Modelling in Clash of Clans

Here is a task I’ve been playing around with lately. Let me know what you think!!!!

Thinking of using this task with my grade 11s functions class/ or more advanced functions classes. I have recently been playing Clash of Clans and if you have played you know that you have to wait for items to be built/upgraded, etc. The time to wait changes based on the your progress and cost of the item/upgrade. You do have the option to SKIP the upgrade wait time by using gems. What has me wondering is that the amount of gems needed to skip an upgrade. What’s the relationship between upgrade time and gems? Our task is to see what that relationship is.

Act 1 : I’ll show this short video to my students:

I’ll ask for any questions the students had from watching the video and settle on —How many gems would it take to upgrade the town hall? — which will take 2 days.

Get the students to make some guesses…..

Act 2 :

Then get them discussing what other info we will need. I want them to come up with the idea they need more instances of upgrade times vs. gems. I can start to show them some pics…..was thinking of revealing each “point” at a time and getting then to guess!

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Here comes the modelling time…….plop these down in Desmos. We’ll start to select a model based on the data we see:

Screen Shot 2014-09-24 at 11.04.31 AMpremade desmos page with some sliders built in for each type of model.

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Have them decide which model they like best for the answer…..use the model to come up with an answer. My guess is that students will assume linear and come up with an answer that is too high (I’ll update later after I use it with students). ……and then we can have the big reveal……

Act 3

Watch the video ….

Or use the image..

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Sequel:

Find the cost of upgrading immediately…..how much wait time can you skip with $20?

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Head on over to 101qs.com to download the files.

To edTech or Not?

To edTech or not???

This was my lesson today where I used some technology….

In our Volume of Cylinders & Prisms grade 9 applied lesson we started out grabbing an Explain Everything file from our Google Classroom.

Our first problem embedded within the file was You Pour, I Choose from Dan Meyer. We watched the Act 1 video and then students filled out a google form embedded right in Explain Everything. The form asked them what questions they had after seeing the video.

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The next slide showed the forms responses in a google sheet!

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The students got to see live what each other were asking. Most kids had the same question…..Which had more or do they have the same!!

We then made guesses using a form……and saw each others guesses.

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After, we set out to work deciding what we needed to know before answering the problem……mades some guesses along the way and then solved the problem!

I’ll admit that we had some internet connection problems accessing google forms and every time we do I seriously think that it wasn’t worth it……but today it seemed worth it because it gave some of those shy kids a voice in my class. I’ve worked on problems like this and when I ask students share their questions….guesses…..usually the “brave” kids make their voice heard and the shy ones are left out (unless I ask them specifically). The tech today even though was spotty……served a purpose……its for small reasons like this that I keep trying out edTech in the class!!

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The Need for Speed!

Here was our lesson today on Instantaneous rates of change/slope of a tangent line

Yesterday we completed the awesome Desmos activity Function Carnival!! Some students were extremely competitive when trying to match the motion of the cannon shot to their graph…..some students not so much……here are their graphs

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After showing the kids this picture we talked about the motion of the guy and how it relates to the graph…..Questions we had

  1. When would he be travelling the fastest? How do we know?
  2. When would he stop? How do we know?
  3. What happened after the parachute opened?

My goal here was to get talking about the speed of the guy. I asked:

If the guy was carrying a speedometer or a GPS…..what would his speed read out the moment before his parachute opened?

We stopped and made some estimates based on our intuition.

We talked about how to determine instantaneous speed from our knowledge of average rates of change, average speed, and slopes of secants lines.

We finally came to the conclusion that we could calculate the average rate of change between two points REALLY close together!!!!!! BINGO.

So I said let’s drop this image in Desmos! (we came to a decision that the cannon ball guy’s max height could have been around 9 metres).

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We looked at the graph and decided that it was HARD to estimate two points really close together.

So we added in some transformations to a basic quadratic function and fit the curve to the graph.Screen Shot 2014-09-12 at 8.44.11 AM

I had pre-loaded some “extra” info in the sketch to demonstrate graphically the idea we were coming up with……the idea of looking a the slope of a secant line and as one point gets closer to the next the slope of the secant line approaches the slope of the tangent line.

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After looking at it graphically…..we used the equation we came up with to algebraically calculate the slope of the tangent line (the instantaneous rate of change).

We then practice that calculation using other points the students were interested in knowing about.

That was our lesson on Instantaneous Rates! Thanks Desmos!!

Guess Who!!!

One of my kids’ favourite game is Guess Who…..remember this one?

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You remember it! I wanted my students to practice recognizing characteristics of polynomials without having to just complete questions out of the text book…..so I thought this game could work great! When you play this game you ask characteristic questions about the person you have picked and try to narrow the choices down…..all before the other person has guessed yours!

Perfect for characteristics of functions!!! Could also be great for my grade 9s who will later learn characteristics of linear relations.

I put this “board” together for the possible choices.

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And kids will use dry-erase markers and “paper protector” sheets so they can re-use the Game boards.

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Here are some pictures of my students playing the game

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Math is Like…. [first day]

An activity I have done every semester since I started teaching is one I call “Math is Like….”

After going through all the course mumbo-jumbo, we talk about creativity!

Then the activity starts like this….

Here is your chance to get creative!! Take your Post-It and write Math is like….”

I then give the students some examples from previous years. The idea is that they are to complete the statement with their own thoughts.

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Some students write funny things, some negative things, some insightful things! I let them know they are allowed to write whatever comes to mind as long as its school appropriate.

I have found that this gives students an “airing- out” of past experiences and we get a fresh start!! My grade 9 students have all come from different backgrounds in math….some great…..some not so great! So I tell them that if you have had a negative experience in math in the past, part of my goal this year is to help them change those beliefs about math

Here are some of this years Math is Like ….. statements. [I've got my work cut out for me!!!]

 

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Minnie’s Juice Cup [3actMath]

Here is a 3-Act Math problem I’ve been working on. My first unit in the fall is measurement and I wanted something to do with volume.

Minnie’s Juice Cup!

Act 1:

Question: How many juice boxes will fit in the cup?

Act 2:

Make them guess for each of these measurements.

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I am open to suggestions on how to handle the two different diameters. I tried averaging them and came up with a pretty accurate answer.

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Act 3:

 

R2D2 – Post-It Note Art!

I loved Nathan Kraft’s Van Gogh Post-It Note art on his windows. If you haven’t seen it…check it out.

I wanted to do something similar for a while now (like @mr_stadel’s File Cabinet Problem) and found some time now that school is over! Following Nathan Kraft’s instructions with Excel I created my own Geek Art…

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Grabbed some Post-Its and got to work…..I also created a time lapse video so I can make a 3 Act math problem for my students (Coming soon!).

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Info for 3 acts
Each Post-It is 2″ by 1.5″
The board measures 42″ by 43.5″
I actually used 609 Post-Its!!

2014 Pictures

This morning I read a blog post from Jonathan Claydon on 180 blog posts. I’ve learned lots of class/math ideas this year from reading 180 blogs and I loved his ideas on 180 days of pictures. My goal next year is to start posting 1 pic for each day. It would be a great thing to show the students at the end of the semester too!

here are a few pictures from this semester.

Commit & Crumple!

Saw this activity in a book I picked up at the NCTM conference a few years back (Philadelphia).

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This book has been great for engaging activities in math….here is the one we did today:

Commit & Crumple
We are reviewing for our exam and I wanted to review average rates of change and instantaneous rates of change. I wanted to see what they remembered…and also how they remembered the graphical representation of rates of change.
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Game of Risk

Recently read a blog post of a review game …. Risk from Angie (@aeakland) . I love review games instead of just textbook questions…..so i adapted this game to be played in my MHF4U Advanced Functions class.

Here are the rules….

  • In teams, each team starts with 100 points. Write your points and names on the board.
  • Complete any of the Risk Questions in any order. (They are just the Review questions from the textbook).
  • For each question: After coming up with a solution, wager any or all of your points.
    • If you are correct – – add the points to your total!!! Yay!
    • If you are incorrect — subtract that many points from your total. Boo!
  • The top three teams with the most points were eligible to enter the draw at the end for the prize!!!

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Great things about the game…

Kids were cheering — when getting the problems right!……that doesn’t happen when just working on review problems from the book.

Kids were self /peer assessing their work — by betting they were deciding how confident they were on their work! They took their time, and thought about their answers making sense!

Kids were doing math!

The winning team won their choice of a geek sticker!

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