Panning for Gold
How it works
Imagine we have one real gold bar and a bunch of fake gold bars, and we want to try to figure out which one is the real one.
The real gold bar and the fakes look exactly the same, but the real gold bar is heavier than all the fakes.
The fakes all weigh the same.
We have a balance with two pans. Can we use it to find the real gold bar? If so, how many weighings will we have to do? What is the smallest number of weighings we have to do in order to guarantee we know for sure which is the real gold bar?
In this activity, students start by trying to find the real gold bar with different numbers of bars. Next, they focus specifically on the number of weighings they're doing. Students strategize to try to figure out procedures that allow them to use as few weighings as possible.
Why we like this activity
- It’s fun! Students enjoy trying to find the real gold bar.
- It helps students develop algorithmic reasoning.
- It helps students develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies to find the real gold bar.
- Making and testing predictions about how many weighings you'll need to find the gold bar every time.
- Finding and using strategies to find the real gold bar every time with a specific number of weighings.
- Understanding and explaining why you can find the real gold bar every time with a specific number of weighings.
- It has a low floor and a high ceiling: It's easy for students to get started trying to find the real gold bar through trial and error, but figuring out the minimum number of weighings you need to do with each number of bars to guarantee you'll find the real gold bar is challenging!