Sums and Differences of Fractions

10 min

Narrative

This Number Talk encourages students to think about sums that make 10, 100, and one whole and look for ways to use these sums to mentally find the value of different expressions with whole numbers and fractions. The understandings elicited here will be helpful throughout this unit as students add and subtract whole numbers fluently, and add and subtract fractions with the same denominator.

When students identify ways to make 1, 10, or 100, they look for and make use of the properties of operations and the structure of whole numbers and fractions (MP7).

Launch

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

Student Task

Find the value of each expression mentally.

  • 38+6238 + 62
  • 3826+623638\frac{2}{6} + 62\frac{3}{6}
  • 3826+6236+171638\frac{2}{6} + 62\frac{3}{6} + 17\frac{1}{6}
  • 13826+16236+1726138\frac{2}{6} + 162\frac{3}{6} + 17\frac{2}{6}

Sample Response

  • 100: I know 38+6238 + 62 is the same as 40+6040 + 60 if we add 2 to 38 and take away 2 from 62.
  • 10056100\frac{5}{6}: The whole numbers add up to 100 and the fractions 26\frac{2}{6} and 36\frac{3}{6} add up 56\frac{5}{6}.
  • 118 or 11766117\frac{6}{6}: I know 10056+1716100\frac{5}{6} + 17\frac{1}{6} is 117+66117 + \frac{6}{6}, which is 117+1117+1 or 118.
  • 31816318\frac{1}{6} or 31776317\frac{7}{6}: 138+162+17138 + 162 + 17 is 317, and 26+36+26=76\frac{2}{6} + \frac{3}{6} + \frac{2}{6} = \frac{7}{6} or 1161\frac{1}{6}.
Activity Synthesis (Teacher Notes)
  • “How were these expressions the same? How were they different?” (Each has 38+6238 + 62, so I can look for ways to make 100 in each. The last three expressions all have a mixed number with sixths. Some expressions did not have fractions. One expression had fractions that had a sum that was equivalent to 1 whole.)
  • As needed, “How could we look for ways to make 100 in each expression? How could we look for ways to make 1?”
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.

15 min

20 min