What’s the Difference?

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for subtracting fractions with unlike denominators. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to subtract fractions with unlike denominators.

Launch

  • Display the first expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each difference mentally.

  • 23−16\frac{2}{3}-\frac{1}{6}
  • 23−26\frac{2}{3}-\frac{2}{6}
  • 23−46\frac{2}{3}-\frac{4}{6}
  • 23−12\frac{2}{3}-\frac{1}{2}

Sample Response

  • 36\frac{3}{6} or 12\frac{1}{2}: 23−16=46−16\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}
  • 26\frac{2}{6} or 13\frac{1}{3}: It is 16\frac{1}{6} less than the previous difference. 
  • 00: They are equivalent.
  • 16\frac{1}{6}: 23−12=46−36\frac{2}{3}-\frac{1}{2}=\frac{4}{6}-\frac{3}{6}
Activity Synthesis (Teacher Notes)
  • Display the first and last expressions with their differences.
  • “How are the differences related?” (16\frac{1}{6} and 12\frac{1}{2} are 23\frac{2}{3} so I can take away 16\frac{1}{6} and that gives me 12\frac{1}{2} or I can take away 12\frac{1}{2} and that gives me 16\frac{1}{6}.)
Standards
Addressing
  • 5.NF.1·Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. <em>For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)</em>
  • 5.NF.A.1·Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. <span>For example, <span class="math">\(2/3 + 5/4 = 8/12 + 15/12 = 23/12\)</span>. (In general, <span class="math">\(a/b + c/d = (ad + bc)/bd\)</span>.)</span>

15 min

20 min