Making Math Moments That Matter – Live

What makes students remember the math they are learning? Is it because you’re using a real world problem that they can relate to? Is it because maybe you used a 3-Act task? Is it because they practiced the content over and over? Is it because you used spaced practice versus massed practice? My good friend Kyle Pearce and I believe it is much more than that.

While at Oame 2018 Kyle and I took a chance and hit record on Facebook Live during our 75 minute workshop title Going Deeper with Math Moments That Matter. If you missed it or want to learn more you can watch the whole thing right here!

Session Description:

What makes a memorable math moment? Is it a real world task? Is it relevant to your students? Is it media-rich or delivered in 3 acts? While many professional development sessions focus on a specific component of an effective math lesson, Jon Orr and Kyle Pearce will model what they believe to be the three key components of an effective mathematics lesson: sparking student curiosity, fuelling their sense making and igniting your next steps. Join them as they lead a task to break each component down and then build it all back up to create a memorable math moment.

What were your moments that you remember from math class?

What do you want your students to remember 5 years from now? Leave comments below. Or jump over to my Facebook Group and you can comment there.

Grab the Making Math Moments Matter Curious Task Template and our file with support resources over at makemathmoments.com

Thanks for being here with us!

How Can We Anticipate to Fuel Sense Making? Stretching Trees

Are you looking to avoid “Lesson Flops” and bring on a “Lesson Successes?” I sure do. That’s why I plan with anticipation of student thinking in mind.

I want to share a lesson I co-created with Brian McBain and teachers at Wallaceburg Secondary School and how anticipating student thinking helped avoid those flops!

Let’s run through the lesson first, then I’ll give you a window into how we planned it.

In random groupings students went to their wall space and were presented this first task.

I have to admit when we planned it we anticipated everyone to draw Christmas trees but after showing the image they all drew a variation of the one above.

Drawing the trees was no biggie since our new amazing whiteboards from Wipebook.ca (wipebook.com) has grids on them. Students counted up 20 units and drew their very best tree! Onto the next part of the lesson.

Draw another tree that has a height that is less than 50% of the first tree’s height.

Here is a typical drawing from my students.

In small groupings and also as a whole class I asked and discussed “How do you know the height is less than 50% of the original tree?”

And then we moved onto this…

Draw a tree with a height that is more than 50% of the original tree’s height.

With this prompt we wanted to dive into the answers a bit more. “How do you know it’s more than 50%?” “How can we verify that 16 units high is more than 50%?” Also with this we had students drawing trees higher than 100%. We paused the class and verified and shared out the different tree heights around the room.

I prompted them to draw a tree that was exactly 30% of the original tree’s height.

This is where I was super interested to see how they would solve this. Their solutions were going to fuel the discussion going forward (Check below to see how we anticipated what they would do).

Most groups of students used the grid and found a unit rate. Can figure out this strategy?

This group knew that 10 units would be 50% so they took the 50% and divided it up into 10 units giving 5% per unit. Then they counted up by 5s until they reached 30% and got 6 units high. Other groups took the whole 100% and divided it by 20 to get 5%/unit. As a class we gathered around these solutions and explained the strategy. Any group that was stuck went back to their boards to use this newly presented strategy and the other groups pushed forward with this new prompt.

Groups progressed through this prompt at different times, but when they were ready I gave them this one: “Draw a tree with a height that is exactly 62% of the original tree.”

This is where the struggles happened. Again we were interested in HOW students solved this problem. Most new that 60 was going to be 12 units high….and then just estimated from there how high the tree would be. Some did guess and check to narrow down how high exactly 62% was. This was exactly what we had planned. We had wanted and led the students here to create this struggle so that we could step in and teach them a strategy!!

We used a double number line: One side showing percent from 0 to 100 and the other side showing the heights of the tree. But instead of a horizontal number line we tipped it up and made it vertical!

We had a discussion on proportions: “Is this a proportional relationship?” “How do we know?” Yes….so we can apply a proportional strategy to solve this. After that the students had a new and improved strategy to try the next few prompts:

Draw a new tree that has a height that is 17% of the original tree’s height.

and then,

And then we switched to a new “starting” tree.

And kids drew this.

After I felt that groups were comfortable, their next task was given out (which stretched into day 2). We changed the scenario from trees to colouring.

Want to get the PDF with all the image prompts and handouts? Click Here.

When reflecting back this lesson was not one of the “flops” it was a “success” and most of the credit has to go to planning with anticipation in mind.

Anticipating to Fuel Sense Making

When Brian, the team, and I set out to design this lesson we were looking for a way for students to feel like they weren’t learning something new. That they could take the idea of percent and just use it like they have already solved proportion problems. We also wanted students to follow the Hero’s Journey and feel that there was a definite need to use a proportion strategy.

Here is what the early stages of the planning process looked like. Yep, scribbles in a journal. We spent a lot time thinking about the right progression of prompts so that we could maximize student work and use their strategies to push learning forward.

We also spent a great deal of time planning out the different strategies we thought students would use to solve the original prompt “Draw a tree that is 30% of the original tree’s height”

We outlined the strategy of finding the unit rate of 5% per unit, we thought many students would already know the “rule”: Turn the % to a decimal and multiply (But no one did do that in my class). We thought it was possible for them to create a proportion. We thought some groups would try a guess and check strategy. Like: “I think the height is 7. Let’s see if 7 out of 20 is 30%.” Only a few groups did this.  We ranked each strategy in order of most likely to least likely.

Anticipating their solutions and strategies puts me in a better position to understand their thinking and help shape that thinking. For each possible attempt I need to be ready to provide feedback to help them achieve our goals.

We take for granted how much time is needed to prepare and anticipate adequately. It takes time to make this happen, but that time is worth every minute. Especially if it puts me in a better place to understand what my students are thinking.

This has been my assessment goal: Understand their thinking in order to push them further. That’s it! That’s the main idea.

Anticipating their thinking will always put me in a better position to fuel their sense making.

Read More: Fuel Sense Making & Black Box Defrost

What Math Lessons Can We Learn from the Game of Nim?

Have you played the game of Nim before? Do you know what lessons we can pull from the game? Watch me play the game with two of my daughters Jules and Lucie.

You can see right when the game gets to 4 left that each girl knows they lost! You can see it on their faces and even Lucie explains it to us by giving us all the options. Jules even wonders out loud “How did you do that” She knows there’s some trick here.

So, let’s see how I’m the World Champion at this game.

This game is a variation on the game of Nim

“Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap. The goal of the game is to avoid being the player who must remove the last object.” 

I also play this game with my students. The interesting thing about this game is that there is a winning strategy. And in our variation of the game if the player to go FIRST knows the winning strategy then they are guaranteed to win. So even though it looks like I’m the World Champion it just comes down to math.

Let’s explain,

Jules and Lucie know they have lost the game when they are left with 4 to choose. So as a player if you can leave 4 objects for your opponent to choose from you have won the game!! So now the game becomes who can leave 4 for their opponent to choose from. How can you always get to a position where you leave 4 for your opponent? Think about it for a moment. What number should I leave my opponent to choose from so that no matter what they do I can then leave them with 4 to choose from?

Right..l Should leave them with 8 to choose from! And then where’s my next winning position? 12 then 16 then 20. Multiples of 4!

So right from the start since there was 21 objects in the pile I can get to 20 on my first move by going first! And win the game every time.

In my class I usually put some cash down on the table to enhance the experience. “Anyone who beats me at the game will get the cash!”

Every time I play this game I’m reminded of my math education as a student. You see, in the game of Nim if you know the winning strategy you win every time. You know the path to follow. You see how it works. If you don’t know the strategy you are playing the game almost as if you are blind. You’re not sure how your choices will affect the final moves near the end. You are hoping the moves will pay off down the line.

As a student most of my math educational experience was like the experience of the player in the game of Nim that doesn’t know the strategy. I followed the teacher (who does know the “strategy”) blindly. I wasn’t sure of how my “moves” would pay off in the end. I just followed the rules hoping for good outcome.

I was such a good rule follower that sometimes it awarded me some success. In the fourth grade I remember earning one of those big puffy, stick off the page stickers for being a master multiplier. Yay go me!!

 

But when it came to being pushed to show my understanding the wheels fell off. Here is a 4th grade test on multiplying (when I look it over now it looks like I must have fixed this up after getting it back). Math for me was like a series of tricks that I could memorize and then try to perform.

 

Thinking back to playing the game with my daughters you can hear Jules, the first girl in the video ask right at the end “How did you do that?” She was thinking this is all a trick! The game was like a magic trick. How many of our students see their math education as a series of tricks? Lots of them I bet.

We don’t want kids thinking math is just a series of tricks to memorize. If they do think the math they are learning is a trick then it’s our duty to uncover the trick. Show them how it works. Like in the game of Nim students should know why the first player has the winning strategy.

This is what I want from my math lessons. Let’s continue to fuel sense making in our students instead of showing them just tricks. So, in your next class play the game of Nim with them. Blow their socks off and win 3 times in a row…..but don’t leave it as a trick. Uncover the math and strategy behind it together!

A great read is Nix The Tricks by Tina Cardone https://nixthetricks.com/

You can read more about how to fuel sense making for students from Kyle Pearce as he describes a task around Donuts.  https://tapintoteenminds.com/3act-math/donut-delight/

and also here from me showing a task about the defrost function on my microwave http://mrorr-isageek.com/fuel-sense-making-black-box-defrost/

Why Consistency Is More Important Than Intensity: Culture in the Math Classroom

Ok so you tried using a problem based lesson like a 3-Act Math Task or maybe you had students solve a task in groups with your brand new whiteboards and it …….flopped! Yep you’re worst nightmare was there with you in that classroom! A failed lesson! You were sure it was going to be a success. You heard that that activity was a great one but for you it just didn’t work.

Don’t worry. It wasn’t you. It’s normal. This comes down to an example of Intensity versus Consistency. I first heard Simon Sinek (an inspiring speaker and author on business and leadership) talk about this on the Tony Robbins Podcast.

Wait, what’s Intensity versus Consistency???

Ok, say I’m looking to get into shape. I want to be physically healthy and fit. Everybody knows that I can’t just go to the gym for 6 hours today and expect to instantly be fit and ripped! No one expects that. That is an example of intensity. Or consider brushing teeth. I can’t just brush my teeth once and hard and then expect my teeth to stay healthy! They’d all fall out after a while! Or let’s say reading books with my kids at bedtime. If I read for two hours before bed tonight with my daughter Lucie it’s not going to make her a better reader. Those are all acts of intensity. Brief intense moments of an event.

We know that we need to brush our teeth twice a day everyday to see results. We know that to go to get in physical shape we need to routinely work out 20 minutes a day and we will see results. We will absolutely get into shape. If we read with our kids every night then they will become better readers and better writers! We know this. These are acts of consistency.

It’s little consistent events that will make the difference not a big one-time or two-time event. But the problem is that we can’t see the benefits of the small acts in real time. I don’t see that my teeth are healthier after the one time brush or that my daughter reads any better…..I have to wait to see those benefits. And it’s hard because those benefits come at different times for different people.

When Simon talks about great leaders he says that great leaders have to build consistency and not intensity. It’s all the little things they do to create a great work culture and not the big hoopla one time event. A great leader can’t just throw an amazing holiday party and expect that to be the solution to a great work environment. They have to show acts everyday that they value their employees. That consistency will create a great work culture!

Intensity versus Consistency for Math Education:

That lesson that flopped was a one-time event! It was because we viewed it as an act of intensity. In order for those lessons to be successful and to bring out deep meaning and learning for our students we need acts of consistency. We need to do this as part of our routine.

That consistency will help create the amazing classroom culture you are dreaming of. That positive, safe, fun learning environment where kids learn with each other and with the teacher! But we have to be willing to put in the work to build consistency.

And the students are not going to be the ones to magically make this happen. We have to do it. We’re talking about middle school or high school here. Students would rather NOT talk to other peers they don’t know. We need to teach them how to help create this environment.

And It’s all the little things we do everyday that will make this happen.

  • It’s the Daily Warm ups where you have kids discussing arguing defending.
  • It’s routinely asking kids to struggle that teach them resilience.
  • It’s your assessment routines.
  • It’s the Random Grouping everyday and using Whiteboards that show them that you value their voice.
  • It’s the problems you use to teach with.
  • It’s how you demonstrate to your students what you value in learning.

It’s the things you do everyday that matter. Those are the things that will build the culture you are looking for. Routine and Consistency are what will drive change in your classroom and student learning.

This takes dedication. I know it’s hard so to help you out I’ve put together a handout that you can download, read and share with other teachers on 5 tips to to build amazing classroom culture. And you guessed it all of them involve being consistent instead of intense.

Click to download 5 Tips to Build Amazing Classroom Culture. 

What are your tips to build amazing classroom culture in your math classes? What are we missing? Just add those in the comments below.