Use Multiples to Find Equivalent Fractions

10 min

Narrative

The purpose of this Warm-up is to draw students’ attention to the multiplicative relationships between the numerators and denominators of two equivalent fractions. These observations will be helpful later as students use the idea of multiples to generate equivalent fractions. 

While students may notice and wonder many things about these equations, highlight observations about a factor relating the numbers in the two sides of each equation.

Launch

  • Groups of 2
  • Display the image.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

  • 13=26\frac{1}{3} = \frac{2}{6}
  • 23=46\frac{2}{3} = \frac{4}{6}
  • 33=66\frac{3}{3} = \frac{6}{6}
  • 43=86\frac{4}{3} = \frac{8}{6}

Sample Response

Students may notice: 

  • There are four equations with a fraction on each side of the equal sign.
  • The fraction on the left side has 3 for the denominator. The fraction on the right has 6 for the denominator.
  • The numerators on the left side are 1, 2, 3, and 4. The ones on the right are 2, 4, 6, and 8. They each follow a pattern.
  • Each pair of fractions are equivalent.
  • The first two pairs of fractions are less than 1. The third is 1. The last pair is greater than 1.

Students may wonder:

  • What might the equations look like if we continued the pattern?
  • Why do the numerators on each side of the equations change, but the denominators don’t?
  • Are each pair of fractions really equivalent?
  • Are the fractions on the right side of the equal sign twice the size of those on the left?
Activity Synthesis (Teacher Notes)
  • “How are the numbers on the right side of each equal sign related to the numbers on the left?” (Each number on the right is twice the number on the left.)
  • “Are the fractions on the right twice the size of the fractions on the left?” (No, they are the same size. They are just divided into different numbers of equal parts.)
Standards
Addressing
  • 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