Representations of Fractions (Part 2)

10 min

Narrative

This Warm-up prompts students to carefully analyze and compare the features of four partitioned shapes. It allows the teacher to hear the terminologies students use to talk about fractions and fractional parts. In making comparisons, students have a reason to use language precisely (MP6).

Launch

  • Groups of 2
  • Display the image.
  • “Pick 3 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
Shape. Square partitioned into 4 equal smaller squares.

B
circle partitioned into 3 equal parts.

C
square partitioned into 3 unequal parts.

D
shape. hexagon partitioned into 3 equal parts. 1 part shaded.

Sample Response

Sample response:

  • A, B, and C go together because the parts are clear, or unshaded.
  • A, B, and D go together because they are partitioned into equal parts.
  • A, C, and D go together because they have straight sides.
  • B, C, and D go together because they are partitioned into 3 parts. 

Synthesis

  • “What does the shaded part in D represent?” (13\frac{1}{3} or one-third of the shape)
  • Shade one part of B and C.
  • “Is each shaded part one-third of the shape as well?” (Yes for B, No for C)
  • “Why is the shaded part not one-third of the square in C?” (The parts aren’t equal in size.)
  • Shade one part of A. “Is it a third of the square?” (No, it is 14\frac{1}{4} or one-fourth.)
Standards
Building On
  • 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>.
Building Toward
  • 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

20 min

15 min