## Thursday, April 24, 2014

### Our First Real 3-Act

We tried our first real 3-Act on Monday with Jeff's fourth graders.  Motivated by issues of perimeter and scale (which I blogged about here), and a great post by Matt Jones over at The Math Lab @ Rm 27, we started out with this photo:

Lots of excitement!  First we asked the kids if they knew what they were looking at.  We were surprised that so many of them knew right away that it was a photo of our school.  In order to orient them, we identified some features together and marked up the photo on the smart board:

Those scale-related issues had led us to Andrew's estimation180 series on flight distances, which in turn led us to wonder: Do the kids even know what a mile looks like?  Could we relate that to the perimeter of the school grounds?  Our school does a Halloween parade every year so...

ACT ONE:
How many Halloween parade routes would you need to walk to go a mile?

 The red line indicates the parade route and also defines the perimeter of the grounds (not including the parking lot and the large field.)

After discussing individual too lows, too highs, and just rights, the class agreed that the answer would lie somewhere between 1/2 times around and 9 times around.

 Although each student is responsible for their own personal number line in their math notebooks, we also like to have a class number line as well.

Then it came time for...

ACT TWO:

What do you need in order to figure this out?

Some representative responses:
• "How long is a mile?"
• "How long is half the parade route in kilometers?"
• "I want a long tape measure that I could stretch around the school."
• "I would need a meter stick."
But we did find enough to build on:
• "What is the perimeter of the school?"
• "How long are the sides?"
• "How many feet/inches/yards in a mile?"
We told them that we would give them some of the information they requested:

 The measurements are approximate.

They liked this, but soon realized that they needed to know how many feet were in a mile.  No one had this answer, though there were some guesses, including 12 and 100.  We had them find the answer in the measurement table in the back of their journal.

 There's quite a bit of information back there, and it wasn't easy for them to locate.

After we established that there were 5,280 feet = 1 mile, we set them off to work.

ACT 3

Figure it out!

 Everyone's first instinct was to add up the side lengths.  Good idea!  Only problem was there was a disagreement about the total, due to both computation errors and the fact that some kids left out a side length.  But everyone went back to check their work and we settled on 1,880 feet for once around.
The kids realized that they would have to go around again...

 We liked that the computation was just the means to an end, not an end in itself.  And it turns out that twice around is still not a mile, but three times is more than a mile.  Hmmm.
The kids needed a bit of help with that...

 We needed to break the side where the parade starts into two separate segments and add on lengths from there until we got close to 5,280 feet.
This is how the class determined that they would need to walk two Halloween parade routes plus most of a third.  We approximated the stopping point along the driveway entrance to the school.
And that would have been the end of that, except...

ACT 4
How long does it take to walk a mile?

We couldn't resist.  Here was a perfect opportunity to build a personal referent for 1 mile, based on something that each child knew well: the route of the Halloween parade.  And since we are now programmed to think of most of our tasks as estimation180-type activities, we had to make number lines for our too lows, too highs, and just rights.

 This student had too low of 5 minutes and a too high of 60 minutes.  Her "just right" is 10 minutes.  Does she think that 10 is about halfway between 5 and 60, as its placement on her number line would indicate?  Jeff and I have talked about this issue, and what our expectations should be.

Ultimately the class was satisfied that it would take us somewhere between 1 minute and 2 hours to walk a mile.  And then we all went outside and walked a mile, almost three Halloween parade routes, as Jeff and one of his students kept track of the time.  It took about 20 minutes.
We collected the kids on the grass under a tree.  "What does a mile feel like?" I asked.
• "A mile doesn't feel like a lot."
• "A mile feels like exercise."
• "It was easy."
• "It wasn't as far as I thought."
• "A mile is tiring."
• "A mile makes me feel hungry."
Jeff and I discussed what had happened and what we might have accomplished.  Did the kids now have an idea about what a mile was?  Were they clearer about the relationship between feet and miles?  Did the activity strengthen their ideas about perimeter?  Elapsed time?
As the discussion wrapped up, one student gazed over at the large soccer field across the entrance driveway.
"I wonder how long it would be around that big field?"

1. I love this! I picture a kid sitting in a math class saying aloud, "what's perimeter again?" A classmate responds, "Remember that one time we..." and all the memories of this task coming flooding back.
It so great when you can get some much out of a task. It helps with continued informal assessments, monitoring student understanding and sometimes previewing new concepts.
Thanks for sharing Joe!

2. Thanks Jenise.
My hope is exactly what you state, that the experience will serve as some kind of touchstone for the concept. We are also doing what we can to explore activities and projects that have embedded within them skills that need to be continually practiced and refined.

3. Sounds fantastic Joe. I really appreciate the detailed explanation of the activity, as well as the rich examples of student questions and work.

Sounds like a cool dynamic with your colleague Jeff. Is that common where you are? Do you Teach together often? Must help in experimental situations like this to have a peer to kick ideas around with!

Thanks again for the post.

4. Steve, thanks so much for your comments. You ask a great question. Jeff and I do teach together quite often, and that collaboration has improved both our practices. There are students in his room that have met what we call a "basic skills" criteria, which means that they are able to receive extra services from the math specialist (of which there are two in our building). Helping them to be successful in their classrooms, rather than pulling them out, is my preferred situation. However there are times when I will meet with them one-on-one to remediate specific skills and concepts.
There are teachers who welcome the collaboration and experimentation. They don't mind if things get messy sometimes. Others are not so comfortable, and prefer me to stay in the background, or just pull their basic skills kids back to my room.