# Polygon Pile Up

When it comes to angles involving parallel lines, triangles, and other polygons I’ve always assumed my grade 9 applied students “get this”. I’ve felt that angles were an easy topic. I guess I thought this because most students seem pretty happy when solving angle problems and for the most part being doing pretty well on assessments. However, this year I noticed two inadequacies that I am trying to address.

1. Most of my students didn’t actually know what an angle measurement of 65 degrees really means.
2. They have a hard time determining what information is needed when solving multi-step angle problems. Lack of a good strategy.

When having students determine angles in triangles almost all of them knew that all three angles should add to 180 degrees. The trouble came when I saw some answers like this (from more than one student).

What bothered me was the location of the 40. I wondered why outside the triangle? I pressed this student for more info. I asked him to draw me any right triangle and label the three angles.

Hmmm…I asked him to point to one of the angles. He pointed to where he labeled the 85. What I found is that this student was mixing up length measurements with rotational measurements and he was not alone.

I found a great activity to hit this head on. Laser Challenge from Desmos worked wonders to get my students to understand and experience rotational measurements. Students have to enter values to rotate the laser and mirror to hit targets.

My students “felt” what 60 degrees is. Experiencing that rotation made all the difference to clear up what we were actually measuring. When second semester rolled around and my new crop of kids came in we started with this activity right away.

Most of our students struggle with solving complex problems where they have to think of a strategy. Before I gave them something like this,

I wanted to them to experience what information would be useful to know first. I decided to turn the problem around and inside out.

I gave them this.

I wanted them to think backwards….just like we need to do sometimes when solving longer problems. On the “easy” side most filled in 3 angles in the quadrilateral. What was great was that prepared them to think what we could leave out for the harder one. This simpler diagram challenged my class to think, plan, and strategize!

It was great to do this before we introduced this puzzle Jim Roesch, Kristyn Wilson, and myself created:

[There is a video embedded here — Can’t see it? Click through to the post page]

Here is the puzzle

And to really challenge yourself or your students here is a blank one. Can you fill it in so it’s “hard” to determine that indicated angle? What is the least amount of info you can give to bring out the most amount of thinking? Share them out!

# Being Picky – Ignite Session OAME 2017

Giving an Ignite talk can be a rewarding but also super terrifying experience. For me it was both. Session participants create exactly 20 slides which will auto-advance every 15 seconds giving a total time of 5 minutes. This year, for the second time OAME invited me to participate in their Ignite session at the 2017 conference in Kingston, ON (my home town).

I wanted to share with you my talk:  Being Picky: How we choose lessons and tools for our classroom.

You can read the transcript with slides below.

I was inspired for this talk by fellow teacher Andrew Stadel and it begins with coffee makers. Here is the super deluxe coffee maker that I was looking to buy for a long while! It has all the bells and whistles, timer, auto shut off, and even a grinder.
and then this baby slides in which is arguably the easiest coffee maker to use in the world, it has only three buttons. I had to make a decision. I wonder? Which would you choose? Why? The why is most important part of the conversation it’s what dictates your choice. That’s because we humans are picky. We’ve got lots of reasons to like what we like. We create a set of criteria based on our wants, needs, beliefs, values. I could swap out coffee makers here for
tv shows or computer choices or hair styles and you’d have lots of opinions, conversations, disagreements, maybe even regrets. How many of you had those haircuts……come on….don’t be shy! I knew you did!

We could also swap those out for our lessons and activities. It’s important that we think about what we want in our lessons to create good student learning opportunities. We need to think critically how lessons we get from others fit into our core beliefs of good learning. For me, I have four criteria I use to evaluate all of my lessons
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.
These are things I value in my lessons so naturally I must select lessons and tools that allow me to meet this criteria! One tool that I use regularly and meets all of these criteria is

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!
As technology advances it becomes a bit more difficult to choose what we want to use. There are literally thousands of apps, websites programs that are in ED tech and globally it’s an \$150 billion dollar industry!! And I know that all of those companies out there didn’t create their software with my criteria in mind. I only want tools that fit my criteria!! So I throw away programs/apps/websites/tools that don’t meet it and keep the ones that do meet it. I want to share two tech tools that meet my criteria and one that doesn’t. First up…

The activities on teacher.desmos.com are amazing and meet my first two check points. Through carefully set up prompts my students can easily show me their thinking in a variety of ways. Their new conversation tools make it easier for us to consolidate and class discussions have never been more interesting.

It also meets my second two criteria. I can see in live time what the students are working on. It gives me the feedback I need to decide to go further. The set up can’t be easier. There are hundreds of pre-made activities ready to just click and run. Just grab a device.

Freshgrade is online portfolio tool that meets my criteria. Showing thinking through pictures is the beauty! Discussions can occur easily and assessment is a snap…which drives where we go next.

Kahoot has been pretty popular lately. Students answer multiple choice questions in a game like format competing against the rest of the class. However, It doesn’t allow my students to show their learning in interesting ways…..just a right/wrong selection. We can have discussion about the ideas but the questions are timed putting a rush on my students thinking and I don’t think that helps good learning.

Assessment is tied in but I see class scores not individual achievement. But hey, its super easy to set up!!! Since it doesn’t meet most of my criteria I decide not to spend time creating on it.

These are my four criteria for lessons and tool selection. If a tool doesn’t meet the criteria then I don’t use it. Our time is valuable. I don’t want to spend time on learning something if it doesn’t fit into they way I think good learning happens.

Going forward you have homework. You need to decide: What kind of lessons do you want in your room? And then create the criteria that will help you evaluate the lessons, activities, tools you get from co-workers, friends, online, or at conferences like this. Be picky! We trust you!

End of transcript

I’d like to thank Andrew Stadel for this post on his Tech Tool Criteria and also Kyle Pearce for feedback and  suggestions and listening to me rehearse!

What are your criteria for activities and tools? Feel free to share them with me through email, twitter, or here in the comments.

# Turbo Texting

The original idea for this lesson came from Al Overwijk. Thanks again Al!
The possible Ontario overall curriculum expectations covered in the activity:
• graph a line and write the equation of a line from given information
• solve problems involving proportional reasoning;
• apply data-management techniques to investigate relationships between two variables;
• demonstrate an understanding of constant rate of change and its connection to linear relation
• solve problems by using proportional reasoning in a variety of meaningful contexts.
• demonstrate an understanding of proportional relationships using percent, ratio, and rate.
• demonstrate an understanding of relationships involving percent, ratio, and unit rate.

### Act 1: Turbo Texting:

I started with “I was with my brother one afternoon and I needed to text my wife. After texting her, my brother informed me that I was a ‘terrible texter’. He said I was soooooo slow. I on the other hand disagreed. Then we decided to settle this once and for all—- race!!!”
What do you notice? What do you wonder? Allow students a few minutes on their own to jot down their ideas. Then share with partners, then the class.
Here are a few questions/tasks I asked them next. I wanted to slowly build into deciding if this relationship was proportional.
• What relationships can you see? — Number of characters in a text vs. the time to text it.
• Create a scatter plot sketch of how the number of characters in a text affects the time to text that message.
• How does this graph look with both texters on the same grid?
• Who is the faster texter? Predict. How does your sketch show who is faster?
• Kevin finishes first does that mean he is the faster texter?
• How will we determine who is the faster texter? What will we need to see?
We took our time with these questions so we could develop and understand the relationship between characters in a text and the time to text it.

### Act 2

If you’re viewing this through email you may have to click through to see the video

ME: “Use any method you choose to determine: Who is the faster texter?” I allowed them time here to work on a strategy. I watched carefully what strategies they used or didn’t use.

Seeing the different strategies gave us a nice discussion the importance understanding what rate we are determining and how to interpret it to answer the problem.

I showed this picture next:

and this piece of info…

Students completed this problem and we discussed the assumptions we needed to make.

### Texting Time

How do your students compare to Jon and Kevin? Have them time each other while texting the 165 character message. Have them determine their texting speed to see who the fastest texter is in the class.

### Linear Modelling

ME: “Now you may have texted that message in 18 seconds, but would you do this all of the time? Would you keep that same rate for a shorter message? Longer message? We better keep this experiment going.
I set them off to text various messages of different lengths using this handout (I modelled the handout format after Mary Bourassa’s Spegettini and Pennies handout – thanks Mary).