Representations of Fractions (Part 1)

10 min

Narrative

The purpose of this Warm-up is to invite students to share what they know about the number 12\frac{1}{2} and elicit ways in which it can be represented. It gives the teacher the opportunity to hear students’ understandings about and experiences with fractions, 12\frac{1}{2} in particular. The fraction 12\frac{1}{2} is familiar to students and will be central in the next activity.

This is the first time students experience the What Do You Know About _____ routine in grade 4. Students should be familiar with this routine from a previous IM grade. However, they may benefit from a brief review of the steps involved.

Launch

  • Groups of 2
  • Display the number 12\frac{1}{2}.
  • “What do you know about this number?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 2 minutes: partner discussion
  • Share and record responses.

Student Task

What do you know about 12\frac{1}{2}?

Sample Response

Sample responses:
  • It is a fraction.
  • I shared half of my sandwich with my friend.
  • It is what we get when we split something into two equal parts.
  • We can “halve” something.
  • Dividing by 2.
  • It is halfway between 0 and 1 on a number line.
  • It is less than 1.
Activity Synthesis (Teacher Notes)
  • “What different ways can we represent 12\frac{1}{2}?” (Cut an object, a rectangle, or another shape into two equal parts, mark the middle point between 0 and 1 on a number line.)
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