The purpose of this activity is for students to make sense of the multiplication table, using what they know about factors and finding the area of a rectangle. They also are encouraged to notice and explain patterns they see as they make sense of the structure of the table.

• Invite 3–5 previously selected students to share their rectangles and how they created them.
• “This is called the 'multiplication table.' The numbers along the top and on the left side are the 'factors,' or the numbers we are multiplying.”
• “The number in the lower right square of the rectangle is the value of the product. The value of the product lines up with a factor above it and a factor to the left of it.”
• “We could represent the factors and the product in the last table in the first group of tables with 3 times 4 equals 12.”
• Display
• “How is the multiplication table different from other ways we’ve represented multiplication?” (It’s harder to see the factors. There’s no equal sign. We can picture a rectangle that helps us find the product.)

The purpose of this activity is for students to find the values of products in the multiplication table. Students are encouraged to find familiar products before working on those that are less familiar. They do not need to fill in all of the products in the table. The Activity Synthesis focuses on patterns students find in the table, how they can show the patterns with equations, and how they explain their patterns, using what they know about multiplication and the properties of operations.

• “What patterns did you find in the products of 5? How did you show them with equations?”
• “Why is that pattern happening?”
• “What other patterns do we see in the table? How could we show the patterns with equations? Why are these patterns happening?”