Incredible Shrinking Dollar 3 Act Task

Today in grade 12 we explored exponential decay with the 3 act task of the incredible shrinking dollar by Dan Meyer. (Available here).

We watched the Act 1 video, noticed he was copying money but shrinking it on the copier. They immediately started to make models. Most were based on percent like this: A(n)=100(0.75)^n

We then started to wonder if the photocopier shrinks the area of the page to 75% of the original, or if it shrinks the length to 75% and the width to 75%. A quick google search confirmed that it is indeed a linear shrinking of length and width both.

we had a good conversation about whether this is linear decrease or exponential decrease. Some groups thought that you’d lose 25%, so after 4 decreases there’d be nothing left since 100-4(25)=0. Others claimed that it’d never disappear just get smaller and smaller and smaller since it would be losing 25% of the current length each time, so it’s losing less and less each time.

Finally someone asked what the dimensions of the original bill were, and we unlocked the “act 2” data where the dimensions are shared.

Groups worked on making tables, graphs and equations for the area decrease, and they looked at domain and range within context of the question.

Others worked on modelling how the linear dimensions would change, and how the dollar would shrink by length and width each time.

Groups got a lot of practice with a skill that is challenging, sorting through information given, like they may see in a word problem, and making equations that make sense which can model the problems.

We’re heading towards our 3rd test soon, and we’re getting lots of practice in each day.