The purpose of this activity is for students to calculate areas in context. Students are not offered an area diagram but rather an image of a flag. Students may label the image of the flag with measurements or make their own area diagram. The lengths are not always presented in fraction form so students may rewrite them as fractions before calculating areas or they may use the distributive property of multiplication and multiply the whole number and fractional parts separately before adding them. Students reason abstractly and quantitatively when they interpret the given information about the flags and make calculations to solve problems (MP2).

• Invite previously selected students to share their solutions.
• Display equation:
• “How does the equation represent the area of the flag?” (I can divide the flag into two pieces, one of them 7 inches long, and the other inch long. Then I add them to get the area of the flag.)
• Invite students to share responses for the area of the red stripe.
• “How can I use the area of the red stripe to find the area of the blue stripe?” (The blue stripe is twice as wide so its area is twice as much.)

The goal of this activity is to examine calculations with measurements of a flag and try to figure out what question the calculations answer. The answers include units and this can serve as a guide to students. Since the first calculation has an answer in inches, the question it answers must ask for a length. Since the second calculation has an answer in square inches, the question it answers must ask for an area. This is an important step in solving the problems as students can then look at the diagram and the measurements and decide what the question could be.

One important part of the modeling cycle (MP4) is interpreting information. That information may be presented in words or graphs or with mathematical symbols. In this case, students interpret equations in light of given numerical relationships and diagrams.

• Invite students to share their responses for the first question.
• “How did you know the question was about length?” (The answer is inch, which is the measurement of length. So, the question had to be about length.)
• “How did you decide which length?” (The calculation took a quarter of the flag width. Since the red and blue stripes are each of the width, the calculation could be for their width.)
• Invite students to share their responses for the second question.
• “How did you know the question was about area?” (The answer is a measurement in square inches so that’s the area of something.)