Barbie Bungee – Special Request Edition

Barbie Bungee is the most anticipated and talked about activity that I do in my 7th grade Pre-Algebra class.  Sadly, I will not get to teach next year’s 7th graders since I am changing schools. So, my 6th grade students asked me if we could do Barbie Bungee THIS year!  Barbie Bungee is such a great learning experience, and what other time do students actually BEG for a math lesson?  Of course I said yes!  I had a blast, and I hope that they gained experience in scatterplots, lines of best fit, and linear equations.

Barbie Bungee – 6th Grade

“I Feel So Accomplished!” – Problem Solving, Noah’s Ark

“I feel so accomplished!” is what I overheard a student say after doing the Noah’s Ark problem solving activity in my class today.  I also heard, “You will REALLY like math class today!  It was so hard, but so much fun!”

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I gave them the Noah’s Ark problem (thanks Fawn)!  I followed Fawn’s suggestions for problem solving because she is the expert.

  1. Give them all their own copy of the problem.  (And a sheet of animals to cut out if they wanted it).  Noah’s Arc PS
  2. Let them read it silently
  3. Let one of them read it aloud while other students read along silently.
  4. Let them work silently for a few minutes.
  5. Let them work together.
  6. Discuss solutions.

While working silently, many students came up with a solution.  However, once they started working with others, they realized that their solutions may not be correct.  I loved how they were explaining their solutions to their classmates, and their classmates would say, “Oh, but then you would have too many zebras.” and I would hear the, “Ohhhhh…”  My favorite had to be “But WHAT is kangaroo?  WHAT ARE YOU?”  Several students asked for another copy because they had written all over theirs and wanted to start again.

 

Some students let the animals equal animal values.

Some students let the animals equal animal values.

Most students had to work together to come up with the correct solution.  A cluster of my students decided to assign point values to some of the animals, and variables for others.

This was an altered version of substitution, and so interesting for me to see.  I loved how they molded the problem to fit their level of understanding.  Their minds work in fascinating ways!

Student Solutions:

Here the animal cut-outs are used to visually show the substitution.  This was helpful for the students who were not convinced by the algebraic solution.

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Noah’s Arc PS

Paper Airplanes for Measures of Central Tendencies

IMG_6886I got this amazing idea from Bruno Reddy, @MrReddyMaths.  Go and read his post here. I love his discussion about mean and deciding who should win!  When I saw his post I knew it would be fun.  I planned on using the data to calculate mean, median, and mode.  However, I did not realize how much mileage I would get out of this one activity!  I pretty much teach the entire data chapter using just the data from this one activity.

I have my students watch the “How to Make a Paper Airplane” video and give them the template.  I do not give them any instructions and do not allow them to help each other.  Following directions is always a skill I am trying to teach 6th graders.

After we make the airplanes, we get to fly them!  Of course, I make it a competition. And of course, I video it!

Everyone gets a partner, to help with measuring, and three attempts at the best flight!  Student’s whose planes fly backward get to record NEGATIVE flights.  All three flights are recorded and then entered into a Google Form.  For homework that night, they had to find the mean of their three flights.

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Line Plots and Scale:

I have students make a line plot out of all three entries.  This year, I only had 21 students, so this is 63 entries.  This is a great time to talk about scale.   I have them record their distances in inches, but then they quickly realize that it is a much better idea to make the line plot using feet.  We find the mean, median, and mode of our data using our line plot.

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Range:

Range is one of my favorites here, especially with the inclusion of the negative flights.  This year, our flights ranged from about -300″ to 600″.  Predictably, almost all students told me that the range was 300″.  Students love plugging values into formulas incorrectly.  To help correct this misunderstanding, I had my -300″ flight student and my 600″ flight student come to the front of the room.  I stood at the starting point (the edge of the blacktop for us, also known as 0) and had them stand where their respective planes had landed.  Students immediately not only saw that 300″ was way off, but they saw why.  This was a wonderful opportunity to show them that 600 – (-300) was indeed 900″, not 300″.  My analogy to help deepen understanding was, “You leave from Charlotte to fly to New York, but you have a layover in Atlanta first”!  Nothing is ever better than visual learning and real life examples.

Box Plots:

The next day we learned about box plots.  I project the line plot of our flight data and as a class we make it into a box plot.  They loved seeing that a box plot can helpfully catagorize  their data.  Outliers are visual here, as well as where 50% of their flights landed.  Next year I am going to take a picture of their airplanes laying on the blacktop to back this statistic up visually.

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I also had the students create a box plot of their mean flight data.  They wrote their mean flight length (in feet) on a sheet of 8×11.5 paper.  Then, they organized themselves into a human box and whiskers plot.  The students who were the lower and upper extremes, Q1, Q3, and median all held index cards with the name on them.  We also decided who was in our interquartile range.

Histograms:

The line plot looks very much like a bar graph.  After a very brief explanation about histograms, we turn our line graph into a histogram.  The students love seeing their data grouped and of course ask why we didn’t do this in the FIRST place instead of making the tedious line plot.  It’s all for the sake of learning.  (Insert evil teacher smile.)

Google Doc Data:

I shared the data with the students and we then all made bar graphs and histograms on Google Spreadsheets.  The students like the histograms better as it condensed the data into groups.  They also learned how to sort the data and find the mean using a formula.  Again, they love finding the mean using spreadsheet formulas, find it less “mean” than calculating it by hand, and call me a “mean” teacher for not showing them this in the first place!  Practice makes perfect.

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Proportional Reasoning – Capture Recapture with Goldfish

IMG_6411You know a lesson is awesome when the Goldfish that the kids get to eat aren’t even their favorite part of the lesson!  I had done the Capture Recapture lesson a few years ago and it didn’t go very well, so I abandoned it.  However, after seeing a video about the concept (thanks to Alisan’s presentation at NCCTM), I decided to revisit it.

I introduced the concept with a question from NRich, then we watched this video on YouTube.  It is imperative that you show your students the video.  If a picture is worth a 1,000 words, a good video can be worth 1,000 explanations.  The video starts with ping pong balls, then moves on to black cabs.  I only showed my student the ping pong portion with my students, and then stopped it before he showed the math.  I had them calculate the estimated number of balls, and then showed them the result.  They were hooked!

We moved on to Goldfish.  I gave each pair of two their own “pond” full of about 150 yellow Goldfish crackers in a container.  I also gave them a small sample of colored Goldfish in a dixie cup.  I first had them estimate the number of fish in their pond.  I would not let them dump the fish out  for the estimation as biologist do not dump the fish out of the pond.  We then counted the colored fish (our tagged sample) and replaced Goldfish with the tagged colored Goldfish.  I let them eat the fish they replaced.  After mixing the tagged fish into their pond, they took a sample and calculated the proportion.  To have accurate results, we repeated this 4 total times and then took an average.  After they calculated their average, they counted their fish and we compared results.  This was the best part!  They were shocked to see how close their calculated proportions were to the actual number!  Most groups were only off the actual count by 10 or less Goldfish!  I even  had groups come within 1, 2,  and 3 of the actual number of fish in their pond!

Procedure:

  1. Estimate number of Goldfish in pond and record.
  2. Count the number of tagged fish, record.
  3. Replace Goldfish with tagged fish.
  4. Mix tagged fish into pond.
  5. Take a new sample.  Count total sample and tagged fish, record.
  6. Calculate proportion to find estimated number of fish in pond.
  7. Repeat this three more times.
  8. Find an average.
  9. Count actual fish in the pond and compare.

Files:

  1. Pdf – Capture Recapture Data Sheet
  2. Powerpoint – Goldfish Proportions Capture Recapture
  3. Slideshare File (same as ppt, but in slideshare)

Goldfish Capture Recapture Worksheet

Algebraic Expressions with 6th Grade

At Twitter Math Camp, Nicole Paris introduced us all to the “orangamallow“.  Wow.  So simple, yet so brilliant.  How many times have I SAID, “a + b doesn’t make an applebanana“?  But Nicole took it one step further and SHOWED this to her students, bridging the gap from the concrete to the abstract.  Never underestimate the power of manipulatives, or visuals.

My students loved this so much, and got so excited about it, that I even recorded them today.  This is big for me because I have never recorded myself teaching.  But, I wanted Nicole to see how her idea inspired my class.  THIS is why you all should be blogging and sharing, even if you don’t think you have that much to add.  OR, if you think that what you have to add is obvious and couldn’t help much.  Please find the time and blog your lessons!  Just watch my students, who got so excited when I brought out the bag today that I was instantly sad I wasn’t already recording.

I also didn’t really want to record myself, so I hid behind the table as much as I could.  I should record my lessons more as I noticed so much that I can improve upon in just one short video.  Wow.  I noticed that I talk way too much, no surprises there.  But, when I talk too much, I say stupid things.  I actually said algebraic equation instead of expression twice.  Oh my.

Kinesthetic Algebra – Making Abstract Variables Concrete

If you haven’t signed up for Explore the MathTwitterBlogosphere initiative, YOU SHOULD.  Because, as Tina said best,

No matter how much time I spend online, I’m always happening upon new parts of our awesome math teacher community. Even yesterday, when we were planning the first few missions for this oh so exciting event, I learned about some sites I didn’t know existed. This is exactly why I am inviting you to join me on an exploration of the best parts of the internet – the Math Twitter Blogosphere.

Tina Cardone

Yes, this exact same thing happened to me on Sunday.  I got this idea from Emma McCrea.   I tweeted her immediately to tell her how much I enjoyed her lesson, and she tweeted back that she has signed up for Explore MTBoS!  Win-Win!

I gathered spaghetti, yarn, and dental floss cut into different lengths, colored index cards cut into squares and rectangles, foam cubes, and then more of these pieces taped to other pieces.  I dumped them into five bins.  This was actually pretty fun for me.

Notice and Wonder:

When the students came in, I gave each table group a Notice and Wonder form and a bin of stuff.  I told them nothing except, “Fill out the Notice and Wonder form with your group.” We have done Notice and Wonder many times before, so they got right to it.

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They were FABULOUS.  Groups had great questions for me such as, “Is this 2D or 3D?”.  They noticed the different size shapes, lengths, and combinations.  They wondered if they were 1D, 2D, 3D or all 3D?  They wondered if they combined shapes were 4D.  Many groups even started sorting them.  Great idea.

Sorting:

I then had the groups sort their objects however they wanted.  I did get a couple of interesting sorts, but almost almost all groups sorted the same way.  So they could see what I was seeing, I had all of the groups walk around and look at all of the sorts.  My crazy sorters were able to see how most of the groups had sorted.

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After sorting, they shared their notice and wonder.  I explained to them that ALL of the objects were actually 3D, but we were going to look at them as 1D (length), 2D (flat paper), and 3D (3D objects).  At this point, the kids all said, “Like Flatland!” and a connection was born.

After that I drew pictures of the objects on the board, starting with 1D and moving up to 3D.  We talked about how the lengths of all of our green string were close, but different sizes, and how we can use a variable to name an unknown length.  To make this more interesting, I let them name the unknown lengths.  This was a HUGE hit, and they picked funny names like Wormy (w) and Doofy (d).  As we picked more lengths, it was a great chat when they wanted to name a new length Wanda (w), but could NOT because we already had a w and it was NOT the same length.  It was a blast!

When we had progressed all of the way to the cubes, the kids noticed a pattern.  They noticed that the variables for the 1D objects had 1 as an exponent, some 2D objects had an exponent of 2, and some variable of the 3D objects had an exponent of 3.  I love it when magic happens.

To end up the first day, we discussed the difference between wormy + wormy and wormy times wormy.  I held two wormy strings together to illustrate addition of two lengths.  I also drew a 2×3 multiplication array to illustrate multiplication and make sure they were getting the difference.

They seemed to get it (and seemed to enjoy it).  Tomorrow, I am going to let them cut their own lengths from spaghetti and draw their own 1D, 2D, and 3D shapes.

The next day, I will do Emma’s great sorting activity!  It is at the bottom of the page.  I will let you all know how it goes!

Snowball Fight Icebreaker

I have never needed to lead an icebreaker – until #TMC13 when I facilitated the Middle School Math Morning Sessions.  I teach at a small private school.  Almost all of our kids have known each other since early elementary school.  The class size goes from 16 to 32 from 5th to 6th grade.  However, they have tons of bonding time and activities together before they go to math class so I don’t really need to do an icebreaker.

I was nervous about leading the MS Morning session, especially since we had almost 40 people signed up!  Several participants had told me they were nervous too so I wanted an icebreaker that would be fun and get us moving.  Since there were too many people in the room to do musical chairs, we had a snowball fight instead!  This was my first time every doing a “Snowball Fight” but I think it turned out pretty well.  I sure had fun and people were laughing, so I think it made us all loosen up a bit that first morning of TMC.  I wish I had taken a picture!

SNOWBALL FIGHT! – How to Play:

  1. Don’t tell them you are having a snowball fight!
  2. Give everyone a half sheet of paper.  You should play too!
  3. Have everyone write their name and three things about themselves on the paper.  You can let them write whatever or chose things for them to write about.  @pegcagle suggested two truths and a lie, which incorporates TWO icebreakers!
  4. After everyone is finished, tell them to crumple their paper up.  You will get strange looks.
  5. Then, tell them to have a snowball fight!  We kept picking up the paper and throwing it for a few minutes.  I would suggest this as the first throw is someone curious/skeptical/reserved and people have more fun as they throw more.  Don’t let them throw too much or it could get crazy.  😉
  6. Call cease snowball!  Then have everyone grab a snowball.
  7. I start to model what to do.  I called out the name on the paper and then read their three things.  Then they read and so on.

** Warning – You may lose a snowball!  We did!  In that case, you will have to improvise.  This ended up funny and then even more funny when we found their snowball later.  I would tell the lost snowball that their snowball has magic hiding powers and then offer them a treat so they won’t feel bad.

Variations – 

  • You could leave the name off and let students guess who it was after reading the things?  I’m not sure I like this as much though bc I really liked looking at the people when they were being talked about.  However, it may be less embarrassing for students if people aren’t looking at them when their items are read.  Thoughts?
  • It would be fun for everyone to get in a line according to whose snowball they have.  Then they would all have to ask names and talk to each other (if they didn’t know each other) in order to line up.
  • I think this could also work really well as an activity instead of an icebreaker using math questions.  Students could make up a math question, have a snowball fight, and then solve the problem on a snowball they pick up.  They could then get with the person to see if their answer’s matched.

I have only done this once and never in a class of students.  I think that it would be fun as an activity in addition to an ice breaker.  I would love to hear any variations that you have done – or can come up with – in the comments!

Differentiation in Math Class – MS Sunday Funday

#msSunFunClick here to submit your MS Sunday Funday post!
This is not the first time that we have blogged about differentiation.  However, it is such a crucial topic that I’m excited to feature it again – especially since we are joining up with
Tina’s blog!  I am adding our previous posts to this list as well.
Next week our topic is “Supplies – What’s in Your Cabinet?” Please blog a quick list of your favorite math supplies (and why if you have time)!  This could be books, manipulatives, or even things like giant whiteboards!

Quadratic Frames – Totally Nguyening

If you teach middle school math or Algebra 1 and you are not reading Fawn’s blog, then you should.  I get all of my ideas and inspiration from her!

She posted a great activity about Quadratics and framing.  Please go read her post for instructions.  I wanted to post how I modified her activity for Pre-Algebra (using simple factoring instead of the quadratic formula).  I followed her instructions exactly, and modified four things.

  1. I teach Pre-Algebra so I made the problem easier for my students so that the numbers would be easily factorable and not need the quadratic formula.  As a result, my students were more easily able to discover the frame dimensions (sadly, they did not beg).  It did take most of them quite a while however and they appreciated when I finally showed them the math.
  2. I had my students draw their own picture on a 3×5 index card.  They could also take a picture and bring it in.  This way I didn’t have to find a picture for them, or print it and make copies, or cut it out.  (Yes, I’m lazy and they love being creative so it was win-win.)
  3. I used index cards so I wouldn’t have to cut up a bunch of paper to the perfect size.  Really Fawn, you are a saint.  I had my students draw the picture on 3×5 index cards, then I used 4×6 index cards for the frame.  I cut them down to 4×5 to make the border an even 1″ (see #1).
  4. I had them post the finish product on a half sheet of paper.  This way they could glue down the picture and the frame instead of using tape.  I am always short on tape.  Also, on the back of the picture is where we all “did the math”.

I am posting mainly to say THANK YOU for Fawn, and to share my students creations!  I am really into notebooks so I also included an idea for adding the work to the students notebook.

The Process:

The finished product:

On the back of their picture, we did the math.

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The Notebook Entry:

Notebook Entry

It's like a foldable!

It’s like a foldable!