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This Warm-up prompts students to compare four rectangles that have been partitioned and partially shaded. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology to talk about the characteristics of the items and the quantities they represent. During the Activity Synthesis, ask students to explain the meaning of any terms they use, such as “partition,” “equal parts,” “halves,” and “thirds.”
Which 3 go together?
Partition the Strips Template
The purpose of this activity is for students to practice partitioning and labeling equal-size parts, with unit fractions. This provides students a physical tool they can use throughout the unit to make sense of fractions.
Have students keep their fractions strips for reference in future lessons. They also will need the fraction strips for activities in Section C. Consider having them glue the fraction strips in their student book.
When students make halves, fourths, and eighths, they observe regularity in repeated reasoning as each piece is subdivided into two equal pieces. They observe the same relationship between thirds and sixths (MP8).
Your teacher will give you some paper strips. Each strip represents 1.
Fold each strip so that the parts represent 1 of the following fractions. Use 1 strip for each fraction.
When you finish folding, trace your folding lines with a pencil, and then label each part with the correct fraction.
Previously, students partitioned rectangular pieces of paper into 2, 3, 4, 6, and 8 equal parts by folding. The purpose of this activity is for students to partition rectangles by drawing, and to continue to practice naming the parts with the unit fractions , , , , and . It’s important that students try to make the parts as close to equal in size as they can, but students’ drawings do not need to be exact. After they practice partitioning, students partition and shade—but do not label—a fraction on a rectangle, and then they trade with a partner to determine the fraction their partner has shaded. The Activity Synthesis focuses on how to name a single equal part, such as “one-sixth,” rather than talking about all the equal parts in a shape, such as “sixths.” This will be helpful as students use non-unit fractions to name multiple equal parts in the next lesson.
Partition each rectangle into halves, thirds, fourths, sixths, and eighths. Then label each part with the correct fraction.
halves
thirds
fourths
sixths
eighths
Partition the rectangle into 2, 3, 4, 6, or 8 equal-size parts. Shade 1 of the parts.
Display a rectangle with each part labeled as a unit fraction and a rectangle shaded to show the unit fraction, such as:
sixths
one-sixth or
“How do you know the first diagram shows sixths?” (It has 6 equal parts.)
“Why do you think the second diagram is labeled one-sixth?” (Only 1 of the six parts is shaded, so it’s just 1 of the sixths. We are focusing on 1 of the sixths.)
“The first diagram shows sixths because the rectangle is partitioned into six equal parts. Each part is one-sixth. The second diagram shows one-sixth because there are six equal parts and we are describing how many parts are shaded. In this case, one of the parts is shaded.”