Stories with Fractions

10 min

Narrative

This Number Talk encourages students to think about equivalent forms of whole numbers and decomposing fractions in order to subtract. When students consider equivalent fractions, look for ways to decompose fractions, or use the structure of mixed numbers to find the value of each difference, they look for and make use of structure (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.

  • 1−8101 - \frac{8}{10}
  • 1410−8101\frac{4}{10} - \frac{8}{10}
  • 2410−8102\frac{4}{10} - \frac{8}{10}
  • 10510−81010\frac{5}{10} - \frac{8}{10}

Sample Response

  • 210\frac{2}{10}: 1 is 1010\frac{10}{10} and 1010−810=210\frac{10}{10} - \frac{8}{10} = \frac{2}{10}.
  • 610\frac{6}{10}: The number being subtracted is the same but the first number here is 410\frac{4}{10} more than the first number earlier, so the difference here is 410\frac{4}{10} more than 210\frac{2}{10}, which is 610\frac{6}{10}.
  • 16101\frac{6}{10}: 24102\frac{4}{10} is 1 more than the first number in the problem before this, so the difference here is 1 more than 610\frac{6}{10}, which is 16101\frac{6}{10}.
  • 97109\frac{7}{10}: We’re subtracting the same number (810\frac{8}{10}) but the first number is 81108\frac{1}{10}more than that in the problem before this. 8110+1610=97108\frac{1}{10} + 1\frac{6}{10} = 9\frac{7}{10}.
Activity Synthesis (Teacher Notes)
  • “How are these expressions alike?” (All involve subtracting 810\frac{8}{10} from a number that is at least 1. To subtract, it’s helpful or necessary to decompose a 1 or to write an equivalent fraction.)
  • “How did you use earlier expressions to help you find the values of later expressions?”
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