The purpose of this activity is for students to directly connect multiplication expressions to equal groups they see within rectangular areas. Students may decompose the rectangular areas in various ways to see equal groups, and they should relate the rows and the columns to the factors of a multiplication expression. This will be helpful in future activities when students multiply side lengths to find the area.

• “How did you decide which rectangle matched each expression?”
• “Where do we see equal groups in the rectangles?”

• “How do you see each factor in a rectangle?” (I can see one factor in the number of squares in a row. I can see the other factor as the number of rows. I see one factor as the number of squares in a column. The other factor is the number of columns. It’s like I see the factors in an array, only it’s squares, not dots.)
• “How do you see the product in a rectangle?” (If we count the squares in a rectangle, it gives us the same number as the product of the factors. The product is the same as the total number of squares in the rectangle.)
• “Why does multiplication give the same number as counting one by one?”

The purpose of this activity is for students to represent multiplication expressions as rectangular areas. Students use a grid to draw the rectangular area that represents a multiplication expression. In the Activity Synthesis, students explain how they interpret the multiplication expression, specifically how they see the equal groups in the rows and the columns of the rectangular area. Give students access to square tiles if needed. When students draw and relate area diagrams to multiplication expressions, they are reasoning abstractly and quantitatively (MP2).

• Have 2 or 3 students share a rectangle for each expression.
• For each student sample ask:
  • “How does the area of this rectangle match the expression?” (I see 4 equal groups of 6 because each row has 6 squares. I see 4 equal groups because each column has 6 squares.)
• Consider asking:
  • “Did anyone draw a different rectangle for this expression?”
• Display a rectangle that two students oriented differently.
• “How can both rectangles match the same expression?” (They have the same number of squares. They have the same side lengths, just switched. I see the groups in the rows in the first rectangle and in the columns in the second rectangle.)
• Display the 3-by-5 rectangle and descriptions from the Launch in the first activity.
• “Which way of describing a rectangle was the most helpful to you when you were drawing rectangles in this activity?” (It was helpful to describe how many rows were in the rectangle and how many squares were in each row. It was helpful to think about one factor as the number of columns and the other factor as the number of squares in each column.)