# More Math…or is it?

I forgot in the last post to share the math we did yesterday!  We are going to see Fatty Legs on Wednesday.  The problem:  there are four classes that all need to get to the Grand Theatre for the same time, all taking Kingston Transit.  But each bus can only handle one class.  So how are we going to get everyone there on time?  The latest we can be going into The Grand is 10:15.

That was just about all I told the kids.  Oh, and no transfers–I hate doing transfers!  They therefore had to generate the questions and the solutions.  (Zoe was astute about recognizing that Google Maps’ walking estimate didn’t account for the pace of a group of 25).

Here’s what they looked like working away at this:

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Don’t they look happy?  And here’s what they came up with, more solutions than we even needed!

# Open Math

First off, I have to apologize (I guess) for the infrequency of posts this term so far.  I’ve been REALLY BUSY!  But I am keen to keep at this, and hope to have the kids up and running as contributors in the next month.  (There, I’ve now said that so I have to try and make it true).

I wanted to share a couple of bits of math work we’ve been up to.  We do a bunch of arithmetic type of math around here–times tables, and multiplication methods and so on.  Stuff that you would probably find familiar.  As much as possible, we are trying to remain open to the possibility of different methodology and even different answers.  (Where the question is clearly 2 x 67, we’re happier with different methodologies than different answers, but it sure is interesting to see kids argue through their differing answers and learn something about how they got there).  So, in several “open” problems recently, we had some pretty fascinating discussions.

The first, you may have seen:  a caterpillar crawling out of a jar, up three centimetres and sliding down two each day.  You can hopefully make out from the work below, that there was some serious disagreement about the answer.  The message from some:  we need more information!  Like, how long is the caterpillar?  There were at least three defendable answers!

This was also a good entry into the quality of our mathematical communication.  If you (or I, or anyone else) don’t understand what the math shown below means that could be a place where we talk about communication.  (It is also fairly often a place where I discover a child can see a problem–correctly–in a way that I am unable to see it.  I love that).

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Later, a party problem:  ten people at a party, everyone shakes hands just once with everyone else.  One answer, but many routes to that answer.  This problem had some sweet traps, like having to realize that this means nine handshakes for each person; and that one handshake means a handshake for each of those people.  Thus, we were into understanding the problem, and having to use logic.  The variety of strategies was rich.  It was particularly lovely to see that one of our most capable, super-advanced math citizens who often leaves us all with our jaws hanging open solved this one literally using a little pile of stones.   Sometimes the simplest way is the best, and making models is more than OK.

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The bonus question took us a whole awesome class:  Would doubling the number of people double the answer?  Is there a way to predict?  Digging into patterns together is so important to seeing the beauty and potential of mathematics.

This week we had this problem:

Not the most elegant problem I’ve written, to be honest.  But once we got past my over-wordiness, this was a good example of the openness of even fundamental multiplication.   All the students could see that this was a pair of multiplication questions.  Our talk about which we predicted would be largest was very interesting.  Giving the students a chance to share their thinking is so important.  (I’ll do another comparison one like this with fewer words–it was very interesting).  And then we got to see the different ways that students were able to show the multiplication.  For some, this involved a lot of counting.  A lot!  This opens questions about efficiency (and also about learning their times tables).  The strategies the students choose must first be rooted in understanding, rather than just mimicking some method I’ve shown them.  As their understanding grows, they can then see the logic of choosing the most efficient strategies.  (Which will, in the end, involve a calculator–a tool that is useless without understanding).

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So, openess.  This is not meant to replace accuracy or the vital role of automaticity in fundamental arithmetic (so yes, please practice times tables–your child should know what they are working on; if they don’t, tell me!).  And it is not all the math we do.  But by being open we allow everyone a door into the math we are doing, and hopefully each child also begins to see a direction for their growth and learning.

Upcoming:  It is high time I did a post about Orthography.  The stuff your children already know about words that I didn’t know by this point in Grade 5 (or, frankly, at age 40) is pretty encouraging.  Stay tuned, there may be one or two things for them to teach you as well!

# Lemoine Point, finally!

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We did it:  one day later and 15 degrees warmer!  A sunny, lovely day.  I am currently working on Biodiversity with the Grade Sixes, while Mrs. Wilson covers Organ Systems with the Grade Fives, so we split into those groupings for most of the day.  My Sixes explored the variety of habitiats and organisms at Lemoine Point.  We are delighted by just how many critters we did see.  In one of our activities, pairs were given a loop of rope and had to create a “Micro Park”, making an argument for why a mall shouldn’t be built on that spot.  What is special here that deserves protecting?  The responses were varied and compelling.  Lucky us, it’s all protected at Lemoine Point.   Ticks are a real issue!  Please check your child just to be sure!

Here are some of the student observations from the day (more to follow):

# Take 2: Lemoine Point THURSDAY!

O.K., it’s late for anyone to read this, but we’re going to postpone until tomorrow.

never postpone due to weather that hasn’t yet arrived (because it often doesn’t) but everything is pointing to a better day tomorrow.  We’ll see.  Tomorrow, we go for sure!

# Lemoine Point Wednesday

Hello folks at home:

The weather is looking less than friendly for our Lemoine Point trip.  Let’s plan to go anyway though and see what happens.  Please ensure your child is dressed with layers to stay warm and dry.