France Thibault

 Sometimes in our life we cross paths with someone who makes a difference in our lives. I have been teaching Math for 24 years, in three different schools, led by 8 different principals. All the principals that I have worked with are amazing. My current principal, France Thibault, has engaged in my teaching in a way that I am not used to. Let me be clear - in a good way. Here is a youtube video from a few years back that indicates a little of what she is like. I am sure she would have much to add to this now as she is a life long learner.

The number one role that I see her engaging in, as the principal of our school, is as an instructional leader. Here are some of her behaviours that I see from her as the instructional leader in our school. I am sure there are more that I am overlooking. Here are my fav five. Or around that many.

1. She walks the talk. She leads by example. She wants everyone in the building to change for the better. I think she strives to do this as well. On her journey she is willing to make mistakes and learn from them.

2. She engages in our lessons. France participates in lesson study at our school at all levels, in departments that are not her expertise, in cross curricular professional learning teams, as part of her evaluation of teachers (TPA). I know she has also participated in lesson study at other schools to help them get started. You can read about her thoughts on lesson study here.

3. She shares / buys resources. I have watched her give out books about teaching to the masses. I have received more books about teaching from France in the last two years than I did in the first 22 years of my career. Maybe she is trying to tell me something!

4. She increases her zone of influence. France has found a way to influence all in the building towards our personal journey of change as educators. It is like we are all changing at the same time. Of course some more rapidly than others but change none the less. She also is helping other principals to create change in their buildings.

5. She encourages risk taking. France has opened the door for people to take risks. It is OK to try something different - successful or not. Learn from it.

6. She provides time. France will find $$$$ for release to participate in lesson study, to co-plan  courses, to present PD to others, among other things. She also takes the time for herself to do these things.

7. ..........

May she have continued success in the role of instructional leader because I think it is working. At least it is working for me as a teacher in the trenches. And I have turned into one of the old ones.....how did that happen?

Area = Length * Width

In grade 10 Applied Math in Ontario our students need to learn about quadratic relations. One of the overall expectations in the quadratic strand is that students will be able to manipulate algebraic expressions as needed to understand quadratic relations.

Instead of calling it factoring and expanding, I like to refer to the two different equations the students are responsible for as this.

y = ax^2 + bx + c as y intercept form or area form.

y = a (x-p) (x-q) as x intercept form or length width form

The curriculum requires that students can work with these equations when a=1

To get at changing from area form to length width form or vice versa, I use rectangles and algebra tiles.

The first thing I like to do is to give the students an equation in area form. They are already familiar with it as we have modelled quadratics with the graphing calculator.

So here is an example. y = x^2 + 4x +3. I will use this example for the rest of the blog post.

Then I ask them to get three different colored piles of cube a links. One for the x^2 term, one for the x term, and one for the number term.
 

Once the students have the three piles I ask them to create a pile of the correct number of tiles for stage 1 (when x=1), stage 2 (when x=2), stage 3 (when x=3) and stage 4 (when x=4). Here are what the piles look like for our example.

Then we create a stack for each stage. Numbers on the bottom, then the x cubes in the middle followed by the x^2 cubes on the top. Nice discussion at this point about the graph of y = 3, y = 4x + 3 and y = x^2 + 4x + 3. Here is what it looks like.

 

Students then deconstruct their towers and I ask them to create a rectangle for each stage. x^2 blocks need to be in a square and the ones blocks touch the x^2 blocks at a corner. We also create the rectangles with algebra tiles. I particularly like doing this as students can see x increase (be variable). Eventually students will get to this.

 

And a little poster action demonstrating some algebra and some key characteristics of quadratics.

 

Open Strategy Cup Stacking

Drafted this post a long time ago and finally getting back to it after @jstevens009 commented about my stacking ability in a picture on my twitter avatar.

I have done this two different semesters. (Make that three now). Sometimes it takes everything I have to write about activities - I just feel like I am such a better talker than writer and it doesn`t feel like I get any better at writing. Anyhow........I have presented this activity so many times in presentations and have just not got around to finishing this post. Today is the day!

Lucky enough to be involved in a lesson study with my incredible principal (@FranceThibault) my incredible math coach from the board (@robintg), my incredible math department head (@BDMcLaurin) and two incredible English teachers from my school. I got to do the first lesson in my class and I choose to do an activity on cup stacking. On a side note this was our very first lesson study as a group. We have now been doing lesson study for three semesters. It has been an amazing journey.

Of course thanks to Dan Meyer, Fawn Nguyen, Andrew Stadel and many others who inspired this idea.... as is typical with our lesson study we are trying to open these tasks up - unscaffolding them. Giving the task a  "low floor and a high ceiling. "

We started with th image below and asked the students to write what questions came to mind. We got a bunch. Here is a sample:

Why is the cup the same colour as your shirt?

How tall is the cup?

How tall are you?

How many cups to make Mr. O?

If we chopped up Mr. O, how many cups would we fill?

How many cups can you drink?
Why are you standing next to a cup?

 

We settled on " How many cups to make a Mr. "O"? as this was the most popular question. Of course this was the question we were hoping for.

We then put the students in groups of three (homogeneous). They were to settle on a stacking plan and then draw a diagram of their stacking plan, a guess to low, a guess to high, and their best guess for how many cups would make my height.

Here is the form they filled out.

GUESS SHEET FOR CUP STACKS

Using your groups stacking idea:

Diagram of stacking plan		Members Names
A guess of how many cups that is “too low”.	A guess of how many cups that is “too high”.	A guess of how many cups that is “correct” or your groups “best guess”.

Once they had done this we gave them ten cups and asked them to do the following on chart paper. Represent their stack with a picture, table of values, graph, equation and show their calculation to get the answer to" How many cups to make a Mr. "O"?  

Groups were given two days to repeat this as many ways as they could think of.
Here are some photos of what they came up with and what it looked like when we built it on day three.

The first one is what I call top bottom top bottom. Direct variation or linear relation with a height intercept of zero. Total of 16 cups to reach my height.

The second one is what I call the inside each other method. Linear relation. Total number of cups to reach my height is 304.

The third one is what I call the triangle method. Quadratic relationship. Total number of cups to reach my height is 136.

The fourth one is a three dimensional triangular pyramid. A cubic relationship. Total number of cups to reach my height 816.

 

This most recent semester a particular group looked at a method I'll call 2 then 1 bottom top bottom top. Of course they wanted to know if it was quadratic or linear. I told them to do both, figure out how many cups for each and then build it to see which model was better. It took 24 cups to reach my height.

 

During this last semester I worked hard at posting student work (anchor charts) around the room.

Here is the top bottom wall.

 



 

Here is the inside each other wall.

 



 

Here is the triangle wall.

 

 

Here is the three dimensional triangle wall.

 

 

 

I love this activity. The students really connect a table of values, a graph and an equation. There is an entry point for every student.



Card Tossing

PEDAGOGY
There are many pedagogical moves in this lesson that I tried for the first time. Bare with me.

First after hearing Peter Liljedahl and Michael Pruner talk at the Canadian Mathematics Educators Forum I tried this lesson with visible random groupings (VRG) of size three and the students did their work on vertical non-permanent surfaces (VNPS). These are two ideas that Peter and Michael presented at CMEF 14 that I thought made sense and could transform my teaching.

First visible random groupings- the idea is that every day students see you make the groups randomly. Hopefully this will break down social barriers. Hopefully this will enable students to collaborate. Hopefully this will put students on the edge.

Vertical non-permanent surfaces. Non-Permanent allows students to make mistakes and take risks when working on a problem or activity. Vertical makes the work visible for all to see. Knowledge can easily be shared around the room. One pen / marker / chalk - person writing cannot write their own thoughts. Hopefully this will help with collaboration within the classroom.

More about VRG and VNPS at another post. (I think these two ideas are awesome!!!)

THE IDEA
Shout out to my buds in the Limestone District School Board who triggered the idea for this activity. I would not of thought of it without them. Great idea. Hopefully they like what I did with it.

DAY 1 DATA COLLECTION



On the first day students folded up their box and grabbed  some cards. We tossed cards for 30 second intervals and counted how many we made from 4 feet (this was an easy distance to choose as the tiles on the floor were one foot by one foot-next time I think I will make it 5 feet- 4 feet might of been a little too close). Students recorded their data and near the end of the period calculated their rate in cards per second.



Here is my chart:

My rate ended up being 2.05 cards per second. Any takers? The dimensions of the boxes were

 L 16 5/8 inches by W 12 5/8 inches by H 12 5/8 inches and were purchased at U-Haul. The students rates varied anywhere from 0.36 cards per second to 1.81 cards per second. Students loved the data collection part of this activity.

After school I calculated a reasonable card advantage I would give each student depending on their rate so that a game against me would take anywhere from 30-45 seconds.

Here are the advantages:

0.3 to 0.4 cards per second gets a 60 card advantage

0.4 to 0.5 cards per second gets a 50 card advantage

0.5 to 0.75 cards per second gets a 45 card advantage

0.75 to 1 cards per second gets a 40 card advantage

1 to 1.25 cards per second gets a 35 card advantage

1.25 to 1.40 cards per second gets a 30 card advantage

1.40 to 1.50 cards per second gets a 25 card advantage

1.50 to 1.65 cards per second gets a 20 card advantage

1.65 to 1.80 cards per second gets a 15 card advantage

And a shout out to Ahmed who had a 1.81 cards per second average. I gave him a 10 card advantage. His rate was the best rate of the 27 students who collected data. (two classes) 

DAY 2

What is the longest game you could play against Mr. O and still win the game given a certain number of cards advantage? (as stated above depending on your rate)

Students came into class and experienced visible random groupings for the first time. We then huddled up and I set up two boxes at four feet and asked for a volunteer.

Me: "Ok my rate of making cards is 2.05 cards per second and Nabil's rate is 0.84 cards per second. If we have a card tossing competition (Oh Oh could I possibly be World Card Tossing Champion!!! WCTC?) how long does the game need to be for me to win?"

Class: ........ "You would win right away- wouldn't you?"

Me: "Right because I am better. Watch - let's play a 10 second game."

We do this and I clearly win.

Me: "Ok so how could we give Nabil an advantage?

Nabil: "Why don't you move back. Throw from further."

Me: "Ok that would be an advantage but....I didn't collect my rate from that distance."

Me: "Any other suggestions for an advantage?"

Class: ........

I walk over to his empty box. Count 30 cards in front of the students and dump them in.

Class: "Oh ya. That would be a huge advantage."

Nabil and I stand back getting ready to toss.

Me: "So now there is a length of game where I would catch up to Nabil but not quite beat him. In other words - there is time for the game for Nabil to win but Mr. O would be super close. The fans would be going wild!"

The class totally gets it.

At this point the groups are sent to their vertical non-permanent services. They are instructed to use the person's rate in their group who is the best card tosser. I come around and tell each group their card advantage. I ask them to figure out the length of time for the competition so that it will be super exciting.

Here are some pictures of some group's work:

Group A

Group B

Group C

Group D



Group's worked on this problem for the entire period. Engagement was awesome. Using vertical non-permanent surfaces allowed me to quickly assess where groups were at and help them move forward. Most groups attacked the task with trial and error at first. I would then prompt them to use a graph, equations and the graphing calculator, or an algebraic approach. Knowledge passed around the room from group to group - a huge advantage to using vertical non-permanent surfaces.

DAY 3 COMPETITION DAY

Groups were asked to go back to their vertical boards from yesterday and put up an algebraic solution to the problem. Here is an example:



Once all groups had a length of time for the game to be close and the number of cards we could expect in the box, we found a time keeper and played our matches.

Here is a head start:

And here is a video of me versus one of the students.



The results were awesome. We played games to the length of time the students predicted with their models and then compared the number of actual cards in the boxes compared to the expected number of cards.

My first period class had these results:

And my afternoon class had these results:

THIS ACTIVITY WAS AWESOME!

If you try it out I would love to hear about it. Comments?











TMWYK Sausages and Equality

Maybe I TMWYK's more than most people.

It is Sunday morning and I am cooking sausages. G is awake and C is still sleeping.

G: "Ya we are having sausages." He walks over to the oven and counts out loud informing me he is having all of them.

Me: "Now that's not fair." I quickly count the sausages and there are 14. I inform G that we will all get 4. Selfishly I will get 6. But I am not telling him that.

G: "There are 14.

Me: "Yes."

G: "We get more than 4."

Me: "How many do we get?"

G comes over and looks in the frying pan and starts splitting it up in groups of 5. When he gets to the third group and realizes there are only 4 for that group. "We can't do this."

Me: "So if we give everyone 4, how many will we have left?"

By now Cole has come downstairs.

G: "2"

Me: "So what if we cut them up and split them up?"

G: "OK"

C: "Dad did you know it is an odd day?"

C has no idea what the date is. I know that.

Me: "How do you know it is an odd day?"

C: "We are learning about odd and even numbers at school. Our last school day was an odd day. So that makes yesterday an even day and today an odd day."

Me: "Oh"

I am trying to get breakfast ready.

C: "One is an odd number. Two is an even number. Three is an odd number. Eight is my favourite number."

This leads to a discussion about favourites everything between C and G and many questions to me about my favourite everything.

Me: "Ok G we are ready to do the sausage thing."

Me: "How many on each plate?"

G: "4"

We put four on each plate and two on the cutting board.

Me: "Ok where are we cutting these."

G blurts out "In thirds." G grabs the knive and with my help shows me where to make the first cut. It is through both sausages at the one third mark-bang on. He quickly says " And the second cut is here." Bang on. And then he says "And the third cut goes." He stops himself realizing there is no sausage left to cut and says "There is no third cut."

Me: "Ok so how are we sharing this?"

G: "We each get two. There are 6, so we each get two."

Great. Too bad mom is already gone to her course-she would of been impressed.

TMWYK

TMWYK means talk math with your kids. If you do a google search of it you get this:

 

So this just happened on my way home from lunch with my two boys in the van.

They are G who is 7 and C who just turned 6. And to be fair I am a math teacher, and we do talk math often (usually in the van). This is just the first time I am writing about it.

G: "There is 60 minutes in an hour C. If you take one minute away you would have 59."

Me: "That's right G. And if I took 7 minutes away from 1 hour what would you get?"

Pause

G: "53 minutes"

Me: "Nice. What if you took 10 minutes away?"

G: "That's easy. 50"

Me: "20 minutes way?"

G: "Easy. 40"

Me: "G, if you had 1 and took away 3, where would you end up?

Pause

G: "At minus 2"

Me: "How do you know about minus numbers?"

G: "From the winter."

Me: "What do you mean?"

G: "When it's cold the TV says it's minus ten."

I wonder how far I can push it.

Me: "So G. If you started at minus 2 and took away 3 more where would you end up?

G: "Minus 5."

Me: "If you started at minus three and added 5 more where would you end up?

G: "2"

We pull into the lane way.

C: "Dad did you know 3 is in the middle of 1 and 5.

Me: "Can you tell me two other numbers 3 is in the middle of?

C: "1 and 6."

Me: "Not quite C. If three is in the middle then you need to go the same amount on each side of it. So with 1 and 5 we go over 2 each way. So C when you said 1 and 6, for 6 you went over 3 from 3, and for 1 you went back 2, so 3 is not in the middle of those two numbers"

G: "So nothing and 6."

C: "So 2 and 4."

Me: "So how far did you go over on that one?"

C: "1"

Me: "Nice. So if we went over 10"

G: "13 and....."

Pause. This is the moment.......

G: "Minus 7"

Me: "Nice G. OK boys let's go in. Mom's going to be home soon and we need to clean the house."

C and G: collective "awww"

As we are walking in C: "Dad can we do some more math?"

Nice!!!!

So  Mr. Danielson- surprising? What I should expect at this age? Other thoughts?

From circle man to triangle man! Love your work.

My first tweet up - one on one with Justin Lanier

Pretty cool evening recently. Tried to explain it to friend. Went down something like this.

Him: "What are you up to tonight?

Me: "Hooking up with a guy from the math twitter blogosphere"

Him: "What's that?"

Me: Long explanation about #MTBoS

Him: "Do you know him?"

Me: "Not really"

Him: "Do you know where he is from?

Me: "No."

Him: "Is it safe?"

Me: "Ya of course it is safe!"

Of course it is safe - in a way. The #MTBoS is a wonderful place. People share, contribute, vet ideas, and get to kinda know each other.

Then this happens:

So for the first time I go out and meet someone from the #MTBoS that is not from my own city.

And it is great. We talk about teaching and education. We talk about math. We share ideas. We tell stories.

We share personal stuff. We put a real face to a name we know online.

We tweet about our tweet up.

We both took a risk. We are that type of people.

We will meet again at twitter math camp in Jenks, Oklahoma this summer.

It is a great time to be in education-take risks-it is worth it.

As @BDMcLaurin would say freefall!