The purpose of this activity is for students to make sense of non-unit fractions and the notation used to describe them. They learn that the denominator tells the number of equal parts into which the whole was partitioned and that the numerator tells the number of parts being described. Students write non-unit fractions that represent the shaded portions of area diagrams.

If needed, especially with the fractions greater than one, clarify that each rectangle represents one whole. The activity concludes with students practicing how to read non-unit fractions. The terms “numerator” and “denominator” will be introduced in a later lesson.

When students notice that the bottom part of the fraction stays the same and the top part of the fraction changes, representing the number of equal parts that are shaded, they look for and make use of structure (MP7).

• Display the completed table.
• “Now that the table is complete, what do you notice? What do you wonder?” (The size of each part always has a 1 in the top part of the fraction. The bottom part of the fraction is the same for each equal-size part as well as for the total of equal parts that are shaded. The top part of the fraction is how many parts are shaded.)
• “Let’s think about how we should describe or name the shaded part in each image.”
• 30 seconds: quiet think time
• Invite students to name the shaded part in each image.
• As students name the shaded part in each image, have them share how they used fraction notation to record the name.

The purpose of this activity is for students to match fractions to shaded diagrams. Reiterate that each rectangle represents one whole. Students also create their own cards, with shaded diagrams, to match given fraction cards.

Students observe and use structure as they identify that the top number in the fraction represents the number of shaded pieces while the bottom number represents the number of those pieces in one whole rectangle (MP7).

• Invite 1 or 2 groups to display a rectangle they partitioned and shaded to match one of the fractions.
• For each rectangle students share, discuss the fraction that it represents.
• Display a diagram of , with all the parts shaded.
• “_____ noticed that to show , we have to shade the whole rectangle. Look back over both activities for other fractions that are shown by shading the whole rectangle.” (, , and )
• Consider asking: “How many _____s would it take to make a whole? How do you know?”
• “These fractions are equivalent to 1 because they represent all the parts of the whole. We’ll work with other fractions like this as we learn about fractions.”