This is a student favorite, simple to start, differentiated, with various levels of success. I’ve done this with grades 2 and up, but my 5th-6th graders have gotten the most out of it.
Most importantly students learn to be very clear in writing their expressions. This activity naturally leads to a discussion about order of operations and mathematical “grammar.” Also, in their pursuit of the strike, students often ask to be introduced to new operations.
Instructions: Begin by rolling a die three times and recording these numbers as your “1st bowl.” You may cross out (knock down) any number that you can write an equation for using those three numbers each only once. For example, if I rolled a 6, 6 and 5, I could knock down the number four by writing: 5=6-6+5, or knock down 1 by writing 1=(6÷6)^5. Notice I used all three numbers, but each only once.
The goal is to knock as many “pins” (numbers) as you can. Knocking all the pins down on your first bowl is called a “Strike.” If you can’t think of any other equations, you may bowl again and try for a “Spare.”
Notes on Implementation:
I’ve created this Number Bowling handout for students to keep track of their games. I’ve also experimented with keeping score, and I think three frames is a good length time for a game. This can get complicated though, since scoring bowling is foreign and not straightforward to many students.
This year, after a few games, I had students write down their “favorite” equations on a notecard. We used these equations during a “strategy session” where we came up with tricks to help knock down more pins. The “tricks” can all be described as using an operation to change a number, or two numbers, into another. For example, 3 can be changed into 6 by using factorial, (3!=6). Some more advanced tricks include using square root, and/or the floor and ceiling function (rounding up or down to nearest integer).
Last year students wondered whether a strike was possible for every combinations. We chose the brute force method of proof :). First students had to figure out how many unique outcomes were possible with 3 dice. For many I assisted them by having them look at this pdf. Obviously rolling 1,6,6 is the same as rolling 6,6,1. Then whenever a student achieved a strike, we crossed that off the list.