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!

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

premade desmos page with some sliders built in for each type of model.

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..

 

Sequel:

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

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