Here Comes the Sum

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding 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 add and 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 expression mentally.

  • 212+16\frac{2}{12}+\frac{1}{6}
  • 26+12\frac{2}{6}+\frac{1}{2}
  • 13+12\frac{1}{3}+\frac{1}{2}
  • 13+32\frac{1}{3}+\frac{3}{2}

Sample Response

  • 26\frac{2}{6} or 412\frac{4}{12}: 212=16\frac{2}{12}=\frac{1}{6}, so I doubled the number of sixths.
  • 56\frac{5}{6}: 26+12=26+36\frac{2}{6}+\frac{1}{2}=\frac{2}{6}+\frac{3}{6}.
  • 56\frac{5}{6}: It is the same as the one before because 13=26\frac{1}{3}=\frac{2}{6}.
  • 1561\frac{5}{6}: It is just adding 22\frac{2}{2} to the previous sum.
Activity Synthesis (Teacher Notes)
  • “How do equivalent fractions help us add fractions with unlike denominators?” (It lets us find fractions with the same denominators and then we can just add the numerators.)
  • “How do you decide on the denominator to use for your equivalent fractions?” (We either use a common multiple of the 2 denominators that we know or we can multiply the 2 denominators to find a common multiple.)
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