Author: Jon Orr

Animated Patterns Gallery Walk

by Jon Orr

A major expectation for our grade 9 applied class is to “connect various representations of a linear relation, and solve problems using the representations.” Early in the spiralled grade 9 course I bring in Fawn’s Visual Patterns website as warm ups. We routinely continue the patterns, create tables, equations, and graphs to show the representations. Students also create their own patterns.

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More and more I notice that grade 9 applied students don’t see what I see when looking at patterns (which is definitely not a bad thing). I love hearing all about how students see the patterns. However, I always see the patterns as growing/shrinking…..what I mean is that I see that one shape morphing into a bigger/smaller version. What I’ve heard from some students though is that they see each figure as a separate object, separate things that looks slightly different. I wanted to explore if students seeing the patterns morph instead of seeing them as separate objects could help them with seeing connections among the different forms of the relation.

To start the class I showed this video:


I asked: What do you notice?
Students described the pattern to each other while sitting in pairs. We decided that if the first set of shapes represented figure 1….then every figure after that showed two more shapes being added in. I asked them to go ahead and find out how many shapes were in figure 108.

I gave out the following set of instructions:

  • Create your own animated pattern video
  • Create a tough pattern for your classmates to discover. Ex: Show how the pattern changes in other ways than figure 1 then figure 2 then figure 3. Maybe show how your pattern changes from figure 1 to figure 3 then figure 5.
  • Create a question for your fellow classmates to solve about your pattern.
  • Display your video around the room for a gallery walk. In your display hide the table and equation and answer to your question.

They went to work on building & shooting their patterns. Having them skip figure numbers made them really think about how to create their patterns and how the equations related. Since they were invested in their own patterns they worked hard at creating the tables and equations.

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After they created their video they were to create a display for a gallery walk. The gallery walk gave us a purpose to practice finding rates of change, determining equations, generating equations and solving problems. We wanted to see the creative patterns from our classmates and see if we could solve each others problems. Like a challenge! Each display showed the video and then under flap of paper was an answer to a problem with a table and equation. Students left their display and visited each others displays with a recording sheet.

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We spent two class days working on building the videos/patterns and the gallery walk. There are a variety of stop animation apps on the app store. My students used various different ones. Some students used iMovie.

I felt students were stronger on knowing why we need to find the rate of change for our equations and not just take the first difference value. The one-two combo of actually building the patterns and then making them move through animation built a deeper understanding of the representations than just completing a worksheet!!

 

 

 

 

Favourite & Fix: Nov. 11

by Jon Orr

For the Favourite & Fix series each week I’m posting one idea from my lessons that was my favourite and one topic that I need help on. A topic I hope to fix. I’m hoping that in the comments or on Twitter #Fav&Fix you amazing readers can help me out with some hints, tips, and suggestions.

Favourite:

This week I introduced the unit circle to my MHF4U class. I wasn’t happy with the way I introduced the circle in years past so I made a change. I want students to see that our special triangles are just reflected around the circle. Instead of drawing them, or imagining that they are reflected….I wanted them to physically pick them up and flip them and move them. I wanted them to see that the lengths are the same. So I cut out 30-60-90 triangles and 45-45-90 triangle each having a hypotenuse of 10 cm. I created a circle with radius 10. Now each time you place the triangle on the circle we can easily see the principal angle it creates and the coordinates of the point on the circle….It’s the lengths of the triangle….and since the hypotenuse is one the lengths correspond to the Cosine and sine value of that angle. The physicality of this I believe helped allow the students to grasp what the circle shows.

Fix

This week in our MEL3E class used Fry’s Bank from Dan Meyer.

This problem, like many 3-Act Math problems, allowed my class to discuss, question assumptions, and uncover math. The problem helped restore some of our great classroom atmosphere that we’ve been missing lately. I want more! This coming week we’ll keep working through compound interest problems. I’m planning on doing Robert’s Not Cashing the Cheque problem.  After that my resources for compound interest problems are pretty thin. I want to continue posing interesting problems to my students. Can you suggest some? Do you have great compound interest problem that keep students curious and questioning? I’m looking for some!! Share those great problems here or on #fave&Fix on Twitter. I’m looking forward to what you come up with.

[Update]

Thank to all of you who commented through Twitter on great compound interest problems. Here is one from Diana,

Here’s where our class went on Monday:
We started off with Robert Kaplinksy’s How Much Did Patrick Peterson Lose By Not Cashing His Check problem. Go ahead and read his lesson plan.

What made this problem great for our class was the discussion that occurred before any math happened. An amazing argument bubbled up with one side saying “Who cares….what’s the big deal” and the other side saying “That’s just super insensitive…..I could use the interest off that account”. My class from the beginning of the year was back! They had put away the drama that had happened between them and focused on the problem. We guessed at the interest he was losing daily. And then using the info from Robert’s site calculated the interest in the first couple of days. Then broke out the Finance Solver to determine how much was lost for the 27 days.

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The class wanted to know more! They wanted to know what he would lose if he didn’t cash it for the year, 2 years, 5 years!! So we did that too.

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Next, we investigated Robert’s How Much Should Dr. Evil Demand?


Read Robert’s post to see the plan.

Again, with this group, we didn’t use exponential functions…but the Finance Solver to determine what $1000000 would be worth 3o years later with average inflation of 5.33% per year. We also extended to find how long we would have to wait for $1 million to be worth $100 billion.

Thanks for the help!

More on Compound Interest, Financial Literacy and More

If you are interested in finding more ways to bring out financial literacy concepts in your classroom, consider subscribing to my podcast called Invested Teacher on Apple, Spotify, YouTube and other platforms. While we focus on how we as educators can better manage and invest our money, we also have episodes where we chat about how we can share that financial learning with our students, too.

One Favourite, Two Fixes: Nov 5

by Jon Orr

I need help! Every time I go through a lesson there is aways something I want to fix. Something that can be improved upon. Something that can get my students to think a little deeper about the math or something that can make my organization better, or class management better. Sometimes I can think of how to fix it, sometimes I know there is a fix out there and I can’t see it. That’s where you come in.

Each week I’m going to post one idea from my lessons that was my favourite and two topics that I need help on. Two topics I hope to fix. I’m hoping that in the comments or on Twitter you amazing readers can help me out with some hints, tips, and suggestions.

Favourite

For the last two weeks one of my class’s atmosphere seemed poisoned (see below).  My favourite this week though helped restore (for a short time) that atmosphere back to where we have spent most of the year. Warm-ups to the rescue! Our warm-ups dive into our Everyday Math curriculum like nobody’s business. Sometimes they take 10 minutes, sometimes 20….and I’m ok with that. Each one has my class engaged for that time. This week my favourite was Dan Meyer’s Dueling Discounts.

The kids each had a copy of a $20 off coupon and a 20% off coupon. For each item I showed, I had them hold up their choice of coupon to use. I was loving that all students were actively engaged and WANTED to know which was the better deal. It was so nice to see this with my kids again.

First Fix

Like I said above, my class’ atmosphere has seemed poisoned for the last two weeks. Before that we had an amazing atmosphere…..all kids worked well together. They sat in random pairs everyday, they were engaged! Then a few things happened.

  • Outside of class somebody was texting things they shouldn’t to somebody else….VP said they are not to work together.
  • A new student was added and talks a lot
  • Two others can’t work together because of a fight they were in last week.

So now we don’t have the awesome —we all can work together and build off each other atmosphere I love and had. I’m looking for tips to try so we can re-create our atmosphere we started with. Any ideas?

Second Fix

In my grade 9 mfm1p class this week we worked on solving proportions through the Smart Car Smash activity. screen-shot-2016-11-06-at-9-22-20-am

After going through super gross lesson and seeing the kids smile and cringe at the same time it was time to practice our strategies. I gave out this sheet below.

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This is where all the excitement for math was lost….”ah man, a worksheet”. Most students solved the problems. Some kids who were actively engaged with the first problem now were shut down. How can I keep the practice portion that I need but keep engagement up?

Thanks for reading. I would love your help. Share your suggestions on Twitter or below in the comments.

Helpful Fixes from Readers:

Math Before Bed

by Jon Orr

Every night since my kids were tiny we’ve read stories before bed. It’s been a time for us to wind down, cuddle, get one on one time with each of them, and chat about the books and our day. Reading at night strengthens their reading skills. I did the reading when we started and slowly, as they get older, they’re reading to me. We do this for reading, but we’ve never done this with math.

I started looking for resources to do some math at bed time. I googled:

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and there were many hits for a website/app called Bedtime Math. I checked it out. You can subscribe to an email to get a daily math scenario to do at bedtime with your kids. It always gives some background on a real-world scenario and then asks some math questions they made up regarding this scenario. For example, here was yesterday’s email:

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They are ok…but it wasn’t exactly what I was looking for. I wanted to discuss more, I wanted a variety of answers, not just one and boom we’re done. I wanted to strengthen my 8 year old and my two 6 year olds numeracy skills just like we strengthened their reading skills. I wanted my kids to share strategies on counting, estimating, adding, multiplying, sorting, patterning, etc all while laying in bed cuddling and comfortable. This site wasn’t doing that for me.

This week I received Christopher Danielson’s book Which One Doesn’t Belong in the mail.

Now this is what I wanted. Every page gets us discussing why we picked one shape over another. We talk about why someone might have picked each of the shapes. On the first night we did 3 pages and they wanted more. I wanted more. But I restrained. “We don’t want to use it all up on the first night!”.

This got me thinking. I wanted to discuss math like this every night, even for just 5 or 10 minutes. I needed more. That night and a few other nights I put together some pages for me, my wife, and my kids to do before bed. Here are a few pages:

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So far we have 20 pages in this book:

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Click to download a copy for iBooks on your iOS device

Each page in this book shows us a perplexing problem. Sometimes there is one right answer and sometimes there are many right answers. The purpose of each question is to generate a discussion about HOW you determined an answer. If you find one answer, try to find another. You could complete one page a night, or many pages. 

You can access the first 20 pages of the book here with an iOS device that has the iBooks app installed. Or you can download a PDF version here. That way you can view the pages while laying in bed with your little ones. I plan to add many more pages as the days go on. We have been doing two or three pages a night….my plan is to have about 50 or so. Please go ahead and download it and read with your kids. Also please feel free to edit the book and give me some feedback on the pages. I haven’t spent much time thinking about math in grades K through 3 YET.

Grab a preview photo book print version at cost here

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Further Reading: 

Christopher’s site Talking Math With Your Kids

Table Talk Math – http://www.tabletalkmath.com/ 

Our math related books for night time: