3-1     Recognizing Factors of a Number (downloadable pdf)

Task: Identify block diagrams that represent the factors of a number.
Learning goals: Explore relationships between a number's factors and its prime factorization.

3-2     Finding all Factors of a Number (downloadable pdf)

Task: Write the value of each diagram. Explain the meaning of the image.
Learning goals: Use prime factorizations to find all factors of number.

3-3     Counting Factors of Powers of Primes (downloadable pdf)

Task: Write the value of each diagram. Find patterns. Explain the meaning of the image.
Learning goals: Discover and describe a simple rule for counting the factors of a power of a prime number.

3-4     A Formula for Counting Factors of a Number (downloadable pdf)

Task: Write the value of each diagram. Find patterns. Create your examples. Find a formula to describe the patterns.
Learning goals: Discover and justify a formula for counting the factors of a number whose prime factorization has two distinct prime factors.

3-5     Generalizing the Formula for Counting Factors (downloadable pdf)

Task: Rewrite the tree diagrams using the values of the numbers. Describe patterns. Create your own examples.
Learning goals: Generalize the formula from 3-4 to count factors of arbitrary natural numbers.