Here’s a really big problem you can work on with your students this holiday season.

Act 1:
Show them this video and ask: What do you notice? What do you wonder?

After allowing them to voice their noticing and wonderings guide them to wonder: How big is that new light? How many times bigger is the big light compared to the old light? How many Really Big Lights would you have to put up to cover the same length as last year?

Act 2: Here are some images to help make some conclusions:

Guess: How long is the big light? How many times longer is the big light than the small light?

Reveal:

Guess: How many small lights are in one string that stretches 15 feet?

Reveal:

Work together to determine how many Really Big Lights would replace the string of 50 lights? What assumptions will you make?

Act 3: Reveal

Why might your calculated answer be different from the answer shown?

If you had 50 Really Big lights how long would could they reach? How many cars could you put in that garage?

For the Favourite & Fix series I’m posting one idea from my lessons that week that was my favourite and one topic that I need help on. Something 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.

I asked the class to make a gut check on which option pulled them immediately….and most said drive yourself. Ok….let’s verify that gut check. “Is there anything we would need to know more about?” A few students had some ideas and we worked as a class to narrow down some open items.

From here they were off to the walls to justify their choice. And I love that there were still more questions from every group

How many people are going?

Does each have to pay $40 each way?

Do you have to drive to the shuttle?

Do you have to pay for parking in option 2?

Are we taking into account getting a speeding ticket? insurance on the car? wear and tear?

I let the groups come up with answers to their own questions…..I added in, “if you drive yourself, is it likely that you only need to park for one day?”

The conversation that comes out of this warm up was great for us. So many questions and lots of answers. Most groups changed their minds after great debate to take the shuttle (if they were going on a trip for a week)…..less hassle.

The Fix

This is not really a fix yet…but I wanted to grab some thoughts from you. On the weekend Jules and I worked on some puzzles. After we dumped the puzzles out I would ask her how big would the puzzle be? She would look up and with that wonder look and say pretty big or pretty small, but nothing exact….she’s only 6. So I would narrow the question down. How many pieces would be along the bottom? Along the side? And she would make a guess. We would do the puzzle and then find out.

I wanted to grab some thoughts from you on a possible lesson idea.

On the weekend Jules and I worked on some puzzles. After we dumped the puzzles out I would ask her how big will the puzzle be? She would look up, and with that wondering look say …”pretty big” or “not too big,” but nothing exact….she’s only 6. I narrowed the question down. How many pieces would be along the bottom? Along the side? And she would make a guess. We would do the puzzle and then find out.

This got me thinking.

I was thinking about factors of numbers and how that relates to the dimensions. I also thought about optimal dimensions of rectangles given a set area.

If a puzzle had 60 pieces what could the dimensions be? 100 pieces? 1000 pieces?

Take Elsa for example. With 48 pieces do you know what the dimensions will be? Think of some possible combinations. Got them?

And….. bam! Did you think of 8 pieces by 6 pieces?

The puzzle we worked on had 100 pieces and it was a 10 piece by 10 piece puzzle.

I feel like there is a lesson here but I’m not 100% sure where it fits. It may fit in many places.

If Act 1 is a short clip of us putting a puzzle together like below, then how does the rest of the lesson go? How do you see the rest of the lesson play out if you teach Kindergarten? Primary grades? Middle school? High school?

I would love to hear your ideas on the lesson goals as well as the lesson format! Together we can do it!

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.

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.

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.

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!!