume of the cylinder will help - maybe I'm missing something?

    Your new school is so fortunate to get you. Best wishes for a fantastic school year?

    1. Hi Mary,

      Thanks for the kind wishes and words.

      RE: "I am not clear on how giving them the volume of the cylinder will help - maybe I'm missing something?"
      I figured this would be an additional little bonus to the estimation challenge. I wanted to have the outcome display a quantifiable relationship between the third and total volume. A teacher can use it or leave it. Thanks again.

  2. Having made a move between levels of education myself, I can tell you that I think its something all teachers should do at some point in their careers. I taught 5-6th for 8 years and then moved up (with my youngest son) through Middle and High School. This has given me the perspective that many teachers who haven't moved don't have. (if only the XXXX teachers had done a better job)

    The activity is great. I'm happy to see someone from the MTBoS working on some lower, but highly important, math concepts. I think giving the kids a good, number sense oriented understanding of fractions can only help them later on. I used to tell my 6th graders that we would be multiplying, dividing by one and "funny ones" for much of the year. Between ratios, fractions and unit conversions there are lots of opportunities to expose these students to thinking about math in different ways than they previously have been.

    I'm frequently asked what level do I prefer teaching and I can honestly say that each level has its own rewards and challenges. Upper-El is great in that many times students are easier to engage with the mathematics than high school students. They also don't have as many pressures in their lives competing for their time. I might finish out my teaching years back at that level (if possible).

    Congrats again...

    1. Thanks Hills! I really want to explore these (6th and 7th grade) concepts too.

  3. Congrats on the new job, Andrew! Looking forward to reading about this throughout the year. Three years ago, I went from teaching (mostly) grades 10-12 to (mostly) K-7 and love it.

    One idea on the fraction activity: rather than students having to verify that 1170/3 = 390, how about showing this amount being poured into the cylinder three times, adding a line after each pour and then fading in to reveal which letter matches the first line? This might illustrate the concept of fraction as part of a whole.

    1. Thanks Chris.

      Re: "how about showing this amount being poured into the cylinder three times, adding a line after each pour and then fading in to reveal which letter matches the first line? This might illustrate the concept of fraction as part of a whole."
      I have more video which contains the two-thirds and three-thirds part of this estimation challenge. Based on the responses, I'll be completing those and posting them soon. I simply wanted to give this idea a test run to see if it was worth pursuing. I agree that illustrating the concept of a fraction as part of a whole is important. Thanks for stopping in.