Mr. Orr is a Geek.com
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We can do this betterSat, 14 Dec 2019 02:05:52 +0000en-US
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https://mrorr-isageek.com
323246847216The Make Math Moments 3-Part Framework Guidebook
https://mrorr-isageek.com/framework/
Sat, 14 Dec 2019 02:05:44 +0000http://mrorr-isageek.com/?p=68226822No Bikes Allowed
https://mrorr-isageek.com/no-bikes-allowed/
https://mrorr-isageek.com/no-bikes-allowed/#commentsWed, 26 Jun 2019 18:24:18 +0000http://mrorr-isageek.com/?p=6689Sparking Curiosity
Students will extend their use of patterning to connect different representations of linear relations. More specifically, students will be exposed to rates of change, calculating the slope of a linear relation, building linear equations, and solving linear equations.

The purpose of this Task is:

to help students develop an understanding of how various representations of linear relations are connected;

create a linear equation given two points; and,

solve linear equations.

Intentionality

As is true for any task, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit.

The mathematical ideas we are trying to elicit when we use this task are connect various representations of linear relations, build linear equations from two or more points, and solve linear equations.

This will be achieved by first having students watch how the cost of renting a scooter is related to the time rented. You can learn more about the actual scooters and the pricing structure at lyft.com.

Spark Curiosity

WARNING!!! Be sure to share with your students the importance of wearing Bike Helmets while riding; we certainly should have. We realize that you may not want to do this activity with your students as a result of our poor judgement.

Show students this video:

Ask students to engage in a notice and wonder protocol. ANYTHING and EVERYTHING that comes to mind is fair game.

Here’s some of the “everything and anything” students noticed and wondered on chart paper:

I noticed that they were riding scooters;

I noticed that they weren’t wearing helmets;

I noticed the map;

I noticed that the cost changes;

I wonder where that was?

I wonder how much the scooters cost?

I wonder what the range means?

Now you can focus in on the big question of the task.

How much does it cost to ride the scooter the entire length of the outlined route?

We can now ask students to make a prediction using their estimation skills. Ensure you use the Too high and too low strategy. Ask them what is a wrong answer? How much would be too high? How much would be too low?

Students will also be uncomfortable here because the length of time of the trip or how the scooter charges customers has not been revealed yet. We encourage you to hold off on revealing these answers because it will build anticipation. Anticipation is what students need so they can start formulating a plan.

At this point, we want to give students the opportunity to improve their predictions by engaging in developing a problem solving strategy.

Ask them: If we are going to improve our predictions what information will we need? Have students share with an elbow partner before sharing this information with the entire class.

As students voice the information they wish to see.

Ask them: “And what would you do with that information if I gave it to you?”

Listen in very closely here. Their responses will give you allow you to assess their prior knowledge and also their thinking into solving this problem.

Slowly Reveal More Information

Once students have asked for information reveal the information that you do have.

Reveal a key fact:

The cost of renting a scooter depends on the time the scooter has been rented for (You may want to reveal depending on your students’ prior knowledge that there is a flat fee to get on the scooter).

Reveal three snapshots showing the cost at different points in the trip. We include three here so that we can verify that the relationship between the cost and the time is linear.

Reveal the total cost of the entire trip.

With this information students can start to develop strategies to determine how much it will cost for a 15 minute and 9 second trip.

Fuel Sense Making:

LEARN HOW TO FUEL SENSE MAKING

MAKE MATH MOMENTS ACADEMY

Create memorable moments in your classroom using our ready made tasks

Full Video Walkthroughs to show you key moves to improve student learning.

After consolidating the learning using student generated solution strategies and by extending their thinking intentionally, we can share what the actual cost of the trip was:

]]>https://mrorr-isageek.com/no-bikes-allowed/feed/2668930 Days in 30 Minutes: A video series that gives you a glimpse in my classroom.
https://mrorr-isageek.com/30days/
https://mrorr-isageek.com/30days/#respondFri, 22 Feb 2019 00:05:07 +0000http://mrorr-isageek.com/?p=663130 Days in 30 Minutes is a 30-episode video series I’m sharing where I’m sharing 1 minute of each day for 30 days in row. I’ll show you the good, bad, and ugly of a real math classroom where we’re trying to spark curiosity and fuel sense making in our students.

By sharing my day-to-day experiences I hope that you’ll see a little bit of your own classroom in my classroom and realize that we’re all doing great things for our students to learn better, deeper, and fuel their sense-making.

Below you can watch the days unfold as they happen.

The first video in the playlist will be the most recent day while the remaining videos will start at day 0 and run in chronological order to the most recent day.

Did you miss a day and want to catch up? You can select any day you’d like to see.

DOWNLOAD THE
BUILDING RESILIENT
PROBLEMS SOLVERS GUIDE

Download the 3-page printable guide that will give you 3 actionable tips to build resilient problem solvers in your math classroom.

]]>https://mrorr-isageek.com/30days/feed/06631Random Grouping Cards For Math Class
http://mrorr-isageek.com/random-grouping-cards-for-math-class/
http://mrorr-isageek.com/random-grouping-cards-for-math-class/#commentsWed, 30 Jan 2019 12:00:18 +0000http://mrorr-isageek.com/?p=5531

[UPDATED – January 2019]

In my class, most often, I pair students up to work through problems. I also, most often have less than 24 students. I’ve updated the cards to include a version for ONLY 24 cards and groups of 2. This will make it easier to create different groupings within the same class period without having to give students new cards.

Ready to download the cards? There are three copies of the cards.ONE DESIGNED FOR ONLY GROUPS OF 2, One with equations/expressions and one without (groups of 2 or 3 – 36 cards).

Transcript of the video:

Alright, this video is about Random Grouping in your class and I’ve a got new way to make that happen!!!

So for the last few years I followed a suggestion from Al Overwjik who followed Peter Liljedahl to have random groupings in my class daily. That’s right kids sit in different spots each day with different people. And like Al I was using playing cards to match them up.A student would walk in the door grab a random playing card our of my hand and then find the matching one on the desk. The class would then randomly be placed in groups of 3. Easy right. I grew tired of always using cards. I wanted to mix it up. So last year I used different colour popsicle sticks, then I created equations on slips of paper, then coloured paper slips. So this coming semester I’m using these new cards I created. Below you can download, print them out and then laminate them.

They have different ways to match. Just tapethe master card to a group of 3 desks (or pairs will work too) .

Then For example, today I may decide that we are all matching by colour. So when you grab a card from me at the door, go and sit at that colour. But tomorrow I may decide to match symbols so if a student chooses this card

They would go and sit at the “gear” table! And maybe the day after thatI’ll say to match expressions, then the student will have to evaluate the expression on the card to discover what table to sit at.

Pretty easy! There are 12 colours, 12 symbols, 12 shapes, and 12 numbers that match expressions. So 36 cards in total.

If you’re like me and have only 24 kids then you can get rid of a few colours and it’ll all still work out. So grab them below here and have fun mixing it up!!

There are two copies of the cards. One with equations/expressions and one without.

]]>http://mrorr-isageek.com/random-grouping-cards-for-math-class/feed/45531Making Math Moments That Matter Podcast
https://mrorr-isageek.com/making-math-moments-that-matter-podcast/
https://mrorr-isageek.com/making-math-moments-that-matter-podcast/#respondTue, 29 Jan 2019 16:24:16 +0000http://mrorr-isageek.com/?p=6614Maybe you don’t know this about me but I’m an avid listener of podcasts! I love pushing play on an episode, putting my phone in my pocket on my way to work or on my run and just being engrossed in the stories I hear.

I’m proud to announce that I’ve thrown my hat into the podcast ring! Along with Kyle Pearce, we’ve launched the Making Math Moments That Matter Podcast officially on iTunes, Google Play, Spotify, Stitcher, and many others with our goal being to offer Moment Makers like yourself an easy way to reflect on your teaching practice and plan intentionally how you might use the Making Math Moments 3-Part Framework as you craft your next lesson.

You can listen right now to our latest episode by clicking play on the bottom of your screen.

In the first handful of episodes, we dive into the Making Math Moments That Matter 3-Part Framework. In other episodes we interview some pretty influential Math Moment Makers as well as invite some teachers from our community to engage in a mentorship call right on the show.

Subscribe right now to the Making Math Moments That Matter podcast on your favourite platform by simply searching “Making Math Moments That Matter” on that platform, or by clicking on the desired link below:

Regardless of which platform you decide to use, we would so appreciate if you SUBSCRIBED and left us a REVIEW to help us reach as many math educators as possible.

I can’t wait to hear what you think!

]]>https://mrorr-isageek.com/making-math-moments-that-matter-podcast/feed/06614Double Jenga [3 Act Task]
https://mrorr-isageek.com/doublejenga/
https://mrorr-isageek.com/doublejenga/#commentsWed, 12 Dec 2018 23:08:06 +0000http://mrorr-isageek.com/?p=6563I have a challenge for you and I hope you are up to it because I’m so excited to see what you come up with!

I have the beginnings of a math task that involves two Jenga sets. The challenge for you is to frame out how the lesson will unfold in your classroom. How would could you use these videos in your elementary class? Your middle school class? Your high school class? Maybe you have an idea on how to use these resources to start a lesson? Maybe you can already see how to create a full lesson using these resources? Maybe you have an idea on how to use the Curiosity Path to shape a lesson? Whatever grade level you teach or whatever lesson you build do these two things:

Share your ideas, photos with your students, or questions either here in the comments, on Twitter, or on Facebook.

Check back to this post next week where I’ll feature some teachers lesson ideas and I’ll also share how I used these resources with my students.

Watch below the first video:

Video 1: Double Jenga – Little Jenga

Video 2: Double Jenga – Little Jenga with Time.

Video 3: Double Jenga

Picture 1: Heights

Picture 2: Widths

Picture 3: Lengths

Video 4: Double Jenga – Time

Using those resources build a lesson for your students and then,

Share your ideas, photos with your students, or questions either here in the comments, on Twitter, or on Facebook

Check back to this post next week where I’ll feature some teachers lesson ideas and I’ll also share how I used these resources with my students.

I’m pretty pumped to see what you come up with.

]]>https://mrorr-isageek.com/doublejenga/feed/165632018 Winter Holiday Math Moments Giveaway!
https://mrorr-isageek.com/2018-winter-holiday-math-moments-giveaway/
https://mrorr-isageek.com/2018-winter-holiday-math-moments-giveaway/#respondMon, 03 Dec 2018 09:33:12 +0000http://mrorr-isageek.com/?p=6530

This holiday season the Kyle Pearce and I want to give back to educators like you! We’ve been so impressed with the dedication math teachers from across the world have been showing to take their craft to the next level and we want to show our appreciation!

What are we giving away?

We’ve put together 4 Jam-packed prizes of our favourite math classroom resources and our favourite professional development resources! These are resources we either use in our own classrooms or share in our online workshop or both!

Each prize pack includes over $800 in value!! This is our biggest giveaway yet!

CONTEST CLOSES DECEMBER 20th, 2018!!!

ALLFOUR (4)PRIZE PACKAGES INCLUDE:

One FREE Entry into our upcoming Online Workshop: Making Math Moments That Matter ($297 value):

Learn our proven 3-part framework for building easy to plan and fun to deliver lessons that kids will not only love, but also learn from regardless of their level of readiness. Registration will open January 25, 2019. Learn more: http://makemathmoments.com/onlineworkshop

Uncomplicating Fractions is a practical, must-have resource from Dr. Marian Small that helps teachers understand how to teach and assess student learning of fractions. ($40 value).

A critical read for teachers and parents who want to improve children’s mathematics learning, What’s Math Got to Do with It? is “an inspiring resource” (Publishers Weekly) ($25 value).

The Coaching Habit: Say Less, Ask More & Change the Way Your Lead Forever ( Michael Bungay Stanier).

”Michael Bungay Stanier distills the essentials of coaching to seven core questions. And if you master his simple yet profound technique, you’ll get a twofer. You’ll provide more effective support to your employees and co-workers.” – Daniel H. Pink ($15 value).

]]>https://mrorr-isageek.com/2018-winter-holiday-math-moments-giveaway/feed/06530Chocolate Mania [3 Act Task]
https://mrorr-isageek.com/chocolate-mania/
https://mrorr-isageek.com/chocolate-mania/#commentsWed, 28 Nov 2018 10:46:13 +0000http://mrorr-isageek.com/?p=6446This post and task was written and created by both Jon Orr and Kyle Pearce.

For about a year now Kyle Pearce and I have been travelling to schools and districts across North America sharing our techniques on how to Make Math Moments That Matter for our students.

In those live workshops we’ve been using a task without a name. On the first anniversary after creating that task we wanted to share it here with you and give it a name.

We’re all about creating tasks and then thinking about how they might be modified for use across a variety of grade levels. With a few modifications, you can successfully run this task in classrooms from K through 10. In particular, you could address the following expectations:

building estimation skills;

building multiplicative thinking and proportional reasoning using arrays;

building multiplicative thinking and proportional reasoning using double number lines;

making connections to the inverse relationship between multiplication and division;

connecting double number lines and ratio tables to creating and solving proportions through algebraic reasoning;

highlighting the value of the constant of proportionality (i.e.: unit rates) so students can “own” every problem possible in a proportional relationship;

determining rates of change;

representing linear relations in various ways;

solving problems using the four representations of linear relations; and,

Here are possible notice and wonders from our workshop participants and also some from our students:

They’re both wearing plaid.

The video is in reverse.

How many chocolates will they eat?

Did they get sick?

How long did it take to eat all the chocolate?

It looks like they’re spitting it out.

Kyle is eating Kisses.

At this point the students’ responses are listed on the board during the class discussion.

After capturing all the notice and wonders on the board steer the class to working on the problem:

“How many chocolate did Kyle eat? How many did Jon eat?”

Have your students estimate how many each of us ate. What is too high? What is too low? Your students may be feeling uneasy about their estimates; that’s okay! The point here is we don’t have enough information. To help with estimates at this stage we disclose that all the wrappers of all the chocolates we ate are showing in the image above.

We encourage you to record many of the estimates in a chart as a class. This will put some pressure on making those estimates carefully.

Act 2: Revealing Information to Fuel Sense-Making

To avoid rushing to the algorithm we’ll push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. This process is key; student anticipation of what is needed is a gold mine for understanding where they are in their thinking. By having them ask for information they have to start problem solving!

Students may ask for the time it takes for the whole video and you as the teacher can then say, “And what would you do with that if I gave it to you?” Listen to how they answer this. You’ll gain valuable information about where that student is on this problem solving journey. You will know after that answer if the student is thinking proportionally or not.

Here is some information to share:

Ask students to share what this series of photos tells them. What do they notice? What do they wonder? Then share this photo. It reveals the total amount of ml each of us consumed.

At this point students will have enough information to determine how many pieces of chocolate each of us ate. Let them go at it!

Fuel Sense-Making to Consolidate Learning.

Note: You or your students may want to work with more familiar numbers compared to what you see above. For example, to get a close prediction to the actual number of chocolates each of us ate a student may round the 111.8 ml to 110 ml and similarly round the 17 ml for 3 chocolates to 20 ml.

Depending on the grade level or skill level of your students we can expect to see some of these strategies

Counting with familiar numbers;

Using arrays;

Number line counting;

Tables of value counting;

Long division;

Unit rates;

Solving Proportions;

Creating and solving equations.

Here are some of those strategies:

Counting Up Chocolates and ml.

Students may count up 17 ml every 3 pumpkins until they reach close to the total amount of ml. If they go over the total amount they may want to subtract a cup of chocolates so they can get more accurate.

Here’s that strategy in action

Working with Fractions:

To get more precise answers we can encourage students to work with parts of chocolates in decimals or fractions. Many teachers would be inclined to stay away from fractions because they feel it may “de-rail” the lesson. We say use this context to reinforce fraction work and understanding.

Counting/Multiplying/Dividing Using Arrays:

Students may organize their counting strategy in a double array model. Simultaneously counting in groups of 3 pumpkins and 17 ml will allow them to see that they will need just over 6 cups of pumpkins, while showing the proportional relationship between the pumpkins and volume.

Double Number Line:

Students who solve the problem with a proportion will benefit from seeing it laid out on a double number line. By showing how to solve a proportion on a double number line we take a familiar concept (counting on the number line) and extend it to work multiplicatively. Students who solved the problem with an additive strategy will see the benefit of greater precision of using a scale factor.

Unit Rates:

Many students may use a unit rate to help solve this problem.

Note: This student will benefit from a conversation on notation, units and order of division.

Linear Relations:

You may choose to use this problem to either introduce or practice linear relations. I used this task to link the idea of finding the unit rate to determining the rate of change (slope) in a linear relation and then use it to build an equation to help solve the problem.

Reveal the Answer:

After consolidating the learning goals you wanted to bring out into the open for discussion with your class show them this reveal video of the actual number of chocolates each of us ate. Be sure to go back and validate those students who estimated the closest early in this task.

Is there a Volume relationship?

We want to leave you with some thinking here. We chose these chocolates for a very specific reason. In fact we hunted down the spherical chocolate that has the same height and diameter of that Hershey’s Kiss.

Your Task: What volume relationships can we pull from this image?

Did you notice the relationship between the amount of chocolate by volume Jon ate versus Kyle?

Look for an upcoming post on how we used this task to teach volume. But before we do that we want to know how you see a lesson on volume forming with this information. Use the comment section below to share your ideas, questions, comments, or even just snippets of what a lesson could look like.

DOWNLOAD THE
TASK AND RESOURCES

Download the videos, animated gifs, and other resources to make sure that this 3 Act Math Task can spark curiosity to fuel sense making in your classroom!

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

]]>https://mrorr-isageek.com/chocolate-mania/feed/16446How learning to ride a bike is like/not-like learning math, and why it should be!
https://mrorr-isageek.com/how-learning-to-ride-a-bike-is-like-not-like-learning-math-and-why-it-should-be/
https://mrorr-isageek.com/how-learning-to-ride-a-bike-is-like-not-like-learning-math-and-why-it-should-be/#respondTue, 20 Nov 2018 22:07:17 +0000http://mrorr-isageek.com/?p=6374What are the moments that truly matter?

For me they are moments where we learn or accomplish something we are exceptionally proud of. They are moments that make us stand back and say “Wow! I did it” They are moments that we say “wait, let me get a picture of this.” They are #Snapworthy moments.

For me they are, playing that first song on guitar, catching a fish for the first time, watching my daughters swim that full length of the pool, scoring a basket in basketball, scoring a goal, singing a song in front of an audience, or riding a bike for the first time.

Learning the skills needed to accomplish these feats takes a similar path. The process has a similar experience.

We learned these things through the process of productive struggle.

Take my daughter Lucie for example. She was the last to learn how to ride a bike (tough when you have a twin too). She finally learned in a similar way, most likely, to how you learned how to ride a bike; by getting on, trying to balance while coasting, then falling over! Then, trying again.

Every time she fell she learned something. She would adjust and try again. She was struggling productively.

The difference between just struggling and productive struggle is Feedback.

Going through the struggle, using feedback and then making small gains gives us a rewarding experience. It makes us want to keep going. We build perseverance. We want to do better. This is one of the key ingredients to make moments that matter.

You know, we learn to ride bikes this way but traditionally we don’t learn or teach math this way. Vice versa is also true. —> we don’t learn to ride a bike the same way we learn math.

For a moment Imagine that we did. Imagine we structured a course on riding bikes like we structure our traditional math classes.

Here’s what the syllabus of bike class might look like, especially if it was taught in our schools. (I’ve adapted an analogy here from Dr. William Rankin).

Day 1:

“Welcome to your first class on bicycle riding. It’s going to be a great semester! We’ll start off week 1 with learning all about the tires. Tires are super important they’re the life of the bike. Learning about tires is important because it will help us be ready when we ride a bike.

During week 2 and 3 we’ll go over how the pedals work. Pedals are vital, they help make the bike move. In those weeks we’ll learn how that happens so when we start riding bikes we’ll be ready.

In week 4 we’ll have a test on the tires and pedals and then we’ll move on to study the handle bars. We won’t revisit the tires and pedals again until the end of the year so make sure you study for this test!

Weeks 5-8 is for Brakes. Brakes are vital to controlling the bike. I know they are related to the handle bars but handle bars were last unit. We don’t want to mix the two.

Weeks 9-10 are for Gears! I know they’re part of the pedal, wheels, and handle bars, but we’ll just talk about gears those weeks. You’ll need to use them when you start riding your bike.

Well ……That’s all we have time for in this course….

If you take our next course we’ll learn all about balance, whoa, that’s a biggie when it comes to bike riding.

When do we actually ride bikes?

That’s when you graduate!“

Silly right!!

What did you do when you learned how to ride a bike? You just jumped on and rode! Just like Lucie did.You felt a purpose to what you were doing. You learned as you were riding. It was a memorable moment.

But that silly bike class is the way we traditional teach math class. We tell our students that a purpose of math learning is so they can solve problems in the real world! We hold it over their heads that real problem solving is only for when you’re in the real world — done all your schooling.

We’ve traditionally taught math concepts in siloed units as if one math strand isn’t connected at all to another.

We say now,

JUST RIDE BIKES

Teach through problem solving. Productive struggle teaches the resilience we are looking for in our students. Just get on the bike and ride it!

In many of my past “problem solving lessons”I wasn’t really teaching students how to become better problem solvers.

If we’re giving step by step guides to solving problems in our classes are we really teaching problem solving? How much genuine problem solving are we doing in our math classes?

Teach content through problem solving. It’s the productive struggle – feedback cycle that really teaches our students to build resilience and their problem solving skills. It’s the productive struggle – feedback cycle that will create moments that your students will feel pride in. Those are the moments that matter. Just get on the bike and ride it!

[UPDATE]

Carla, a participant from our Making Math Moments That Matter online workshop pointed me to a fascinating video –> “The Backwards Brain Bicycle” from SmarterEveryDay. The video illustrates the notion that we may have the knowledge of how something works but we don’t always have the understanding of making it work.

Watch:

How does the message of this video relate to math education? –> We may have the knowledge that we need to Just Ride Bikes so that our students can become better problem solvers while at the same time creating meaningful moments but we don’t understand exactly how to do that.

We ourselves need to Just Ride.

We have to unlearn what we understand about teaching math class so that we can build a new path towards Making Math Moments That Matter.

Resources to help “ride bikes”

DOWNLOAD THE
BUILDING RESILIENT
PROBLEMS SOLVERS GUIDE

Download the 3-page printable guide that will give you 3 actionable tips to build resilient problem solvers in your math classroom.

ACCESS THE
SPIRALLING MATH CLASS VIDEO SERIES & GUIDE

Learn the concept of spriralling your math class and why you should do it. You’ll walk away from the video series with practical tips to implement spiralling in your classroom.

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

]]>https://mrorr-isageek.com/how-learning-to-ride-a-bike-is-like-not-like-learning-math-and-why-it-should-be/feed/06374Creating Math Moments: How we can transform typical textbook problems into moments that matter.
https://mrorr-isageek.com/creating-math-moments-how-we-can-transform-typical-textbook-problems-into-moments-that-matter/
https://mrorr-isageek.com/creating-math-moments-how-we-can-transform-typical-textbook-problems-into-moments-that-matter/#commentsWed, 14 Nov 2018 13:58:17 +0000http://mrorr-isageek.com/?p=6343In an ongoing effort to demonstrate that we can apply the 3 part framework of Spark Curiosity, Fuel Sense Making, Igniting Teacher Moves to any lesson in math class we’ll tackle the common problem of finding the equation of a line between two points. Like this basic problem:

Sometimes textbooks may even jazz it up a bit to give it some context like this one.

Even though this is a grade 9 and 10 expectation here in Ontario you’ll find that this problem is quite accessible for many grades.

In particular you could use it to uncover:

Find the slope (rate of change) of a line between two points;

Find the equation (rate of change) of a line between two points;

Model real-life relationships involving constant rates;

Model linear relationships using tables of values, graphs, and equations.

Spark Curiosity

We’ve been arguing that instead of finding a context that will make students interested we should follow the curiosity path which we’ve described in Lessons One and Two from our 4 part video series instead.

Let’s consider the big idea here: We want students to build an algebraic representation of a linear relation using only two values.

To withhold information and build anticipation we will strip all the numbers and questions and ease into the lesson. To help create the classroom culture that values student voice, student thinking, and growth we’ll ask students to fill in the two blanks here:

Setting the floor low will help our students feel attached to the math problem that is coming. The more attached and invested they will feel the more internal motivation they will have to pursue the problem to the end.

In behavioural economics there is a theory known as The Sunk Cost Fallacy.

Escalation of commitment is a human behavior pattern in which an individual or group facing increasingly negative outcomes from some decision, action, or investment nevertheless continues the same behavior rather than alter course. The actor maintains behaviors that are irrational, but align with previous decisions and actions.

You see, we humans are inclined to avoid loss. We will continue with a project or line of thinking if we feel that if we abandoned it we would incur loss. Even if that abandonment was better for us.

For example, my first car, a 1993 Ford Escort – you know, this is the car that had the automatic seatbelts. When you sit down and turn the car on the seat belt came up and automatically moved over your shoulder. One winter the heater in the car stopped working and I paid over $1000 to have it fixed. Then not long after something else broke on the car and instead of saying enough with this car I said, “Well, I just paid $1000 to fix it if I don’t fix it now then it’s like my $1000 was wasted.” This bias I just exhibited is an example of the sunk cost fallacy. I wanted to throw bad money after good. The $1000 I previously spent was a sunk cost and there’s no way I could get that back so the $1000 shouldn’t play a roll in my new decision to fix the car. I should decide to fix the car or not fix the car without letting that $1000 affect this decision.

The sunk cost fallacy makes us feel that if we invest time, money, resources into a project or decision that we should keep going with that project or decision so we avoid loss. The escalation of our commitment keeps us in the game.

In math education we can use our students own tendencies of avoiding loss for their own good. By setting a low floor in activities, we are easing our students into those activities and lessons so that it will be harder for them to just quit and give up once they are deeply invested in the activity . They won’t want to feel that what they’ve done so far in the activity was a waste of time and resources. They’ve sunk a cost into the activity and will continue with it to avoid loss. You can read another application in education of the Sunk Cost Fallacy from Robert Kaplinsky.

Your students will fill in various items and values for this problem. In my class this was a fun moment as we shared out what they wanted to buy and for how much.

Fuel Sense Making by Revealing Information

So now we’llmove down the Curiosity Path and narrow the focus to give a little more information.

How much would 12 shirts cost?

Students can make quick predictions before revealing the information slowly…

We don’t want to waste all the work we’ve done on escalating our students commitment so we’ll move down the curiosity path a little bit more and avoid the rushing to the algorithm. Students will use the given information and their prior knowledge to build a strategy to solving this problem.

Fuelling Sense Making by Anticipating

We are strong believers and practitioners in the PDF or the book 5 Practices For Orchestrating Productive Mathematics Discussions. So in preparation for this lesson we used our Anticipation, Selection, and Sequencing template to brainstorm possible solutions and strategies our students will try.

To maximize your mathematical discussions you may want to sequence the strategies from most common to least common.

For example;

You can expect many students to try to find a unit rate to solve this problem. This is quite natural! It makes sense to find the price per shirt. However, not all situations are directly proportional. We can ask our students: How do we know this is a direct proportional relationship?

When students find the unit rate for 12 shirts at $122 and then again for 24 shirts at $209 they will see that it doesn’t cost the same per shirt! WHAT!?

Something else is going on here. You may want to give a small hint here asking, “hmmm, If 12 shirts cost $122 does 24 shirts – which is double the amount of shirts cost $122 x 2? How much more does 24 shirts cost? What would 36 shirts cost?

Students who noticed this right away may draw a double number line to show the changing prices and eventually determine the cost per shirt.

Students who have found the cost per shirt will still notice that simply multiplying the cost per shirt by the number of shirts STILL doesn’t get the cost — there is some other value that consistently needs to be added – The initial value or fixed cost.

Have a discussion at what this fixed cost could be — shipping charges? Overhead costs? Printing rental fee? ect. With this new calculation rule students can move on to verify that it does indeed work with 200 shirts, and then finally find the cost of 1100 shirts. You may even want to steer your discussion towards finding an algebraic representation of this relation.

Some students may represent this pattern as a table instead of a double number line. Depending on your grade level you may also want to use the word slope to represent the cost per shirt. If you see this solution from your student you’ll want to push for an algebraic representation

You may see some students turning toward Desmos and graphing the points to find an algebraic representation. We definitely anticipated this having taught this lesson in a grade 10 applied class.

The order you present these strategies/solutions will depend on your lesson goal. If you are trying to achieve the goal from the top of this post (Finding an equation of line between two points) then you most likely will want to end with finding the algebraic representation and then showing how you can use Desmos to verify that representation.

Finally we can show students that if the relation is linear, we really only need two points.

We feel that if we can take this particular learning goal and modify the delivery and teacher moves to create a math moment that matters we can do this with any textbook problem. What lesson should we make over next?

]]>
https://mrorr-isageek.com/creating-math-moments-how-we-can-transform-typical-textbook-problems-into-moments-that-matter/feed/26343Hour Glass Multiples
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https://mrorr-isageek.com/hour-glass-multiples/#commentsSat, 10 Nov 2018 21:21:31 +0000http://mrorr-isageek.com/?p=6315Sparking Curiosity & Fuelling Sense-Making with the Least Common Multiple.

In this 3-Act Task students will be presented with a puzzling video of 3 “hour glass” sand timers. They’ll solve a brain-teaser like problem while ultimately learning about common multiples and the least common multiple (LCM).

Ask your students to write down anything they notice and anything they wonder while viewing this video:

Then have them share with elbow partners and then finally with the entire class.

Some possible notices and wonders:

I see three different colour timers.

Is that sand?

Whose house is that?

Are they timing the same amount?

What times will they time?

Will all three timers ever end at the same time? If so, when?

Is the timer in minutes?

I think the yellow timer times for 3 minutes.

After capturing all the notice and wonders on the front board steer the class to working on the problem

“Will all three timers ever run out of sand at the same time? If so, when? If never, why not?”

Assume that we will keep turning over a timer after the sand runs out.

Take a few minutes to have your students estimate when the timers will all run out at the same time –> “Predict with reasoning”.

Act 2: Reveal Information to Fuel Sense-Making.

To avoid rushing to the algorithm push down the curiosity path some more. Instead of just handing over all the necessary information to solve a problem ask the students what they want to know more about. For example student 1 might say “I’d like to know the times of all the timers”. As a teacher your next question should be: “I see, and if I gave you that information what would you do with it?” We can learn what our students understand and are thinking with their response to one prompt. By asking them to anticipate what they need forces them to develop a problem solving strategy.

After hearing a few students out, give them this information: But make them guess first. What time does each timer time?

Reveal the timers:

After this reveal send students to their vertical spaces to explore the strategies they began in the anticipation stage to determine when the timers will run out of sand at the exact same time.

Strategies you may see:

Drawings that show how much time is left every time one timer runs out.

lists of the multiples of 2, 3, and 5.

tables that track minute by minute.

Fuel Sense-Making to Consolidate Learning.

Depending on your grade range and student ability you’ll want to frame your consolidation so showcase your target learning goal.

I’m sure most learning goals will include a triple number line showing how multiples of 2,3, and 5 overlap.

Clearly show using the lines how the 2 and 3 minute timer will be turned over at the same time at the 6 minute mark. Then show them all the common multiples between 2 and 3.

Finally bring in the multiples of 5 to the mix.

As part of your consolidation show this video which overlays the common multiples as they occur in the reveal video. Students can clearly see that when the timers are turned over at the same time we have a common multiple.

Here is a reveal video without the number line overlay.

Try this lesson out in your class and report back here in the comments to tell us how it went.

DOWNLOAD THE LESSON FILES: VIDEOS & IMAGES

Download the lesson files so you can run bring out great moment around least common multiples.

Are you new to 3-Act Math problems? Grab our guide to running these problems in your classroom. Learn tips, suggestions, and avoid common mistakes of using these types of tasks.

New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

I want to thank Michael Jacobs for turning my thinking towards thinking about the least common multiple. The creation story of the above task comes from this hour glass timer I bought from David’s Tea

I just bought this triple “hour” glass timer! I think we can pull some math from it. What do you wonder? What do you want to know more about? Let’s build some math lessons together. What can we do with this? #iteachmath#mtbos#mathchatpic.twitter.com/6FCz8ivpsO

if you flip it over every time the sand runs out from one timer, how many times will you flip it over before all the timers are empty at the same time?

Which made me start thinking about how that couldn’t work with all three timers attached. So I set off to buy some new timers. I found the ones you see in the problem above.

]]>https://mrorr-isageek.com/hour-glass-multiples/feed/46315Promote Struggle – A Hero’s Journey in Math Class
http://mrorr-isageek.com/promote-struggle-a-heros-journey-in-math-class/
http://mrorr-isageek.com/promote-struggle-a-heros-journey-in-math-class/#commentsWed, 31 Oct 2018 09:18:43 +0000http://mrorr-isageek.com/?p=4450How many times have I seen a student give up before they even start an unfamiliar problem in my class? A lot! It happens way too much. How can we build resilience and determination in our students? One thing we can do is to let them experience unfamiliar problems regularly and help them struggle through the process of working on a solution.

Let me share with you how the Hero’s Journey story arc can help with learning productive struggle in math class.

While in Miami for the Apple Distinguished Educators Institute we saw a speaker from Pixar Randy Nelson discuss the aspects of Story. More specifically he spoke about the Hero’s Journey. That talk really hit home for me. Below is how I interpreted his message and how it relates to my classroom.

A Hero’s Journey

All of these characters take a hero’s journey….

Since I’m a math teacher describing the Hero’s Journey is best done with……a graph (English teachers will know it’s shown as a cycle).

On a time vs. Tension graph the Hero’s Journey looks like this: Time is the length of the journey….or story. The tension is felt by the audience.

In the beginning the hero is introduced, the main conflict is introduced, his/her world starts to change. As the story continues the hero must battle the forces of evil & go through struggle. They must experience conflict. It’s the conflict that the hero learns about themselves. They learn their strengths and weaknesses. It’s the struggle that makes the ending awesome. Its the struggle that make the hero see the solution. It’s the lessons they’ve learned in the struggle that let’s them go aha! I know what I need to do! The story would mean nothing to the hero and the audience if the climax was much earlier in the timeline. As the story ends the character returns to a NEW normal. They take their learning and come out stronger on the other side.

This curve we see above is nothing new to us. This curve is what learners go through. It’s a Learner’s Journey too.

Now, if we take a look at our traditional math classrooms we have a format much like this:

Photo credit: Kyle Pearce

Let’s look at that structure on the Time Tension graph.

After we take up homework, we introduce the new lesson or topic or problem to work on. It’s unfamiliar so tension in our students starts to increase. But what happens is that as the tension rises it immediately falls back down. And my good buddy Kyle Pearce mentioned to me that the tension doesn’t fall all the way back to the axis….a good number of our students feel that tension permanently.

Why does the tension fall immediately?

We make that happen. We relieve students of their pain by immediately telling them HOW to solve the problem.

It’s Our examples & solutions. Students don’t get a chance to struggle & discover, Therefore the math formula, strategy or algorithm means nothing to them! The memorizers will memorize and do ok, and the non-memorizers lose again. The ideas and strategies have no real value to them.

I think students should feel the need for the math they learn. They should experience struggle ….just like the hero.

Let’s take the old model of our lessons and change it to match the Hero’s Journey. It’s the struggle that adds value to their learning. Let’s move the reveal of math rules etc farther in the timeline. Let’s let the students productively struggle through problems. The reveal of the “math” will mean so much more after students see and/or feel the need for it.

DOWNLOAD THE
BUILDING RESILIENT
PROBLEMS SOLVERS GUIDE

Download the 3-page printable guide that will give you 3 actionable tips to build resilient problem solvers in your math classroom.

An example in my class this week came when I wanted to teach students how to determine an equation of a quadratic function when given some key points.

I gave them this simple Desmos Activity Builder slide from Match My Parabola

Students already knew about vertex form of a quadratic function so I knew they could put in most of this equation. It’s the “a” value that they really didn’t know how to get efficiently. So I saw a lot of this…

Students used trial and error to find -1/4 as the right “a” value. But we then asked “How do we know that’s the right one?” We then discussed plugging in a point to check to see if the right side equals the left side. They had a few more slides just like this but with different points. By the end of the last slide you could see that they really wanted a more efficient way of determining the “a” value than guessing and checking. This is where I stepped in and we discussed the idea of using one of the points and the equation to solve for the “a” value. Everyone was on board! They all had struggled before we discovered an efficient strategy. They all wanted it. If I had started class by showing them the first slide and then just telling them how to do it, I would see lack of understanding of why and bored faces.

It’s the struggle that makes the math worth it! Let’s let our students be Heroes. How are you promoting struggle in your classroom? I would love to hear of your ways. Leave a comment below.

To help you wrap your mind around the Hero’s Journey as a lesson model I’ve created a Hero’s Journey Lesson Template. The exercise is to choose a lesson you have coming up in your class. How can you modify that lesson so that the flow follows a hero’s journey? Use the template below to help plan your lesson out.

Exemplar: I used the template to model how I use the Pentomino Puzzles activity to teach solving linear equations.

You can see that we slowly build up the need for a helpful efficient strategy to solve the puzzles. When my students have struggled and persevered 3 or 4 times to solve a tough puzzle, the timing is now perfect for us to step in and help them develop that skill of solving equations.

]]>http://mrorr-isageek.com/promote-struggle-a-heros-journey-in-math-class/feed/114450How We Can Avoid a Major Lesson Planning Misconception.
https://mrorr-isageek.com/how-we-can-avoid-a-major-lesson-planning-misconception/
https://mrorr-isageek.com/how-we-can-avoid-a-major-lesson-planning-misconception/#commentsWed, 24 Oct 2018 09:38:20 +0000http://mrorr-isageek.com/?p=6247One common misconception around how we should plan our lessons is that planning and creating lessons, course outlines, and assessments is all done in isolation.

There’s an iconic image of famous Fiction authors shutting themselves up in a cabin in the woods for months at a time and then emerge with this great manuscript.

This is actually a false image.

Most authors go through intense iterations of their books with many editors and audiences that provide feedback.

You many have this image that math lesson creators also lock themselves up in the teacher prep room to think up great lesson ideas only to miraculously emerge with perfect lessons. Or maybe you believe that we have magically created spiralled course outlines all by ourselves with little input from anyone else.

These things can’t be further from the truth. Every one of the lessons shared on this site and also any unit or course plans were all created in consultation with other teachers.

In fact, when Kyle Pearce and I first decided to change our course plans from the traditional textbook order to mixing up topics so we can maximize student retention through spiralling, we created a joint outline with Google Sheets that we could each have input to. Planning lessons and courses should be collaborative effort.

In January 2018 I asked the twitter community “Your colleague is thinking of trying to teach through spiralling the curriculum. What are some SMALL changes they can make NOW so that’s it’s not overwhelming?”

Many teachers gave their suggestions but one comment really stuck with me, It was from Mary Bourassa,

She said,

“Lots of great replies but I would argue that most are not small changes. Switching to spiralling is a big change! My best advice is to plan a meeting with someone who has spiralled so that you can talk through your plan together. And make sure you know the curriculum really well.”

We need other people on our same teaching journey as we learn to create new lessons that meet our students need.

The main idea of this book is, and quoting from the publisher,

“We have been spoon-fed the notion that creativity is the province of genius — of those favoured, brilliant few whose moments of insight arrive in unpredictable flashes of divine inspiration. And if we are not a genius, we might as well pack it in and give up. Either we have that gift, or we don’t. But Allen shows that simply isn’t true. Recent research has shown that there is a predictable science behind achieving commercial success in any creative endeavour, from writing a popular novel to starting up a successful company to creating an effective marketing campaign.”

One of Gannett’s Laws of creativity is the law of creative communities. He argues that creatives leaders like Paul McCartney, Steve Jobs, and J.K. Rowling, didn’t create their great works in isolation, but were surrounded by a community of people. Gannett’s also argues that if you don’t have a community of supporting people around you then your chances for creating something is drastically reduced.

So, if you want to make math moments that matter for your students on a regular basis then you will need a community of supportive people!

Alex Overwijk is a high school math teacher in Ottawa Ontario Canada. What I admire so much about Al, is that after teaching math the “traditional way” for over 25 years he realized that he had been robbing his students of great thinking and made significant changes in his classroom routines with an emphasis on “Uncovering curriculum instead of covering curriculum”.

Al has written on his blog slamdunkmath.blogspot.com about Lesson study — a collaborative lesson design structure — that has led him to create many active great thinking lessons for his students.

Basically, lesson study in a nutshell is a group of educators, teachers, and administrators who will together plan a lesson for a teacher to deliver. They will all observe to witness how the students respond to the questioning and tasks included in the lesson, then they debrief to make changes. Then this process repeats. The group will plan, observe, and debrief for another teacher, and so on.

The group is planning lessons collaboratively, not in solitary isolation. The success/ or failure of the lesson is felt by the whole group and not just from the teacher delivery it.

When responding to teachers who say “I can’t afford to be out of my classroom that many times”…. Al says, “How can you not afford it? Your classroom will become a different place-a place you’re not familiar with. Your instructional practices will be challenged and will probably change as a result. Your belief in what students can do will change. You need to try this!”

Al and so many other teachers know that the success of great lessons and course plans can hinge on your access to a community.

What can you do? —- Find one or two teachers who also want to plan, talk ideas through, and collaborate on lessons or course designs. Please. Don’t do this alone. We need to avoid isolation. Sharing ideas, strategies and resources is how plans not only get created but how we stick to them.

Your next step to avoid Teacher Isolation → Join our closed Facebook group: Math Teaching & Learning K-12. It’s closed so that you can feel comfortable asking math lesson related questions on Facebook without bothering your Aunt or your college friends with math related stuff. It’s a place just for us! It’s a place where if you’re feeling teacher isolation in your school come here and share your question or even just to vent.

For example, a group member asked the following question….and other group members jumped in to help out.

Or here’s another example of a team effort

So, I’m hoping to see you in group! Remember, don’t do this alone! We can create better things together.

]]>https://mrorr-isageek.com/how-we-can-avoid-a-major-lesson-planning-misconception/feed/16247Pumpkin Time-Bomb Activity
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http://mrorr-isageek.com/pumpkin-time-bomb-activity/#commentsMon, 15 Oct 2018 10:30:04 +0000http://mrorr-isageek.com/?p=4376For the last few years I’ve shared out a Google Form for classes to record measurements around their pumpkins and make them explode! I shared that form on Twitter so that we could crowd source as many pumpkins as we could to make the sample size large enough. I was pretty shocked at how many schools from North America took on Pumpkin Time-bomb. By the time Halloween was over the spreadsheet had over 90 entries. That’s over 90 pumpkins exploded in the name of math and data collection.

[Update] – October 2018 – The form now has over 500 entries!!

This coming week let’s add to the data and use the it in our classroom to discuss: Scatterplots, Trends, Correlation strong, weak, no-correlation, lines of best fit, correlation coefficient, etc.

Here’s a sample lesson you could use on the day you make your pumpkin explode.

SPARK Curiosity

Play this video which shows Jimmy placing rubber bands around a pumpkin.

NOTICE & WONDER

Using a notice & wonder strategy, have your students record anything they notice and anything they wonder from the video.

ESTIMATION:

Steer you class’ wonders toward the questions: How many rubber bands will make the pumpkin explode?
Have students write down a guess that is too low. Too high. Then estimate their best guess.

If you’re looking for your lesson goal to be around estimation then show the act 3 video next, but if you’re looking to go further and tackle a learning goal around Using scatterplots, lines of best fit, or linear regression jump down the post.

Show the Act 3 Video

Using Scatterplots & Trends to Improve Your Prediction.

Use the PAUSE tool on the activity to lock their screens while you show your students the video on your main screen. Encourage your kids to discuss what they notice and wonder from the video! In pairs, I have my students TALK first and then TYPE second when collaboratively working on a Desmos activity.

ESTIMATION:

Consider pausing the screen again while you use the snapshot tool to grab student responses! This will lead into predicting how many bands will make Jimmy’s pumpkin explode. Have your students TALK first and TYPE second on screen 2 to make a prediction. Again, share students predictions using the conversations tools Desmos provides.

FUEL SENSE MAKING – IMPROVE YOUR PREDICTION:

Bring your students down the curiosity path a little more. Ask them about how we can improve our predictions? What other information would you like to know about the pumpkin or the bands?

Have a discussion on variables & relationships. Write all the variables on the board they come up with. Narrow down the list to items that are measurable with the pumpkin we have in the class. What affects the explosion the most? Height, diameter, circumference, thickness of the wall?

Using the PACING tool in Desmos move your students few the next few screens to make a scatterplot prediction of the relationship between the diameter of a pumpkin and how many bands will make it explode.

Screen 5 shows a scatterplot of pumpkins that have already been blown up and the relationship between diameter and bands (or non relationship). Have your students move the orange point to a place that helps them predict the number of bands. What placement would be wrong?

The next few screens ask your students to do that all over again while looking at the relationship between the height of the pumpkin and the number of bands.

Finally, reveal the answer after students have improved upon their predictions.

Now Bring out your pumpkin for the class to see! Have them predict how many rubber bands it will take before it will explode. Repeat the estimation process. Have them save their guess till the end of class. Where will YOUR pumpkin fit on the scatterplots shown in the Desmos activity?

If you are not planning on using the Desmos activity then you can use the original activity post from October 2015.

FUEL SENSE MAKING – Making A Model

Throw out the question: “What about the pumpkin do you think affects how many rubber bands are used to make it explode?” Let your students brainstorm a list of variables. Have a discussion on variables & relationships. Write all the variables on the board they come up with. Narrow down the list to items that are measurable with the pumpkin we have in the class. What affects the explosion the most? Height, diameter, circumference, thickness of the wall?

Have them choose a variable that they feel should have a relationship with the number of rubber bands. Fill out the prediction part of the handout.

Click here to grab a copy of the prediction handout

As a class measure all variables needed. Write them on the board for all to see.

FUEL SENSE MAKING – Analyzing Data

Give students the link to the spreadsheet of all the pumpkins to date (You should copy and paste the data to your own sheet so you can filter/sort the results and share that sheet out to your students.)

Discuss with your students the lack of consistency in the selection of rubber bands from all over the country. How can we minimize this variable skewing our results? Filter the data with your students(or before hand) showing one type of rubber band (Most common is a rubber band of length 8.65 cm). This will only show all the pumpkins that have been destroyed using that type of band.
Get your students to grab the data that relates to their relationship.

For example:
If Kristen chose the relationship Circumference vs. Rubber bands she should copy and paste the circumference column and the rubber bands column into a new sheet side by side. Then copy and paste all that data into the pre-made Desmos File.
She can adjust the scale in Desmos as needed. Have her move the movable point and drop it where she thinks your class’ pumpkin will lie. Or you can have her find the line of best fit to help predict how many rubber bands it will take. Either way we want her to predict with more accuracy.

So Kristen would predict that if her circumference was 90.5 cm then it will take 272 rubber bands to blow up the pumpkin!

Now if Kristen chose a variable that it was clear there is no relationship then you get to have a discussion about correlation vs. no correlation. Have her choose new variables to predict on.

Once everyone in the class has a new prediction start wrapping bands around that pumpkin (You may want to start this as early as possible).

Watch your pumpkin explode and give congratulations to the student who predicted closest to the actual number of rubber bands.

Don’t forget to enter all your data to the sheet by filling out this form (you can also use the form to show the videos to the class).

]]>http://mrorr-isageek.com/pumpkin-time-bomb-activity/feed/14376Eye To Eye – A Similar Triangle Problem
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https://mrorr-isageek.com/eye-to-eye/#respondWed, 10 Oct 2018 10:00:31 +0000http://mrorr-isageek.com/?p=6119

Here’s a common similar triangles application problem that shows up in most middle and high school textbooks. A mirror is placed on the ground between two objects, showing two triangles with a bunch of measurements given and we’re supposed to find the height of one of the objects.

A typical approach to showing how this problem is modelled with similar triangles is to walk students through a full solution.

In lesson 1 of the video series that Kyle Pearce and myself have shared to make math moments that matter in your class we outline how why and how we can reshape our lessons to become more curious. If you haven’t yet watched the video series go ahead and watch video one now!

Let’s take this similar triangle problem and remodel it so it follows a Curiosity Path so we can fuel student sense making with similar triangles.

Recall that the first part of changing a problem to include more curiosity is to determine how you can withhold information to create anticipation.

Here’s my attempt at doing this for our students.

Have your students set up their page or whiteboards to record what they notice and what they wonder after watching this very short video clip.

After discussing what students notice and wonder, bring out the wonder (if your students didn’t already) — Will they see eye to eye through the mirror?

Allow your students to analyze the video again and have them predict if they could see eye to eye. Then hit them with these three images one at a time.

For each image, ask them to predict the answer to: Can Danielle and Dylan see eye to eye? Which image is it easy to see that the two can’t see eye to eye? Which image is harder? Why is it easier in one image over another? Have your students draw a picture to show you why Danielle and Dylan can’t see eye to eye in the second image? To bring students down the curiosity path a little further and deepen their investment into this problem ask them to predict where Dylan SHOULD stand so that they can see eye to eye.

What information is useful to know? Hearing your students insights at this moment is fuel for your formative assessment of their understanding and their problem solving toughness. When a student asks for the Danielle’s distance from the mirror ask “What would you do with that information if I gave it to you?” Listen closely to the answer of that question. You will discover quite quickly who is anticipating possible strategies and the reasonableness of those strategies and who’s strategies will need some assistance. Consider giving Danielle’s distance from the mirror to help update their prediction.

You can reveal the information as students request it.

Now that we’ve build up student curiosity by bringing them down the curiosity path we reach the fork in the road we outlined in Video 2 and 3 of our series. We can either rush to an algorithm or we can keep following the path towards making a math moment that matters.

In this activity we can fuel student sense making by having students experience what it’s like to see eye to eye. Students can mimic what they saw in the video to see how far a partner should stand away a mirror so the two partners will see eye to eye.

Students will arrange themselves as shown in the activity handout, determine how far one partner must stand to see each other in the mirror, then they test that distance to see if they actually see each other! Students will collaborate, peer and self assess, be active, and engage in purposeful practice.

Finally, students re visit the three scenarios presented at the top of the lesson to determine if Danielle and Dylan will see eye to eye. They essentially will prove if the triangles are similar or not.

An alternate or extension problem students can work on is “Where should we place the mirror so that they do see each other eye to eye?

Download ALL LESSON FILES

Grab the handout, images, and video files for your classroom!

]]>https://mrorr-isageek.com/eye-to-eye/feed/06119A Squiggle-Line Dilemma: How Creating Bends Gives us Freedom in Planning
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https://mrorr-isageek.com/a-squiggle-line-dilemma-how-creating-bends-gives-us-freedom-in-planning/#respondTue, 02 Oct 2018 10:06:05 +0000http://mrorr-isageek.com/?p=6085

Have you read one of my all-time favourite books The Dot and the Line: A Romance in Lower Mathematics by Norton Juster? It’s not a new book it was originally written in 1963. I not only read it to my classes on Saint Valentine’s Day but I gave it to my wife as a present way back on our first valentine’s day together.

I love that every time I read it it makes me reflect on who I want to be as a human and also as a math teacher!

If you haven’t read it you can watch the Academy Award winning Short Animation by Chuck Jones right here, now! Watch it before reading the rest.

Lately I’ve been thinking about this story as it relates to how we math teachers feel the need pursue the “perfect” math lesson or that shiny new tool/technique we hear we should try.

We seem to be after the perfectly engaged class (behaviourally and cognitively) learning the chosen standard at just the right pace for all students. And why shouldn’t we? It sounds great. But, what is the likelihood that we’ll ever achieve this “perfectness”. The reality is that teaching is messy; all classrooms are different.

We see so much positivity on the internet and from our peers. Looking at twitter or blog posts suggests that so many teachers are having these perfect classes or that the shiny new tool/technique solves all our problems. And it leaves us sometimes feeling inferior and overwhelmed.

I think some of us feel that we need to be using that iPad, or new tech tool, or shine new learning model everyday to create this perfect happy class.

Let’s relate this situation to The Dot and the Line story.

Imagine for a moment that you are the main character from the book; the line. The dot is ….. well, the dot is that “perfect” class lesson where all students are using that new shiny tool or technique that we’re not quite sure about.

When the line first meets the Dot and sees that “she” only has eyes for the whimsical squiggle, the line feels that “he” needs be more like the squiggle.

Many of us teachers also feel or have felt that we have to become the whimsical squiggle to win the dot to our side. We feel that we have to become not just entertainers, but we have to become someone we are not. Many teachers also feel that we have to give up core beliefs on what creates good a good learning moment so we can have this other, supposedly great learning tool or technique.

But that’s not true. We don’t need to change our core beliefs of what creates great learners. We don’t need to give up on teaching students dedication, determination, and rigour to bring in curiosity, creativity and openness into our lessons.

For example, some math teachers believe that by teaching through problem solving with tasks like Popcorn Pandemonium, or Kyle Pearce’s Candle Burning problem you HAVE to sacrifice procedural fluency. They believe that you can’t have both mathematical rigour and learning through problem solving. You either have to be a squiggle or a straight line. They believe it’s one way or the other.

What I believe is that we may have to BEND, just like our pal the Line to truly create math moments that matter for our students.

Like the line, Bending gives us permission that it’s not an all or nothing transformation. We don’t just have to choose between a squiggle and a perfect line.

Like the line, bending means though that we may have to work harder and smarter.

Like the line, bending means that we can teach through problem solving as well as getting students the practice they need to become fluent without sacrificing time.

Like the line, bending means that we can recreate ourselves — in a stronger way that supports learning.

Bending means that we need to actively think about how we can incorporate our core beliefs of good learning in our lessons while meeting the needs of ALL our students.

To address one common Line vs. Squiggle comparison:

How do we incorporate practice and procedural fluency in lessons while building resiliency in problem solving — without sacrificing time?

I use purposeful practice routines that encourages student discourse, self assessment, peer assessment, movement, and error checking that bring my students closer to procedural fluency after we’ve used productive struggle to learn a topic.

Download and learn more about 5 practice structures I highly recommend you add to your practice routines.

Download Now! 5 Practice Structures in Math Class

Learn about 5 of my go-to practice structures for self assessment, peer assessment, movement, and error checking!

]]>https://mrorr-isageek.com/a-squiggle-line-dilemma-how-creating-bends-gives-us-freedom-in-planning/feed/06085My #1 Go-To Tool In Math Class
https://mrorr-isageek.com/whiteboards/
https://mrorr-isageek.com/whiteboards/#commentsThu, 12 Jul 2018 11:01:36 +0000http://mrorr-isageek.com/?p=5844

Let’s start with this one question:

For me, I use a set of 4 criteria to evaluate all resources, tools, and lesson ideas. It helps me quickly narrow down whether a tool will help me achieve the desired results I look for in my classroom.

Here are the four criteria.

I want ALL my students to show me their thinking and understanding in interesting ways. I want them to show me what they think first instead of just telling them what to think! I want to open up the questioning that goes on in my room. So I look and create lessons that allow for this.

I want my students to discuss, collaborate, argue, defend, and justify with each other. I believe this helps clarify their learning and understanding so I must make sure that discussion and collaboration happen in my best lessons.

I am always assessing! I’m constantly looking to see who gets what we are doing and who needs help. I need to be able to assess quickly the abilities in my room so I can use that on the fly to decide where to go next. Assessing easily must be apart of my lessons.

Every lesson or activity must have a ratio between the cost of set up and the payoff where the payoff heavily out weighs the set up. Nothing is worse than spending a huge chunk of time, making, cutting, designing and then when you run it the learning outcome wasn’t worth it. The payoff must out weigh the set up.

My #1 Go-To tool/technique is WHITEBOARDS!! Having my students work in random pairs daily at vertical whiteboards is the tool that easily allows my students to get to work faster and hit all four of my criteria.

On a whiteboard students can easily show off their learning. They are quicker to get to writing on a whiteboard than on paper. Especially when the boards on the wall. Students get to defend, argue, justify their thinking with each other. I can easily see if students are understanding and the set up ratio is a no brainer. Here’s a whiteboard, marker….Go!

I’ve had students use small personal whiteboards at their desks before, but I couldn’t believe the change in active engagement and cooperation once they were standing. The discussions they were having about the math was much more insightful and meaningful.

Our whiteboard work usually starts as soon as the bell rings. In random pairs students would put up a few homework questions from the previous day. I could see students looking around verifying their work with their peers. They were self assessing.

We continue to make use of the boards while we work through our new challenges. Students have no problem leaving their space to go and talk to another group to gain some insight on new strategies….This is how we create great classroom culture. I can easily circulate the room to engage students in conversations and challenge their reasoning.

WHITEBOARDS IN YOUR CLASSROOM

Recently, Kyle Pearce and I took Wipebook Chart Packs on the road with us to some conferences and district presentations for our Making Math Moments That Matter workshop series and they worked great! In a breakout session we held at The OAME Leadership Conference in 2017, we had a room of over 100 teachers, consultants, and coaches up at the walls doing a math problem with us. It was fantastic!

We had so many participants asking for more details on how to get their own Wipebook Chart Packs that they are now offering an exclusive Educator Starter Pack you can only get through us!!!

EDUCATOR STARTER PACK

The education starter pack includes:

A Wipebook Flipchart (pack of 10);

A Wipebook Notebook Plain;

A Wipebook Workbook Graph;

A single correctable marker; and

A single tri-plus marker.

Your exclusive Making Math Moments That Matter offer is 25% off the list price value!!!

Full disclosure: Kyle and I love this product so much that we became affiliates for Wipebook. Which means if you purchase through our link here YOU get a discount and WE get a small percentage with no extra cost to you! Win/Win!

]]>https://mrorr-isageek.com/whiteboards/feed/25844Hurry Up/Kill Time Math Classes – How Desmos Can Help
https://mrorr-isageek.com/hurry/
https://mrorr-isageek.com/hurry/#respondThu, 28 Jun 2018 11:42:00 +0000http://mrorr-isageek.com/?p=5834Seth Godin brought up an interesting idea: If you think about it, everyone at the airport is in one of two modes. In a hurry, or killing time. You can imagine it right now! That impatient person in the TSA line just waiting to speed walk to the gate, or the group of people jockeying for position to board the plane first. On the other hand the only other people are just waiting around to speed up!

This is also happening in math classrooms. Both teachers and students.
Students want to hurray through lessons, get the homework done, move onto the next thing. Or they are just killing time. Teachers are hurrying up to start lessons, give examples, get the ideas out, give the homework. Some teachers are just waiting around until the day ends.

But this is not all students. Some are focused on learning to learn. And this is not all teachers. Many like you and me are actively making moments that matter in our students lives. Let’s help others slow down the “Hurry up to wait” classrooms.

One way I do this is to create and share those moments that matter through enhancing classroom discussions through a tech tool that creates discussions, not limits them like so many others do.

Hey, I’m Jon Orr, a math teacher from Chatham Ontario, Canada.

I’ve been on a mission lately to make moments in my math class memorable. Like you remember specific moments in your life because they were meaningful. Something that sticks with you. When I think back to my experiences as a math student I remember grade 4. I thought I was a master multiplier. My teacher even gave me stickers for doing extra work….and these stickers weren’t just normal stickers they were the ones that stand off the page like puffy stickers. You know, the ones that make the book not close all the way.

That sticks with me because of the feelings that go with the moments. I want to create those for my students; not with stickers, but memorable math moments. Like moments that students will remember years later. Like I have students years after my course still remember the toy car lesson we did or the pentomino puzzle solving lesson! I want this for every student in my class.

One tool that I think does this amazingly well is Desmos. And I’m not talking about just the online calculator. I’m talking about the earth shattering online activities that they create for us to teach with for free!

What I love is that each activity they build helps me make those moments. And they do that by allowing my students to show their thinking in interesting ways, they allow me quickly assess on the fly the abilities in my room…and they allow my students to have discussions! The tech creates discussions!

The activity is super easy to get into, just move this tile around until you cover a sum of 65. You can see students can easily share their thinking and strategies. I have kids use 1 device for 2 people so they can talk about their strategies. It keeps that collaboration I’m looking for. But then each new task builds towards solving the problems using an algebraic approach! I get kids to learn how to solve equations through this puzzling type of game!

As a teacher I get to see what student is on what screen, allowing me to help kids that need help and allow kids to move forward that are ready for it.

I can pause the screen on everyone’s devices so we can discuss strategies. The software is built to enhance classroom culture and discussions, not limit them like other tech does.

So one recommendation for you to try to make math moments matter for all your students is to explore the activities on teacher.desmos.com.

Thanks,

Find out more on desmos over on my website mrorr-isageek.com where I share all my custom made desmos activities and many other resources and ideas for your math classroom.

Take care.

]]>https://mrorr-isageek.com/hurry/feed/05834Making Math Moments That Matter – Live
https://mrorr-isageek.com/making-math-moments-that-matter-live/
https://mrorr-isageek.com/making-math-moments-that-matter-live/#respondSun, 06 May 2018 14:47:20 +0000http://mrorr-isageek.com/?p=5783What 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.

[UPDATE] – Facebook has removed our video — maybe we were too awesome?? So I’ve included three short snippets from other live workshops here:

and another,

and another,

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!

]]>https://mrorr-isageek.com/making-math-moments-that-matter-live/feed/05783How Can We Anticipate to Fuel Sense Making? Stretching Trees
https://mrorr-isageek.com/how-we-can-anticipate-to-fuel-sense-making-stretching-trees/
https://mrorr-isageek.com/how-we-can-anticipate-to-fuel-sense-making-stretching-trees/#commentsSun, 29 Apr 2018 11:33:00 +0000http://mrorr-isageek.com/?p=5731Are 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.

]]>https://mrorr-isageek.com/how-we-can-anticipate-to-fuel-sense-making-stretching-trees/feed/25731What Math Lessons Can We Learn from the Game of Nim?
http://mrorr-isageek.com/what-math-lessons-can-we-learn-from-the-game-of-nim/
http://mrorr-isageek.com/what-math-lessons-can-we-learn-from-the-game-of-nim/#respondSun, 22 Apr 2018 17:33:52 +0000http://mrorr-isageek.com/?p=5720Have 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 mathematicalgame 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!

]]>http://mrorr-isageek.com/what-math-lessons-can-we-learn-from-the-game-of-nim/feed/05720Why Consistency Is More Important Than Intensity: Culture in the Math Classroom
https://mrorr-isageek.com/why-consistency-is-more-important-than-intensity-culture-in-the-math-classroom/
https://mrorr-isageek.com/why-consistency-is-more-important-than-intensity-culture-in-the-math-classroom/#commentsSun, 15 Apr 2018 12:01:42 +0000http://mrorr-isageek.com/?p=5709Ok 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.

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

]]>https://mrorr-isageek.com/why-consistency-is-more-important-than-intensity-culture-in-the-math-classroom/feed/15709How To Get The Most Out of the Conferences You Attend
https://mrorr-isageek.com/how-to-get-the-most-out-of-the-conferences-you-attend/
https://mrorr-isageek.com/how-to-get-the-most-out-of-the-conferences-you-attend/#commentsTue, 10 Apr 2018 16:37:06 +0000http://mrorr-isageek.com/?p=5695Okay wow! You did it. You ponied up for that conference entrance fee, you reserved the hotel, made arrangements for travel! Substitute? Booked! You took a risk! You told yourself I’m a going to that conference! Good for you. Now, you wonder

Is it going to be worth it?

That’s a question I ask all of the time. And my answer now is always yes. And it’s yes as long as I, myself, MAKE it worth it! Great experiences at conferences aren’t just great because we go….they’re great because we made the most out of the experience. My answer to the “worth it question” used to be “I’m not sure it’ll depend on what resources I can get”That’s because my thinking years ago was that the conference and sessions were there to give me that next great activity or project, or worksheet to fill a gap in my unit. And don’t get me wrong conferences are good for that…..but there is so much more to get out of the conferences you attend.

Here are 4 ways to make the most out of the conferences you attend. So that you can always answer yes to the worth it question!

1. Build Your Community.

If you’re like me you’re an introvert. Yes, I shy away from social interaction. I’m that guy at a party standing off to the side with his one or two good friends and avoiding more social interaction. And let’s face it so many of us math teachers are introverts. It’s hard to be social. Going to a conference means we can gather new activities and lesson ideas for our classroom but another huge benefit is Networking. Imagine a group of math educators you could rely on. Imagine you could share your lesson ideas with this group;get feedback from this group; they even teach like you! Maybe that’s your math department already? Maybe not. A conference is meant and partially designed for you to help create this group. It’s structured for you to easily meet new people who share similar interests. Here are a few tips to help create that group of teachers you need.

Bring a co-worker with you. You’re more likely to meet more people if you are not alone. You’ll have confidence to talk to other small groups. Grab those emails. Learn their twitter handles. You don’t need to do it alone.

My #OAME2018 is going to be great! I brought a friend-colleague to be able to discuss over wine after our sessions!

Go to at least some with a partner. It seems like going to diff ones will get more info, but they’ll be things you hear that s/he doesn’t and vice versa. Deeper learning to me. And everything else everyone said

Talk at your tables. I know you want to find a table where no one is sitting when you’re at a session but DON’T DO IT. Sit at one with other people. Interact with them. Sitting at the same table already puts you on their team. Now just get to know them. Work together while in that session and get their contact info before they leave if you feel they would make a great team member going further.

Hit a Social event either before or during the conference. Many conferences will have a games night, trivia night, wine and cheese, or a dinner. Don’t skip on these. This is where so many great connections and friendships can be made. When I attended the annual NCTM conference in San Francisco in 2016 hanging out at Desmos’ games night and the Trivia night were huge aspects of making that conference great. I met so many great teachers that I feel are now apart of my Team!

2. Be Picky

Choose sessions where you recognize the presenter(s). If you recognize a presenters name its likely that you’ve used their activities or ideas from them in the past. By picking those presenters this time it’s highly likely that they will give you more good ideas to go with. When I started choosing sessions based on presenters my whole conference experience changed. It went from “maybe ill get one good idea to try in my classes” to getting a ton of new ideas and left me feeling refreshed and resilient! Even though I had maybe heard them speak before, by choosing them again I always felt rewarded. The conference was definitely “worth it”

I also highly recommend that if you find yourself in a session that you feel is clearly not right for you then leave. Sometimes we feel like it’ll hurt the presenters feelings or you feel that it’s our fault for choosing this session and we have to “stick it out” Don’t! Just get up and leave. And now….sneak into a different session!

3. Check Out The Goods

You probably have filled your schedule up with sessions but don’t forget to budget time to hit the publishers display area. Some conferences have huge value in this area. So many companies get booths just to show off their products to you. You never know what you’ll discover there. While I was at NCTM 2012 in Philly I stumbled across this small booth with this young guy named Eli. He showed me all about this new graphing software I could do on my new iPad or online for Free!! I was in love. Ever since that meeting I’ve been using Desmos in all my math classes. I’ve since gone on and joined a select few to become a Desmos Fellow. So definitely schedule time to check out the publishers area at your conference! It’s worth it.

4. One New Thing

Vow to implement 1 new thing you learn while at the conference. You may get lots of ideas and resources but how many will you actually implement? Thinking about all of those ideas at once can be overwhelming and may result in you not doing any of them. Choose one idea, one resource, one activity, or one routine to try out in your classes when you return. Let’s make it so that you WILL do it. Write down the “one thing” on paper or in your planner. But write it as if it’s past tense, like you’ve already done it. That way it’ll look like you are doing it. For example, if your “one thing” is to try random groupings as a routine then write “I randomize kids everyday when they come into the classroom” By writing it the past tense will help make you do it. Then plan to implement that change routinely. Make a schedule and stick to it. Don’t break the chain. For example, Jerry Seinfeld said that he writes everyday. Not just when he feels inspired or ready to write. He writes everyday. And he focuses on marking each day off on the calendar. A big X right through the day.As he built up X’s he didn’t think of his goal of writing every day anymore, he just thought, “I can’t break the chain” Breaking the chain meant that he would have to start all over again. Breaking the streak is a more powerful motivator than just “I have to write”.So set up your goal and then “Don’t Break The Chain”.

Whew! Once I started doing these tips and strategies my conference experience changed. They changed from “I hope it’s worth it” to “This experience is priceless”

Now, there’s a ton of tips listed for you to make your conference worth it above so I created a downloadable PDF for you.It’s a Conference Companion.

You can either print it out or use it digitally on your device. It has places for you to keep important information, like contacts you meet, new ideas, and hashtags. It even has a small scavenger hunt style reminder list along the edges.

Go ahead and start making all the conferences you attend worth it!

Do you have tips we can add to this list? Please add a comment below.

]]>https://mrorr-isageek.com/how-to-get-the-most-out-of-the-conferences-you-attend/feed/25695How Small Nudges Could Have A Big Impact On Math Education
https://mrorr-isageek.com/how-small-nudges-could-have-a-big-impact-on-math-education/
https://mrorr-isageek.com/how-small-nudges-could-have-a-big-impact-on-math-education/#respondWed, 04 Apr 2018 11:06:11 +0000http://mrorr-isageek.com/?p=5682Do you ever notice that many decisions are secretly being made for us? You probably missed them like I did.

Consider this: Last Friday, and much like every Friday our math department headed out for a quick snack and recap of the week at one of our favourite restaurants. We enjoyed stories from a week’s worth of lessons and working with students while looking forward to new stories for the upcoming weekend. Like every Friday when it’s time to leave I get the bill. What do you notice?

The tip was suggested for me!

I didn’t have to think too hard about what to leave. The restaurant has made it real easy for me to include that good tip. How many more tips do you think this restaurant earns compared to other restaurants that don’t have this feature? A bunch more is the answer.

Here’s another example of a subtle suggestion that has a big influence on our decisions. Have a look at this image taken at the University of Pennsylvania.

We have to do a double take and think about what side to place our trash in. We are pushed to consider our trash placement instead of just tossing it in a bin. A subtle suggestion that influences our decision. Recycle or Landfill?

Both of these scenarios didn’t just happen by accident or without careful thought, both are using a branch of behavioural economics to influence decision making called Nudge Theory.

From wikipedia: “A Nudge is a concept in behavioural science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals.”

If we go back to the tipping example: the suggested tip amount on the bill is a small indirect suggestion for me to give a good tip. The restaurant has made it real easy to leave that tip (they did the math for me). Also notice that they didn’t provide tip amounts less than 15%. They nudged me to make a tip of 15% or greater! They nudged me to choose the behaviour that was favourable to them.

In the garbage bin example the creators drew your attention to the negative impacts of putting items in the garbage side. If you toss on the garbage side that trash goes directly to the landfill. They nudged you, very subtly, to think before you toss trash.

The basic idea behind a successful nudge is to make it very easy to do the favourable behaviour and hard to do the unfavourable one. It was easy for me to make a tip of 20% and harder if I wanted to tip less. It was easy for us to make a decision to recycle because choosing the alternative was something we generally want to avoid: filling landfills.

In Austria, more than 90% of their citizens are organ donors. In the neighbouring country Germany? Less than 15%. Are Austrians that much more conscience about organ donation? Nope. In Austria citizens are auto-enrolled in the program and have to opt-out if they would rather not be a donor. In Germany you are not auto-enrolled and have to opt-in to be a donor. That’s a nudge! A small subtle change can have big outcomes in decisions. Auto-enrolling capitalizes on our laziness factor. It’s easier if we do nothing compared to doing something.

“It’s a question of putting the best outcome along the path of least resistance and letting your automatic system do its thing.” Mark W Riepe writes regarding nudges.

What implications does Nudge Theory have in the math classroom?

Nudging in Math Education

In my opinion one of the most poorly designed calculator features on my smartphone is the percent button.

Students often misuse the % button the calculator and are not sure what is going one behind that it. It’s like a black box of percent calculation. Many misconceptions arise in my grade 9 applied class when students use this button without knowing the math behind it.

Desmos has auto-added the word “of” after the percent symbol. There is no way for a student to delete the word of. It’s stuck there. It forces us to think about how we use that button. Both teachers and students are now auto-enrolled in finding the percent of a number before doing anything else. It’s an amazingly small change that has a huge impact on learning. They have made it easy to do the right thing. And impossible to do the wrong thing. That is a nudge!

Have you seen these charging stations for phones in classrooms?

Teachers are making it super easy for students to choose to put their phone away if it’s a distraction to their learning. A student will gladly get the juice and put that phone away for an hour. Nudge!

I want students to regularly self assess their learning in my classroom. I want them to be more accountable to get what they need. I make it very easy for them to see their own progress on the learning goals in our course. By auto-enrolling them in their Freshgrade portfolios student can access all the learning goals anytime and work towards showing improvement on them! It’s my way of giving them a nudge to make good decisions regarding their assessment.

What kind of nudges are you trying?

What are you doing to make the right behaviours easy and the wrong ones hard? What are you doing to affect choices your students make in your classroom?

]]>https://mrorr-isageek.com/how-small-nudges-could-have-a-big-impact-on-math-education/feed/05682What Mr. Rogers and Breakdancing Can Teach Us About Risk-Taking Teachers
http://mrorr-isageek.com/what-mr-rogers-and-breakdancing-can-teach-us-about-risk-taking-teachers/
http://mrorr-isageek.com/what-mr-rogers-and-breakdancing-can-teach-us-about-risk-taking-teachers/#respondTue, 06 Mar 2018 11:28:48 +0000http://mrorr-isageek.com/?p=5677You remember Mr. Rogers right? Watch him here trying breakdancing with Jermaine.

Mr. Rogers gets it. Look how he ‘s willing to look potentially silly to show his audience something new. Something different. A different experience and to share a story. He knew the value of not worrying about what others might think of him while being curious and exploring amazing experiences. He definitely stepped out of his comfort zone!!— “Like there’s a wave going the whole way through your body” — That’s gold!

As math teachers we get comfortable and complacent with our audience and that sometimes makes us reluctant to try something new. Maybe we’re afraid that the class will be unruly, the day would be wasted, not as much learning will happen, We’ll lose our authority?

But like Mr. Rogers, we too should try something new if it means that our audience may experience something amazing or a different way of seeing the same old thing or getting another “a-ha” moment. We want to inspire learning so students can continue to inspire themselves into the future. That may take us to step out of our comfort zone and we will need to try a little break dancing.