The purpose of this activity is for students to consider how known products in the multiplication table can help find an unknown product in the table. They notice and use patterns in the multiplication table to deepen their understanding of strategies based on the properties of operations. While students may use various strategies based on properties of operations to find the unknown values, look for opportunities to highlight strategies based on the commutative property.

When students use a multiplication fact that they know to determine a multiplication fact that they don’t know, they look for and make use of structure (MP7).

• Invite previously selected students to share how they used the patterns they noticed in the table to find unknown products.
• If possible, display and annotate the table to illustrate students’ reasoning. Use drawings of equal groups, tape diagrams, or arrays as needed to make the reasoning visible to all students.

The purpose of this activity is for students to articulate how they use known products to find unknown products, using a structure similar to that used in an earlier lesson. Students may describe strategies that are based on any property of operations. The focus should be on the description of the strategy (such as “multiplying two numbers in any order gives the same product”) rather than remembering the property on which the strategy is based (such as “commutative property”).

• For each given product, invite 1–2 students to share the products they wrote and explain how those products are related to the given product.