factorblocks.jpg

Credit for this problem goes to Brian Errey.

Prologue

8m15 Determine common factors and common multiples using the prime factorization of numbers

Act I

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1. Do any of these models represent prime numbers or composite numbers?

2. Which of these best represents a prime factorization?

3. Do these numbers have a common multiple? How can you tell?

Act II

4. What mathematical tools can we use to help us find the prime factors?

Students might suggest Factor Trees or Venn Diagrams. It can be helpful to draw these out on paper. Have linking cubes handy, in case students want to put together their own models and play around with them to figure out how they work.

Act III

5. We'll discuss the solution together in class.

Sequel

6. Is there an easy way to figure out the Greatest Common Factor of any two or three numbers? How about the Least Common Multiple?

7. Can you find the Greatest Common Factor or Least Common Multiple of any two 4-digit numbers? How about 5-digit numbers?