Different Ways to Subtract

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate the strategies and understandings they have for adding and subtracting a fraction and a whole number. For these problems, students do not need to focus on a common denominator as either the numbers have the same denominator or one of the numbers in the sum is a whole number. Their strategies for thinking about the sums and the differences will be helpful throughout the lesson as students calculate more complex differences involving mixed numbers.

Launch

  • 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.

Student Task

Find the value of each expression mentally.

  • 3+783+\frac{7}{8}
  • 3−783-\frac{7}{8}
  • 158+681\frac{5}{8}+\frac{6}{8}
  • 158−681\frac{5}{8}-\frac{6}{8}

Sample Response

  • 3783\frac{7}{8} (or equivalent): I just put the two numbers together.
  • 2182\frac{1}{8} (or equivalent): I thought of 3 as 2 and 1, and took 78\frac{7}{8} from 1.
  • 2382\frac{3}{8} (or equivalent): I added 38\frac{3}{8} to get 2 and then 38\frac{3}{8} more.
  • 78\frac{7}{8} (or equivalent): I took away 58\frac{5}{8} to get 1 and then 18\frac{1}{8} more.
Activity Synthesis (Teacher Notes)
  • “How did you find the value of 158+681\frac{5}{8} + \frac{6}{8}?” (I made a fraction from the mixed number and then added the numerators. I added on to get 2, and then added the rest of the eighths.)
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