Put It All Together: Add and Subtract Fractions

10 min

Narrative

The purpose of this Number Talk is for students to use different strategies to add fractions. Each pair of fractions has 18\frac{1}{8}, and the difference between the expressions is the denominator of the second fraction, which is chosen to suggest different strategies for finding a common denominator. Students will explore these strategies in depth in this lesson.

Launch

  • Groups of 2
  • Display the first problem.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record students’ answers and strategies.
  • Keep the problems and the work displayed.
  • Repeat with each problem.
  • “Discuss your thinking with your partner.”

Student Task

Find the value of each expression mentally.

  • 18+58\frac{1}{8} + \frac{5}{8}
  • 18+616\frac{1}{8} + \frac{6}{16}
  • 18+13\frac{1}{8} + \frac{1}{3}
  • 18+512\frac{1}{8} + \frac{5}{12}

Sample Response

  • 68\frac{6}{8} (or equivalent): I just found 1+51+5 and knew it was eighths.
  • 48\frac{4}{8} (or equivalent): I know 616\frac{6}{16} is 38\frac{3}{8} and then I combined the eighths.
  • 1124\frac{11}{24} (or equivalent): I used 24 as a common denominator.
  • 1324\frac{13}{24} (or equivalent): I used 24 as a common denominator.
Activity Synthesis (Teacher Notes)
  • “How did you decide which denominators to use when you found the sums of the fractions?” (The first two were the easiest because I could use eighths. For the others, I used the product of the denominators for 8 and 3, and then I knew 24 also would work for 8 and 12.)
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>

20 min

15 min