Mills, Bills, and Trill

The first week of school lesson plans usually consist of getting-to-know-you type activities.  In planning, I figured it would be a great time for exploring in math.  I hemmed and hawed about it.  At first I thought I’d do a 3 act lesson.  They are always exciting and engaging, but I couldn’t think or find one that these kids hadn’t seen in 5th grade.  

But then I found this……

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This was a picture I found a long while ago and kept it in my files, never knowing what to do with it.  I saw the math in it, but didn’t have a solid idea.  However, over the summer, inspiration struck and I got to work.  

Have you ever asked your students about millions, billions, or trillions?  Do they truly understand the magnitude of these ginormous numbers?  It was worth a conversations.

Part one of our investigation was showing the above picture and simply asking “what do you notice and what you wonder?”

My students recognized notice/wonder which thrilled me.  Some perked right up when they saw those questions (which made me smile).  I noticed that my students focussed on the picture itself.  Some of my higher thinkers started pondering the saying.  Finally, we got to the question I was looking for….which was how many pictures are in a video.

Here’s the information we were looking for…Screenshot 2017-08-19 21.24.24.png

We decided we needed to figure out how many pictures were in a second, then a minute, and so on.  They determined that one second of video would be worth 2400 words.  And the video would have to be less than 1 minute.  One minute of video would be 1,440,000 words.   Not bad for my 6th graders.  They were getting the hang out this.  

 

Then I asked them how long it would take them to draw a billion circles.  Saw this at a workshop given by Graham Fletcher back in January and I finally found a use for it. The students were thrilled to investigate this for sure.   

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With much enthusiasm, the students were jumping with energy on this one.   One girl raised her hand and asked, “are were really doing a billion?”  I looked at the clock and responded, “we got a few hours left so I don’t see why not.”  Their eyes got bigger.  

First we took guesses.  I felt like I was on the Price is Right.  “I’ll say 7 hours…I’ll say 7 hours and 15 minutes.”  One group kept whispering about the question and concluded that it should take about 1 second per circle.  I loved this observation because I could tell they were not only thinking, but trying to make sense of the problem.   The class concluded that we should just try it for a minute.    Before we got started though, there was more discussion on how big of a circle they should draw.  Wouldn’t that be a factor in how many they could draw in a minute?

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I started the timer and the students worked vigorously on their circles.  The looks on their faces was priceless.  They focussed, they concentrated, they were super-serious about getting this done.

When the timer went off, they counted up their circles.  We took a poll to see how many circles were drawn and the range was between 80 to 120.  For our purposes, we kept using 100.  Next, we figured out how many circles in an hour, a day, and then a year.  Finding out how many circles in a year was a bit of a doozy for them, but they persevered.  I was also happy to report that they knew how to read their place value very well.  Whew!

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We even discussed what would 2 years looked like, and they told me it would only be one hundred  million circles.  “That’s not enough.”

I revealed the answer and they were floored.  I’m not going to reveal the answer in this post because I want to leave a little mystery to the question.  Go ahead…do the math yourselves.  (Answer is in the lesson PDF below).

We weren’t done yet.  For the last piece to this investigation,  I remembered this Twitter pic from Mark Chubb.   And I also saw a ripe opportunity to break out the clothesline.  I asked my students “Where would 1 million go?  Where would 1 billion go?”

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After much debate and moving cards back and forth, this is what they agreed upon.  I was puzzled because they didn’t really know the relationship between billion and trillion.  I let them watch a video I found on Youtube and some referenced that when they were validating their answers.

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However, I wanted to push them further.  I inquired why each of the cards was equally spaced.   Were there an equal amount of numbers between each number?  Some answered yes.  Some were completely puzzled.  Rather than beat the horse to death, I wrote a few new numbers on cards to see if they could show me the relationship.  I wrote 0, 10, 100, 1000.     The conversation got a little more exciting because my students were dealing with numbers they could relate to a bit more.  Unfortunately I forgot to take a picture of the final clothesline and specifically where they moved the cards.  

Final thoughts…

  • We hear how the US and other countries have trillion dollar debts, but how many people truly know the size of that number.  It’s quite “ginormous” but how does it relate to millions and billions?
  • The students loved that they got to “investigate” something tangible.  They could all draw circles.  It was an easy task that they all handled.  It was hilarious to see them take it so seriously.  
  • The idea of the trillion clothesline was spot on with the investigation, but I saw many blank stares because the students couldn’t really fathom a trillion.  Instead of beating the idea to a pulp, we went with something they were familiar with based on their discussion and reasoning.  
  • This showed their lack of knowledge in how 10 related to 100 and so on. 
  • Considering this was the 2nd day of school, this showed that we will be making math fun, accessible, and worthy of their attention.   Many of my students said this was their favorite thing of the day.  

 

Here’s the lesson if you’d like to try it out for yourself.

 

Until next time,

Kristen

 

 

Welcome to Acosta Academy

Welcome back to a whole new school year!  I’ve spent the whole summer steadily preparing for my new assignment and it’s one that I’m embracing.  

Here is it…the night before my first day at a new school, new routines, new students, new colleagues—actually, they aren’t that new to me.  I’m supposed to be trying to rest up and review my plans for tomorrow and all I can think about is “I have to blog about this!”

To catch you all up….I used to be a middle school math teacher for 16 years.  The last 2 years, I was a elementary math coach.  Now I’m going to conquer teaching 6th grade, but at an elementary school.    I get to be with little kiddos again.  Ok…my kiddos won’t be so little, but I get to experience the joy, the smiles, the high-five moments, and the celebrations that come with learning.   

This transition was tough at first.  In the months following my decision, I had weeks where I was raring to go and then weeks when I was doubting myself.  I kept asking myself if I made the right decision by heading to an elementary school.  My 6th grade buddies at the other elementary schools were cheering me on every step of the way.  And with positive mindset, much support from the other 6th grade teachers, and lots of studying over the summer, I’m ready for my challenge.  This is going to be an awesome year.

In diving into this new experience, my inner elementary teacher started coming out.  I spent a good 2 months planning for decorating my classroom.  One of the kindergarten teachers at my site asked me back in March, “what’s your theme going to be?”  My reaction was “Theme?!?!?  Middle schools teachers never did a theme!?!?!?”  I go home and tell my husband about the conversation and he starts looking up things on Pinterest (he is totally a teacher’s husband!).  Low and behold, he holds up this picture….

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the inspiration for my classroom

My classroom is completely decked out with college stuff for my theme.  I created something from nothing.  All of what I’m about to show you is because of this single picture.    As a matter of fact, I’m calling it Acosta Academy.  I’ve had colleagues come in to see my progress and were completely floored with what I had done.  

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I also had a revelation.  I put more energy into putting together this elementary classroom than I had in all my 18 years of teaching.  I embraced the belief “Go big or go home!”  More is more in elementary.   

And in the little time that I’ve been in the elementary community, I’ve learned so much.  For instance, who knew that you could buy Walmart flat bed sheets for $5.00 and they were big enough for your bulletin boards/walls?  And I’ve discovered the joys of lamination.  It’s such a magical treat.  I can’t get enough.

And I’ve created some goals for myself for this year….

  1. Integrate 3 Acts, Which One Doesn’t Belong, Estimation,  Clotheslines, Open Middle, Numberless Word Problems, number talks and engaging math activities/stations into my math curriculum.  
  2. Learn and implement Google classroom as well as other Google tech with my students (Recently took a Google Cue Launch workshop and will be taking the first test soon)
  3. Conquer my fear of teaching English/Language Arts.  It’s a monster. 
  4. Find creative activities for partnering my kids with kindergarteners.  The kinder teacher and I have a few great math ideas/activities.
  5. Use my time in the classroom to embrace the joy, to foster curiosity, and to give my students the best for their last year at elementary school.

 

On a side note, I’m proud to announce that my kindergarten collaborator and I have been asked to speak at 2 conferences.  One of them will be at Calif. Math Council’s northern conference in Asilomar.  The other is at the Southern California Kindergarten Conference in February in Pasadena.  

I’ve also been asked the speak at my alma mater, Frostburg State University.  Sloop Institute on Leadership & Excellence has asked me to present on “Empowering Others.”  I love the topic choice and have already outlined what I’d present.  Even though the conference isn’t until March, it’s never to early to brainstorm.

There’s more exciting plans coming in the 2018-2019 year, but I’ll wait to report on that when things are more finalized.  

Until next time,

Kristen