Ping Pong Lottery

3 Act Math

Act 1

1. Which number did he pull?
2. Write down a guess.

I’d start this lesson before Act 1 by doing this Estimation 180 type challenge. How many ping pong balls are in the bag?

Package Picture

Here’s the reveal:

From there, jump into Act 1 and begin the big task for the day.

Act 2

3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.

The students may be tempted to assume that 144 balls are in the box (based on the estimation intro). Therefore, we need the fill height.

Height - Width

As well as the depth…


And the ball diameter…

Ball Dimensions

Finally, the total #1 balls in the box are given as well as a ratio for the other numbers. The students won’t know the exact number of balls (there are 99), so they will have to rely on their volume calculations from above. One error to look out for is simply taking the volume of the box and dividing by the volume of a ball. This makes sense but leaves out the space between each ball.

Ball Count

Act 3


5. What would happen if the ratio was 2:3:1?
6. What would happen if he pulled 5 balls out before picking the winner?

Common Core Standards
Understand ratio concepts and use ratio reasoning to solve problems.
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions
solve problems involving the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids


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