Boogers and Bloody Noses

I suppose I should no longer be surprised when a simple estimation180 activity explodes into a full blown lesson.  Or lessons.  But ones filled with tissues?  A definite first.
 Several months back, Theresa and I decided that we needed to start getting the third graders into the "estimation180" routine.  We wanted to get them comfortable with making number lines, coming up with "too lows", "too highs", and "just rights", and justifying their decisions.
 So a few weeks ago, in Jane Garvin's third grade class, I threw this one up:

After giving them some time to get their work down, and doing some discussion, I showed them the reveal:

Some of the kids were surprised.
Kids: Only 10?  What a rip-off!
Me: Well, yes there are ten.  But it says on the package that there are Ten 3-ply Tissues.  What do you think that might mean?
Kids: ???????
Me: (as I searched for the classroom tissue box) It means that each tissue (and here I pulled one out of the box) is actually made of thin tissues stuck together.  This tissue is actually made of two thin tissues stuck together (I separated them and held up the thin tissues).  So this is a 2-ply tissue.
Kids: !!!!!!!!
Me: Why don't you think the company puts them in the pack that way?
Kids: Because if you blew your nose with one of those thin tissues the snot would come right through!

Now we were talking third grade language!  I taught this grade for many years, and knew that anything related to boogers would be met with great interest.  About as "real world" for a third grader as you could get.  I pushed on.

Me: So now that you know what a 3-ply tissue is, how many tissues are in the package?  Turn and talk with a neighbor.
Kids: (after some discussion) 30!
Me: How do you know?
Kids: Because 3 x 10 = 30!

That was certainly fun.  But I knew there was something else there, and it was related to multiplication, an important grade 3 topic.  What if I gave kids their own personal pack of 10 3-ply tissues, and asked them to separate them all?  They'd have 30 1-ply tissues to mess around with, and could arrange and rearrange them into different combinations.
 I asked Jane if I could steal her class for a period to try it out.  She agreed, and this is what we came up with:

Jane put her class into partnerships.  I reminded them about our tissue estimation activity, and explained that they were going to do a project with tissues.  I gave them no oral directions, just the sheet and a pack of tissues.

They got right to work.  When I tried it out, I had a hard time separating the tissues, but the kids did it with no problem.  One boy made a 15 2-ply tissues, folded them back up, and tried to stuff them back into the packet.  Here you see 3  10-ply tissues.

One student slipped over to her desk and pulled out a multiplication table.  What was she looking for?  

     Time was running out, and Jane helped me collect all the tissues.  Once all the kids were back in their seats, I asked them to talk about some of the different combinations they had found.  Here's what they came up with:

The only one they missed was the 1 x 30, which I was able to pull out of them with some leading prompts.    

Then Jane asked them an interesting question:
   "What do you think of a 30-ply tissue?"
The kids laughed; clearly it was overkill.  A 30-ply tissue made no sense.
    As the kids filed out the door, a quiet boy showed me the back of his sheet.
    "Is this OK?" he asked.  "Would 3 8-plys and 1 6-ply work?"
   "You tell me," I prompted.
   "Well 3 x 8 is 24, then there would be 6 left.  24 + 6 is 30."
    I gave him a high five, and turned to Jane.
   "I have to come back,"  I said.  "We're not finished here."

I returned about a week later.  I thought I would start them off with another estimation activity.  So we looked at this:

The reveal gave us a chance to practice a newly-acquired skill: multi-digit multiplication!  The kids got to work on finding how many single ply tissues there were.  Some multiplied 85 and 3 using the traditional algorithm, others used partial products.  This is a good example computation being a means to an end, not an end in itself.

 
My plan was to move the kids towards using counters rather than tissues.  We discussed the difficulties they encountered working with the tissues: they crumpled easily, they flew around and got mixed up with the tissues from neighboring groups, they were difficult to count because they got stuck together...the kids came up with an impressive list.
      "What could we use as a stand-in for tissues?" I asked.
     "Counters!" they volunteered quickly.

     Next came this question  What about 3 8-plys and 1 6-ply?  Is that an OK way to arrange the tissues?  They took a few minutes to debate this at their tables.  Some kids were bothered that not all the groups were equal; but most felt it was a perfectly reasonable option.  Time to get to work.

They worked out their combinations on poster paper.

I asked them to include a picture and a number model.

Again, the period was drawing to a close and we wanted to wrap up.  Thinking about the question Jane had asked regarding the 30-ply tissue, and the boy who had folded up 15 2-plys, I asked each group to share one of their combinations, and how practical the tissues would be if they came packaged that way.
   "I have to come back one more time," I said to Jane.  "Then we'll be done.  In the meantime, get the tissues back out!"

Several days later I was back.  This time we started with the third and final activity in the series:

     What I really wanted to accomplish in this third session was to focus on the first part of Standard for Mathematical Practice #3: "Construct viable arguments...".  I also wanted them to do a little writing, something I know I need to incorporate into lessons on a more regular basis.  So after giving back the posters and allowing them to do a little more exploring, Jane and I gave them the following task:
 
We know that personal tissue packs come with 10 3-ply tissues.  The tissue company has asked you to come up with a different way to package them.  Your group must come up with a recommendation to present to the company.  

     Jane gave each group their 30 1-plys back, and we told them to fold them up the way they wanted, as if they were going to put them back in the package.  They also had to write some sentences justifying their choice, and then present their decision to the class.  The groups came to consensus, and organized and folded their tissues.   After the previous lesson, I think they knew this was coming.
     Jane and I could hardly wait to see what the kids would come up with.  We weren't disappointed; but we were surprised at the extent having a bloody nose haunts the minds of third graders.  Here were some of their combos:

• 2 10-plys (for bloody noses) and 5 2-plys (for stuffy noses)
• 2 5-plys (for bloody noses) and 10 2-plys (for "normal snot")
• 2 4-plys (for runny noses) and 2 11-plys (if you have the flu)

     The kids enjoyed sharing their proposals, and Jane and I had a hard time holding back our laughter. This time I remembered to have them give us some reflective feedback, which was overwhelmingly positive.  They described the activity as, "fun", "imaginative", and "exciting".  And who wouldn't love hearing those words used to describe math class?

Test Prep I Can Believe In

As we wrapped up a unit on volume, and with the state standardized test looming on the near horizon, Rich and I decided to try out a project involving cereal boxes.

The kids brought these in from home.

First, they needed to find the volume of their box.  Since we figured they could use some practice multiplying mixed numbers, we decided to alter the requirement: instead of measuring to the nearest centimeter, the kids would need to measure the length and width of the base of their box to the nearest 1/8 inch.

We decided that they should use the rulers they were going to have to use on the state test.  The 7-inch rulers were not up to the task of measuring the heights and the widths of the boxes, but Rich and I decided that was OK...

...they would figure it out.

     I was most excited to use the opportunity to revisit an area model for multiplying fractions and mixed numbers, so we had the kids outline the area of the bases on square inch grid paper.

7 1/2 by 2.  We had originally thought they would do it on blank paper.  But we decided the grid paper was better because it more effectively expressed the idea that the fractions were pieces of actual squares.

At some point I had the idea that the model might be made more powerful if it was color coded by each partial product.  I felt it lent a visual aspect that was missing in the original design.  Then they had to multiply the area of the base by the height of the box to come up with the volume.

Rich's student teacher, Shannon, made a chart to to help the kids keep track of the data. (Note to self: next year have the kids create the chart themselves).  This would be used to compare findings, and also to provide them with referents for the dimensions of a standard sized cereal box.

This continued for several days.  They got a lot of practice working with fractions, multiplying, dividing, and measuring, and the fun was just beginning... because now they would have the chance to create their own cereal, and design the box.

Drawing a three dimensional shape on paper presented some challenges.  This student's ingenious use of two rulers gave Rich and I the idea that protractors could be used to make the representations even more accurate.  Duly noted for next year.

Nike is into everything these days.

Love the mascot!

For the One Direction fan in all of us.

Check out the expiration date.

This is a "mini-box".  Each group had to come up with one that was half the length, width, and height of their standard sized box.

We also had them come up with the dimensions of a jumbo box by tripling the length, width, and height of their standard sized box.  There was quite a bit of calculation involved here, but we felt it was good practice, and it was embedded in the project.  Multi-digit multiplication and addition, multiplying and dividing fractions and mixed numbers, adding fractions, converting improper fractions into mixed numbers...lots of opportunity for review, formative assessment, and on-the-spot reteaching.  Turns out that there were quite a few kids who forgot how to do many of these operations.  Go figure.

     The kids loved it.  There was a high level of engagement, great collaboration and problem solving, and a nice blend of computation, measurement, and geometry.  As we put the projects away (we're not done with them yet!), and headed into the week of the NJASK, my one thought was: That's the kind of test prep I can believe in.

Teacher Appreciation Week

I am grateful for Mr. Tom DiGanci, my social studies and history teacher at Watchung Hills Regional High School.

He taught me that there was a world out there much larger than the one I could see.
He taught me that history was alive, and encouraged me to take my place in it.
He knew that we had to be engaged in order to learn.
He played Moody Blues records on a beat up school record player before class.
And he always had time to listen.
Thank you, Mr. DiGanci.

And thanks, Christopher Danielson.

Another 3-Act

Fresh off their mile walk around the perimeter of the school, the fourth graders took a crack at another 3-Act.

ACT 1:

How much would it cost to spread grass seed on the field?

The kids are quite familiar with this field.  They've been playing on it for years.  

 

We thought it would be a good idea to give the kids a visual.  Jeff found a video for the afternoon class to watch.

ACT 2:

What do you need to know?

What the AM class wanted to know.

What the PM class wanted to know.

Here's what we gave them:

I made copies of the screenshot for them to have at their desks.

Jeff likes the Pennington grass seed.

  
ACT 3:

Let's Get to Work!

Some kids wanted to work on the task on their own, in their math notebooks, and I gathered a few kids back at the whiteboard and we tackled the problem together.  I tried to let them take the lead, facilitating and questioning to keep them on the right track.

We've done a lot of math and we're not even finished yet!

     The kids in the AM class had some trouble getting started.  I suggested a table, which I began and they finished.  An interesting discussion then took place around what we teachers would call "interpreting the remainder", but what they called, "Do we buy 15 bags or 16 bags?"  Ultimately they came down on the side of 16, after learning that the store would not open up a bag and give them just the amount they needed, and after overruling one boy who wanted to save $50 and leave some of the field unseeded.

The kids in the PM class started right away, using something like a "trial and error" method.  After a discussion much like the one that took place in the AM class, they also decided to buy 16 bags of seed.

And also came up with a price of $800.

I believe that the most important piece takes place in Act 2.  It's so strange, and so unlike what we normally ask kids to do in class:  just answer the question.  Yes, they're going to get to do that, but first they need to figure out what they need to know.  We can learn so much about their understanding of concepts from the information they request!  And some of that information we will provide (like the measurements of the field, and the grass seed specifications, although the project would even be better if the kids did their own work on Google Earth and researched grass seed on the Home Depot website), but the rest they'll need to get for themselves (with a little nudge or redirection when needed).  And we've got lots of computation, but as a means to an end, not an end in itself.
  There are some things we need to think about:

• How will kids be held accountable for their work?
• What exactly do we want to assess?
• How involved should we be in the problem-solving process?    

 But I think we've made a good start. Now where can we come up with $800?