The purpose of this activity is for students to consider the numbers when they choose a strategy to find the value of a product. Some students might choose to use the same strategy for any multiplication problem. In this activity, the numbers were chosen to encourage students to choose different strategies in order to generate discussion about why certain multiplication problems lend themselves to different strategies.

When students choose a multiplication strategy based on the factors, using the associative and commutative properties of multiplication and the distributive property, along with known facts, they make use of structure to facilitate their calculations (MP7).

• Invite students to share their strategies for finding the value of .
• “Is there a mental strategy you can use to find the value of this product?” (Yes, I know is 1,400 and then I can add 14 to that.)
• Invite students to share their strategies for finding the value of .
• “Which strategy did you use to find the value of  ? Why?” (I used the standard algorithm because I did not see a quick mental strategy for finding the value.)

The purpose of this activity is for students to try new ideas from the previous activity and practice multiplying using the standard algorithm. 

• Ask students to share their strategies for the first three expressions.
• “Did anyone use a strategy other than the standard algorithm for any of the expressions? Why did you choose that strategy?” (For , I knew 199 is just 1 away from 200 and I could find in my head. I just needed to take away 15, and I could do that in my head also.)
• “Does the standard algorithm also work for these expressions?” (Yes, the standard algorithm always works.)
• “What strategy did you use to find the product ? Why?” (I used the standard algorithm. The numbers are complex, and I could not see a good mental strategy.)