Solve Problems

10 min

Narrative

The purpose of this Estimation Exploration is for students to reason about the size of a complex fraction sum with large denominators. Students can see that 1 is a good estimate because one fraction is small and the other is close to 1. In the Activity Synthesis, students refine this estimate to explain why the value of the sum is a little greater than 1. 

Launch

  • Groups of 2
  • Display the expression.
  • “What is an estimate that’s too high? Too low? About right?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Record responses.

Student Task

What is the value of the sum?

317+1719\frac{3}{17}+\frac{17}{19}

Record an estimate that is:

too low about right too high

Sample Response

Sample responses:

  • Too low: less than 1
  • About right: 1 to 1141\frac{1}{4}
  • Too high: greater than 1141\frac{1}{4}
Activity Synthesis (Teacher Notes)
  • “How do you know that the sum is greater than 1?” (1719\frac{17}{19} is 219\frac{2}{19} short of a whole. Since 17ths are bigger than 19ths, adding 317\frac{3}{17} makes it greater than 1.)
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