The purpose of this activity is for students to analyze and describe how images and diagrams can show “ times as many.” Students generate ideas for how to use a multiplication equation to represent the comparison.

Students begin by interpreting an image in which the multiplier (3) and the numbers are given. They explain how some number of times of the lesser amount can be seen in the greater amount. Next they create their own diagram and see different ways of representing the iterations (groups of) the lesser amount to create the greater amount.

During the activity, make connecting cubes accessible for students who may choose to use them for problem solving—either to reason about the quantities or to explain their reasoning.

• Invite selected students to share diagrams and explain how they show “times as many.”
• If needed, use cubes to represent statements.
• “How could you write an equation to compare Kiran’s and Jada’s cubes?”
• “What do the numbers in the equation represent in the situation?” (4 is the “4 times as many.” 2 is how many Kiran had. 8 is how many Jada had.) 
• Write equations for each situation, and ask about what students notice about the relationships.

The purpose of this activity is for students to deepen their understanding of how diagrams and multiplication equations can represent “ times as many.” Students explain how the diagrams and equations represent the situation. In order to match situations, diagrams, and equations, students reason abstractly and quantitatively (MP2).

• Select students to share their matches. 
• Record students’ explanations to show how they connected the diagrams and the equations (display or draw the diagrams and the equations, and annotate).