Slice of (Math) Life

Way back in September, I had read about this neat activity from Marilyn Burns called “The Door Project“and had decided to use it to start my school year.  On day one I always like to take the students for a walk around the building.  If anyone is new, or even if they are just coming to my end of the school for the first time, I want to make sure they have a chance to orient themselves, find the washroom and drinking fountain – that sort of thing. On the first day of school, I combined that with some math.  It was our first provocation, if you will.

When we got back to class, I asked, “Did you notice how many different types of doors we have in our school?”  We took a look around the class, and started thinking of ways to sort the doors in our school. Some have windows, some don’t. Some are metal, and some are wood.  Some go to the outside, and some into closets.  I gave everyone paper, asked them to think of 2 or 3 categories to compare, and away we went.  (I’ve condensed it here – we actually spent a whole class period on this!)

It was a disaster. I just looked back to link you to my post, and found I didn’t write about it at all!  That’s how bad it was.  As I recall, we were having a lot of trouble managing our data.  The categories were all mixed up, the tallies were not organized, and nobody could do anything with the information we collected. I had intended to graph our data, but, alas, it was not meant to be.

Today we tried again.

I reminded everyone about this activity, and some sort of remembered it.  We quickly reviewed our door types.  I gave everyone a choice of paper – plain, lined, or graph.  They grabbed clipboards and pencils, and lined up like pros!

We made it all the way around the school, gathering all of our data, in very little time.  Nobody had to shut their door when we stopped to count!  When we got back to class, everyone was able to count their tally marks by 5’s and find their totals in record time!

I reminded them how far we had come.  I reminded them that in September this activity had been really hard, but now it was barely a challenge.  Everyone collected the information independently, found their totals, and is now ready (and able!) to graph it tomorrow.  Now I am sorry I didn’t keep our first disastrous attempt so they could see how far they’ve come! (Who am I kidding…I probably do have it and will find it on the last day of school when I am finishing my clean up!)

What a difference a year makes!

Just about every Tuesday I blog for the Slice of Life challenge over at Two Writing Teachers. You can read posts from others on that blog.

Mapping

I sat down with the social studies curriculum the other day, double checking to make sure I hadn’t forgotten anything.  As I looked at all of the expectations, I realized I hadn’t done that much with mapping this year.  We did a bit, but not much.  Then I looked over the geometry things I knew I had left and realized that I really hadn’t done enough mapping.  So last week, we worked on mapping!

After talking about maps and their need to make things really clear and help people find things, I gave everyone a piece of graph paper.  They all drew a map of our school yard.  They did a pretty good job!

Then when we went on a walk for science, I asked everyone to pick up a small rock.  Back at the class, we painted them different colours.  The next day, I asked everyone to think of a place where they could hide their rock, then mark that spot with an X.   We were going outside to hide our rocks in that spot, then trade maps and see if someone could find our rock. Everyone was very excited to head outside and get started.

I hadn’t, of course, anticipated that the kindergarten would be outside at this exact time. It’s ridiculous because they go outside at the same time every day, but I was so excited about my own thing that I forgot about their thing.  Soon, as you may have guessed, there were 10 or so kindergarten completely over the moon because they’d found a gorgeous rock unexpectedly in the yard.

New plan:  The next day, I drew a map.  We were talking about symmetry, and I had shown a picture of school on Google Earth.  It’s a completely symmetrical building!  My map was an ariel view of the space just outside the fence.  We’ve walked there a million times.  During recess I ran back to a less than secret spot, and hid a bag of candy.

When the bell rang, I met everyone outside.  I had them join their May Learning Partner and share a copy of my map while they searched for the treasure.  Everyone wandered around for a about 10 minutes before someone said, “This doesn’t make sense.  The X is behind the school, not in the play yard.  It doesn’t make sense!”

“Why not?” I asked.  He just kept repeating “It doesn’t make sense.”  Finally I prompted, “Well, are you trying to say we need to leave the play yard and go behind the school?”

He gave me a blank look and then said, “Yeah.  I think we do.”  He then went about trying to see if anyone agreed with him and soon we were headed to the back yard.

“Pick a landmark,” I told them. “Someplace where you want me to stand.” They picked a spot; I reminded them that if they found the treasure they were to keep it a secret and come sit beside me.  Two people actually did that before another person was overcome with excitement and gave the hiding place away with a loud, “Here it is!!”  But they were all in the general vicinity when he did that, so I’m calling this a success.

For the past few weeks I have been experimenting with using the outdoors as the classroom.  We go out to do work we could be doing indoors, but I am also trying to do things that teach about the outdoors, and use the outdoors as a resource, not just a work space.  I feel like this activity would have been less successful inside because we would have all been a bit more stressed about the noise we generated.  (Ok, mostly that would be me.) I also feel like it would have been less successful if we hadn’t been outdoors so much lately, taking the time to notice the yard and the trees, and exploring the landmarks (natural and human made) around us. I feel like putting the math and mapping skills into this context helped everyone see meaning in the activity.  (Another example of how Cathy Fosnot is right about everything!)

Technically I have now accomplished what I wanted to accomplish.  But there are only a few weeks left until the summer break and that is when the really good stuff happens if you ask me.  I am quite sure that I could do this activity a few more times.  My map drawing skills will greatly improve!  I also think I can get some members of the class to draw the maps for other members to follow.  I have 6 grade 3s and the drawing is more for them anyway.  They will love drawing a map to help their classmates get to the ingredients for an ice cream party on the last day!

 

Patterning

So – Patterning.  I’m thinking a lot about this skill and how to make it meaningful for my mathematicians. I’m thinking a lot about its connection to algebra and how to set my grade 2’s & 3’s up for success and start them on the road to algebraic thinking.

I put them to work on Monday.  I put baskets of math manipulatives out and told them to go make patterns.  As predicted, they made a bunch of repeating patterns.  They were quite proud of them in fact.  On Tuesday, we talked about growing patterns.  They weren’t really showing an understanding of reading the pattern left to right, so we had a bit of a chat about that on Wednesday when we talked about shrinking patterns and about how the direction matters. As seems to happen often this year, they were amazed by this knowledge.  I think it will stick!  Here is one of the examples I built to show them that direction matters:

Today, Thursday, I asked everyone to actually put their pattern on a number line.  We have done a lot of work with number lines this year, and with the 100 chart.  I feel like it is really paying off!  I started with some guided inquiry.  What, I asked, would my pattern look like on a number line?

Together we constructed a few:

Really glad I put this on top of the gross old tape line that children have been slowly picking off for 2 years!

Then I sent them to make some patterns of their own, and map them on number lines.  I didn’t hand them the paper until they had their patterns made and could talk to me about how the pattern was growing and shrinking (by ones, by 3’s, etc.  Actually, no “etcetera” because everyone either did ones or threes, like our example.  I’m not worried though because tomorrow I can tell them they are too good to stick with ones and threes and they need to choose something else!)

This one led to a conversation about how they actually have 2 different patterns: add 3 tiles to each term, OR add one column to each term. They hadn’t noticed the second and were trying to figure out why I was so excited about it! I feel like there is a double number line opportunity here, but we aren’t ready for that!

I know it might not be right to have favourites, but this is my favourite conversation:

First, there was this:

The child who made this pattern was insistent that it was a growing and shrinking pattern.  His partners were not convinced.  In fact, they were downright mad because he was so sure and they couldn’t see it. I couldn’t see it either, to be honest.  I wanted so badly to tell him that this was not going to work!  But Cathy Fosnot’s voice echoed in my head, “Productive struggle…productive struggle…”  so I handed him the strip of paper and a marker, and walked away.  A few minutes later, I returned to this:

He’d figured out on his own that to make a number line his “special stones” needed to be laid out in a straight line.  He was also able to finally show us that the green stones aren’t actually part of the pattern.  They just mark the end/beginning of each set of clear stones.  As soon as it was straight, he could help his partners see his thinking – he could explain it so much more easily.  He’d made it through the struggle and came out successful on the other side.  (He did write in the numbers and finish the number line – I didn’t get a picture though.)

Two others made this pattern. (I’ll add the picture later!)

When we chatted about it, they told me that they knew 22 should come next, but didn’t have enough special stones. This was a huge piece of info for me! I thought they’d just been rote counting, but are perhaps ready to make a line without having to build the concrete pattern first.

I am, however, left with one question:  How does one put a repeating pattern on a number line?  ABABABA patterns, or ABCABCABC patterns – can they be put on a number line?

*update* Today I challenged everyone to try something besides 1 & 3.

They tried 2, 4, 5 & 10.

…backwards…. We still have work to do!

This one went on and on, but there are kids in the picture near the end.

They made a “counting by 1” pattern and had to be convinced to add the second row and then to understand the second row. I had to start the number line for them, but it felt like an appropriate scaffold.

I can’t show the “100” at the end. But I can say there was a great conversation about why 10 and 50 were so close, but 50 and 100 were so far away! They decided they needed a “refresh” and drew a new underline with perfectly iterated lengths between the numbers. Also, they realized they didn’t need to build every term in the pattern to draw the number line.