T: What product is represented in both arrays? S: 18. T: Record the multiplication sentences for each array. S: 1 × 18 = 18 and 2 × 9 = 18. T: Circle the factors. Write the factors of 18 that are represented in order from least to greatest. S: (Write 1, 2, 9, 18.) T: With your partner, draw an array to represent another pair of factors with the product of 18. T: (Pause while students work.) What new factors of 18 did you find? S: 3 and 6. T: Revise your list of factors of 18. S: 1, 2, 3, 6, 9, and 18. T: How can we make sure we found all of the factors of 18? S: I can use my multiplication chart. I can think through my multiplication facts. But what if the number is really big, like 92? I don’t know all the factors of 92. I could draw arrays to find all the factors, making rows of 3, then 4, then 5, and all the way to 92. That will take a long time. T: Look at the list of factors for 18. Draw an arrow from 1 to 18. These are factor pairs because 1 × 18 = 18. With your partner, draw the rest of the arrows to connect the factor pairs. S: (Draw as pictured to the right above.) T: Notice that 3 and 6 are the middle pairs. We’ve checked everything up to 3, and the counting numbers between 3 and 6 are not factors of 18, so we found all the pairs. Try that with the factors of 8. Problem 2: Identify factors to define prime and composite numbers. Display the number sentence 2 × 8 = 16. T: What are the factors? S: 2 and 8. T: What other multiplication sentences can you write using different factors that will give us the same product? S: 1 × 16 = 16. 4 × 4 = 16. T: So, what are all of the factors of 16? S: 1, 2, 4, 8, and 16. T: How do you know those are all of the factors of 16? S: I listed them in order. When I got to 8, I noticed
T: What product is represented in both arrays? S: 18. T: Record the multiplication sentences for each array. S: 1 × 18 = 18 and 2 × 9 = 18. T: Circle the factors. Write the factors of 18 that are represented in order from least to greatest. S: (Write 1, 2, 9, 18.) T: With your partner, draw an array to represent another pair of factors with the product of 18. T: (Pause while students work.) What new factors of 18 did you find? S: 3 and 6. T: Revise your list of factors of 18. S: 1, 2, 3, 6, 9, and 18. T: How can we make sure we found all of the factors of 18? S: I can use my multiplication chart. I can think through my multiplication facts. But what if the number is really big, like 92? I don’t know all the factors of 92. I could draw arrays to find all the factors, making rows of 3, then 4, then 5, and all the way to 92. That will take a long time. T: Look at the list of factors for 18. Draw an arrow from 1 to 18. These are factor pairs because 1 × 18 = 18. With your partner, draw the rest of the arrows to connect the factor pairs. S: (Draw as pictured to the right above.) T: Notice that 3 and 6 are the middle pairs. We’ve checked everything up to 3, and the counting numbers between 3 and 6 are not factors of 18, so we found all the pairs. Try that with the factors of 8. Problem 2: Identify factors to define prime and composite numbers. Display the number sentence 2 × 8 = 16. T: What are the factors? S: 2 and 8. T: What other multiplication sentences can you write using different factors that will give us the same product? S: 1 × 16 = 16. 4 × 4 = 16. T: So, what are all of the factors of 16? S: 1, 2, 4, 8, and 16. T: How do you know those are all of the factors of 16? S: I listed them in order. When I got to 8, I noticed