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! this math?  

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):

I went to lemoine point today and it was so fun.  But my feet were hurting and i felt like ticks were on me.But the trees and the nice grass were so cool.  But the bathroom sorta sucked and I kept saying”not worth it not worth it!”

Noah 😀

    Today at Lemoine Point, we found a salamander, two frogs, two little brown snakes, lots of malards ducks, a family of turkeys, crickets, dragonflies, three monarchs (one had broken wings😞), and a ladybug.  When we ate lunch, people were freaking out (because a wasp landed on him/her) and at the end of lunch, Jyotsana was stung by a wasp.  (I got to feed two of the turkeys too😊).

    Near the end of the trip, we played a game where we were all bears and Mr. Caldwell put popsicle sticks (that was food) in the open space and we had to get as many as we could to survive ten days.  I ended up not getting any but other people got lots.  Basicaly only one person survived.  

    I brought bird seeds but I only got to feed the turkeys…

…but I got a really close look!       


Today at lemoine point we walked really far. Our classes were split into grade 5 and 6. We walked a couple of kilometres.  The coolest animal i saw was a tiny snake that was as long as one of my fingers. We also saw a blue jay, and a bunch of turkeys. Ms. Wilson’s class went on the field trip to. In the middle we stopped to have a snack at the water and near the dog park. After that we started walking again and that is when we saw the blue jay. The trail was really beautiful and there were a lot of big trees. Then we saw the big group of turkeys. Soon we saw lucas and noah find a salamander the salamander was dark grey with black spots. When we got to the spot where the groups were going to meet the grade six group wasn’t there yet. Since they weren’t there, a lot of the kids in the grade 5 group played triangle. Triangle is a game where you pass a football and if its a bad pass or you don’t catch it you are out and the last person still in wins. When the grade sixs get there we played a game where we were bears and we had to find popsicle sticks that counted as food. Then the feild trip was over and we had to go back to school.


Oct 12 2017

Jacob. G

We went to Lemoine Point we got pot in separate groups grad 6 went with mister Caldwell grad 5 went wish miss Wilson 😀 it was really fun But we had to do a lot of walking.    D: But miss Wilson said we could take a break for 5 Minutes.  But when we got to our destination we played a game i thinc it was call Bears. It was fun.  I found a hickory nut at the end.  :D.


Today at lemoine point we saw snakes and frogs.  And there was moss.  It was soft and pretty.  We played an activity–we were hungry bears!  We saw brown snakes when we were walking out.  They were small.  It was fun!  

By sitara

Today at Lemoine Point we walked over 5km. We saw some Blue Jays. There was a dusty mushroom. We saw a totem pole. It had a bird a person and other animals. I found acorns & walnuts. There were red berries. We even saw ducks and loons. Some of us found shells. There was even a fish skull. There was a group of turkeys. They were all big. The two groups met at a spot. We saw 4 frogs and 2 big crickets. There was some small crickets too. We saw bees and wasps. Everyone was freaking out. We played a game where we were bears and had to get enough food to survive for 10 days. The bears needed a lot of nuts, plants & berries. On the by to the bus we saw Little Brown Snakes that were little and brown.


    This week at thursday, October 11, 2017 Mr. Caldwell’s class and Ms. Wilson’s class went to a conservation park for a science field trip. The conservation park’s name was Lemoine Point. Each grade 6’s had a partner and a clipboard with a sheet of paper. We listed things we saw at the park on the paper.

    We saw lots of different kinds of animals like birds, mammals, reptiles or amphibians, and even invertebrates (bugs). We saw ducks, loons, chipmunks, squirrels, salamanders, and other animals.

    We also had a little fun research. Each group had a loop of string. We had to find a space worth saving. When we found one we put the string around the space. My group’s space was a hole in a tree. We thought it was worth saving because it was a shelter for the animals. It would be the bunnies, chipmunks, and other rodents that could use it for shelter. It was also kind of deep so it was a very safe place for preys to hide in.

Geoilli (*u*)


Craig P T, 10/12/17

Hello. My name is Craig! which you know that’s in the top left corner of the page. Anyways, I’m writing a story about my experience at Lemoine’s Point… LET’S START!

Paragraph 1

Today, I woke up in a sunny day. My eyes were very tired. I heard my grandma yelling,


I checked the time and it was 8:10…

Paragraph 2

Wait let’s stop right there. My grandma always wanted to bother me to wake up.

She also wakes me up at 7:30 and she would panic and say,

“CRAIG, IT’S 8:50 even though when it’s not!”

Funny right? Well if it’s not funny, then just read the next one instead…


Paragraph 3

I  got to school on time around 9:01 am.

I went to the bus with my classmates, and I was with Edan.

It took kinda forever to get there. 10 minutes later, we arrived at Lemoine’s Point.

Our second teacher from another class is Ms.Wilson.

We separated each other in a group, and started to learn habitats including plants and other animals like ducks etc.

Edan and I, we were quick at spotting some living creatures and plants.

What was cool was he had entire camo suit on him, including food, binoculars, etc.

The thing is I was kinda sleepy inside the bus…

Paragraph 4. Did you know?

Did you know that I used to go here with my mom during summer and fall? So the paths and trails were all familiar to me today. It’s one of my favorite area.


Overall, I appreciated to see the leaves falling, the paths straight, trees moving and the calming effect of the wind on my face. It reminded me how great God’s creation was.

When we got back to school, I was sleeping on my desk and took off my leather jacket and making it as a pillow. I wasn’t listening the whole time because of the long trip that we had…

That’s all folks!


     Hi!  Today at Lemoine Point, we saw a lot of animals and they were all really, really cute😊😃!  These are some of the animal that I saw.  The first animal we saw was a Bluejay, and it was landing on a oak tree, and it was very startled when it saw all of  the faces looking at it so, not many people got to see it.  The next thing we found was a Monarch Butterfly and it was flying all over the place. I was very excited about the next animal we saw, and it was the first chipmunk of the day!!  Right after that we saw another Bluejay in the distance.

    The animal that popped out to me was the Wild Turkey, at first I thought it was a duck but as we got closer, almost everybody thought it was a turkey that just got out of the barn but, Ms.Wilson said that it was a wild turkey.  

The last animals that we saw was a Salamander and Snake and, last was a

monarch  that broke it’s wing but on the way we lost it☹.                                  

Hey my name is Adham .  Today at lemoine point , we saw lots of things like snakes, wasps ,bees ,frogs ,salamanders and a spider ,we played a game we were bears and we should get colours they are food ,we should get enough food to survive.. I also played.  I got a stick and  wrote some mathematical equations

.What was special  about lemoine point was that everything was beautiful and natural and quiet.  

Lemoine point

When we got to lemoine point we split into 2 groups a grade 6 group with mr. caldwell and a grade 5 group with ms. wilson. and once we were ready we took of our first stop was at this marshy place by the water and we stopped. to see if we could hear any animals we heard a couple birds then we took off.

We walked over to the water and met some birds when hannah called them over with her duck caller and beside the water was a hole bunch  of milkweed. and all of the fuzz inside the milkweed was blowing everywhere i found a milkweed plant that had a really nice design. the seeds were overlapping each other which made it look really nice.

Then we finally got to the woods and we walked of the path for a bit and we used magnifying glasses and searched for some bugs and salamanders. we found a lot of salamanders under only one log we also found some pretty big mushrooms too.

Then we went into some tall grass with our magnifying glasses and got down low in the grass looking for bugs. and when i asked Mr.caldwell why there was random holes in the grass he said because mice live in there. and when he said that i was out of there.

Then we went and had lunch some people were playing football. after lunch we played a game where you are a bear and you have to crawl on four feet. which was ok and the point of the game was to collect the popsicles sticks from the ground.     ( the popsicle sticks were food in the game)

And we had to collect the most .after we collected all of the popsicles we met back in the circle with our sticks. and they had colors on them and if you got a certain amount of that colour u would survive i was the one with the most food. so i survived after that we got our bags and got on the bus and left.

I got the back and had to sit with Mr. Caldwell lol : )