The purpose of this activity is for students to use the structure they noticed in the previous lesson to solve real world problems in which a whole number is multiplied by a unit fraction. Students may use a variety of strategies to solve these problems. They may relate the situations to multiplication of a whole number by a fraction or division of two whole numbers. During the Activity Synthesis, connect the different interpretations of the situations.

Students share their different representations and expressions and explain to each other how they relate to the running situation (MP3).

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• “What do you know about this problem? What are you trying to figure out?”
• “How would you solve the problem if the length of the road was 8 miles long?”

• Ask previously selected students to share their solutions.
• “What are some expressions that represent the distance Han ran?” (, , , )
• “How does each of these expressions represent the distance Han ran?” (He ran of 7 miles and we can write that as . We can figure out how many miles that is if we divide 7 into 4 equal parts. That’s or or .)

The purpose of this activity is to match different expressions and diagrams with one situation. Some students may match the expressions, diagrams, and situation by finding the solution to the problem and the value of each expression. Some may match the representations without finding the value of the expressions. During the Activity Synthesis, highlight how the different expressions relate both to the situation and to the diagrams, and connect the relationships to the meaning of the expressions and diagrams.

Students reason abstractly and quantitatively (MP2) when they relate the story to the diagrams and expressions. All of the diagrams and expressions involve the same set of numbers so students need to carefully analyze the numbers in the story, the diagrams, and the expressions in order to choose the correct matches.

• Invite 2–3 groups to share how they matched an expression and a diagram to the situation.
• Display Cards J and K.
• “How are these diagrams the same? How are they different?” (They both show or . The first one shows of each whole. In the second one, the shaded parts are all together, so they show of a single whole.)
• Display the expression: .
• “How does this expression relate to the situation?” (The race is 3 miles long and each person will run of the race.)
• “How do the diagrams represent the expression?” (In the first diagram  of each whole is shaded. It is harder to see in the second diagram because I can't tell that the shaded parts are of the 3 rectangles.)
• “How can we adapt Card K to show there are 4 equal sections of ?” (We could show the sections.)
• Mark Card K to show the 4 equal sections of . For example, use different colors to show the other 3 sections of .