The purpose of this activity is for students to interpret situations involving equal groups of a fractional amount, and to connect such situations to multiplication of a whole number by a fraction (MP2).

Students write expressions to represent the number of groups and the size of each group. They reason about the quantity in each situation in any way that makes sense to them. Although images of the food items are given, students may choose to create other diagrams, such as equal-group diagrams used in grade 3, when they learned to multiply whole numbers. This activity enables the teacher to see the representations toward which students gravitate. 

Focus the discussions on connecting equal groups with fractions to those with whole numbers.

• ”What do you know about multiplication?”
• ”How would you describe the amount of the slice of pie on one plate? How would you describe two of the same slices? Three of the same slices?”

• Select previously identified students to share their expressions and how they reasoned about the amount of food in each image. Record their expressions and supporting diagrams, if any, for all to see.
• If students write addition expressions to represent the quantities, ask if there are other expressions that could be used to describe the equal groups.
• “How is the quantity in Clare's situation different than those in other situations?” (It involves whole numbers of items. Others involve fractional amounts.) 
• “How is the expression you wrote for the eggs different than other expressions?” (It shows 2 whole numbers being multiplied. The others show a whole number and a fraction.)

In this activity, students start with given multiplication expressions and consider situations or diagrams that they could represent. Situating the expressions in context encourages students to think of the whole number in the expression as the number of groups and the fractional amount as the size of each group, which helps students reason about the value of the expression. When students make explicit connections between multiplication situations, expressions, and drawings, they reason abstractly and quantitatively (MP2).

Allow students to use fraction strips, fraction blocks, or other manipulatives that show fractional amounts to support their reasoning.

• Invite students to share their responses. Display their drawings or visual representations for all to see.
• “How did you decide what the numbers in each expression represent in your story?” (It made sense for the whole numbers to represent how many groups there are and for the fractions to represent what is in each group.)
• “How did you show the whole number and the fraction in your drawing?” (I drew as many circles as the whole number to show the groups. I drew parts of objects or wrote numbers in each circle to show the fraction.)