engagement

Modelling in Clash of Clans

by Jon Orr

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!

Clash-of-Clans-Act-2

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.

Screen Shot 2014-09-24 at 11.21.16 AM

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..

IMG_0909

 

Sequel:

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

IMG_0890

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The Need for Speed!

by Jon Orr

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

Screen Shot 2014-09-12 at 8.35.50 AM

 

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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).

Screen Shot 2014-09-12 at 8.44.25 AM

 

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.

Screen Shot 2014-09-12 at 8.51.26 AM

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!!!

by Jon Orr

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

guess_who_1

 

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.

Screen Shot 2014-09-08 at 8.52.31 AM

 

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

GuessWHoGameBoard

Here are some pictures of my students playing the game

September_08__2014_at_0126PMSeptember_08__2014_at_0125PM September_08__2014_at_0127PM September_08__2014_at_0134PM September_08__2014_at_0137PM

Minnie’s Juice Cup [3actMath]

by Jon Orr

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.

Minnie'sCup

 

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.

JuiceBox-DImension

 

Act 3:

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