Prime Factorizations
Math Concepts:
Multiplication, prime factorizations
Materials:
None
Players:
Whole class
Set up:
Put your students in a circle.
Play:
Start counting around the circle starting at 1. For each number, state the number, and then give its prime factorization. If the number is a unit or a prime, say that instead of the prime factorization. Make a habit of saying the primes in the factorization in increasing size– for example, saying that 12 is 2 squared x 3, and not 2 x 3 x 2 or 3 x 2 squared – this will keep them organized and easier to understand and fit together.
If done correctly, you should hear:
- unit
- prime
- prime
- 2 squared
- prime
- 2 x 3
- prime
- 2 cubed
- 3 squared
- 2 x 5
- prime
- 2 squared x 3
- prime
- 2 x 7
- 3 x 5
- 2 to the fourth
- prime
- 2 x 3squared
Goal
See how high your group can get before it starts slowing down
Discussion and Tips
Understanding and being comfortable with prime factorizations is incredibly helpful. It provides insights into how numbers are put together multiplicatively. It is key to doing fraction work where being able to find common factors and common multiples is so important. Stating prime factorizations using powers also provides excellent practice with exponents.
When someone gets stuck, give them ideas for how to get unstuck. For example, point out that the number is even (so it’s divisible by 2), or that it ends in 0 or 5 (so it’s divisible by 5).