Math = Love: Using Probability to Find Contents of Mystery Bucket

## Thursday, April 27, 2017

### Using Probability to Find Contents of Mystery Bucket

When I dreamed up this activity, I envisioned myself using a box.  Therefore, I typed up the notes as "Mystery Box Probability."

Then, my husband ended up borrowing the box I planned to use for an activity with his geometry classes.  I happened to notice a bucket on top of the shelf that I purchased a few summers ago at Dollar Tree.  And, that's the story of how my "Mystery Box Probability" activity became a "Mystery Bucket."

I decided to use my ever-handy linking cubes (affiliate link) for my mystery items.

See the piece of paper sitting in the bottom of the bucket?  That's an attempt to fix the fact that the bottom of the bucket was quite see through...

That view, however, was NOT visible to my students.  I carefully guarded the bucket throughout the class period so that they could not see the contents.

I walked around the room and gave each student a turn drawing a block from the bucket.  After the class recorded the color on their tally sheet, the student returned the block to the bucket.  Once each student had a turn, I asked the class if we had enough data to make an informed decision.  Each class agreed that the more data we had, the better.

After the class decided we had sufficient data, we calculated the experimental probability of drawing each color.  Then, we multiplied the experimental probability of each color by the number of blocks in the bucket.

Having never done this activity before, I wasn't sure exactly how well it was going to work.  But, I figured even if our estimates were way off, it would still teach my students something about probability.

After our predictions were recorded, it was time for the big reveal.  Instead of just showing them the contents of the bucket, I removed the blocks one at a time.  I wanted to make the anticipation slightly painful for them.  I drew it out as long as I could.

One of my classes had all five of their predictions wrong.  That class unfortunately had a tendency to draw that black block from the bucket over and over and over despite it being the only block of its color in the bucket.  This really threw off their data!  My other two classes each got one or two colors spot-on.  The other predictions were close but not exact.  We discussed how we'd need to collect a large amount of data to arrive at a more accurate prediction.

All in all, I really enjoyed using this activity with my students.  I will definitely use it again next year!

File for this activity is uploaded here.

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