Sums and Differences of Fractions

10 min

Narrative

This Number Talk encourages students to rely on what they know about fractions to mentally find the value of differences with mixed numbers. 

Launch

  • Display one 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.

  • 238−382\frac{3}{8} - \frac{3}{8}
  • 238−582\frac{3}{8} - \frac{5}{8}
  • 238−22\frac{3}{8} - 2
  • 238−1782\frac{3}{8} - 1\frac{7}{8}

Sample Response

  • 2: The fraction being subtracted, 38\frac{3}{8}, is the same as the fraction in the mixed number, so what's left is the whole number, 2.
  • 1681\frac{6}{8}: I know that 58\frac{5}{8} is 28\frac{2}{8} more than 38\frac{3}{8}, so I subtracted another 28\frac{2}{8} from 2, which gives 1681\frac{6}{8}.
  • 38\frac{3}{8}: I subtracted 2 from the whole number in 2382\frac{3}{8}.
  • 48\frac{4}{8}: 1781\frac{7}{8} is 18\frac{1}{8} less than 2, so I added back 18\frac{1}{8} to the value of 238−22\frac{3}{8} - 2.

Synthesis

  • “How did the first few expressions help you find the value of the last expression?”
  • “When subtracting 1781\frac{7}{8}, why might it be helpful to first think about subtracting 2?” (2382\frac{3}{8} has a whole number and a fraction, so we can easily subtract 2 from the whole number and then put back the extra 18\frac{1}{8} that we took out.)
  • Consider asking:
    • “Did anyone have the same strategy but would explain it differently?”
    • “Did anyone approach the expression in a different way?”
Standards
Addressing
  • 4.NF.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
  • 4.NF.B.3.c·Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

20 min

15 min