Name Parts as Fractions

10 min

Narrative

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.”

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 rectangles that go together. Be ready to share why they go together.”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2–3 minutes: partner discussion
  • Share and record responses.

Student Task

Which 3 go together?

A
Diagram. Rectangle partitioned into 2 parts.

B
Diagram. Rectangle partitioned into 3 equal parts, 1 of them shaded.

C
Diagram. Rectangle partitioned into 2 parts.

D
Diagram. Rectangle partitioned into 2 parts.

Solution Steps (5)
  1. 1
    Examine shape A
    →Rectangle into 2 equal parts → halves, each part is 1/2
  2. 2
    Examine shape B
    →Rectangle into 3 equal parts → thirds, each part is 1/3
  3. 3
    Examine shape C
    →Rectangle into 2 UNEQUAL parts → cannot label with fractions
  4. 4
    Examine shape D
    →Rectangle into 2 equal parts → halves, each part is 1/2
  5. 5
    Group by equal parts
    →A, B, D have equal parts and can be labeled 1/2 or 1/3; C has unequal parts

Sample Response

Sample responses:

A, B, and C go together because:
  • They have a vertical line or part of a vertical line in the partition.
A, B, and D go together because:
  • They have equal-size parts.
A, C, and D go together because:
  • They have two parts.
B, C, and D go together because:
  • They are partitioned into rectangles.
  • They are partitioned with a straight cut.
Activity Synthesis (Teacher Notes)
  • “Can we label the parts of each rectangle with the same fraction? Why or why not?” (We can label the parts in A, B, and D with the same fraction because they are equal in size, but not in C because the parts aren’t the same size.)
  • “What do we call the parts in A, B, and D?” (“Halves” in A and D, and “thirds” in B.)
  • “What fractions do we use to label the parts in A, B, and D?” (12\frac{1}{2} in A and D, and 13\frac{1}{3} in B.)
Standards
Building On
  • 2.G.3·Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
  • 2.G.A.3·Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words <em>halves</em>, <em>thirds</em>, <em>half of</em>, <em>a third of</em>, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Building Toward
  • 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.

15 min

20 min