Fractions as Partial Quotients

10 min

Narrative

The purpose of this What Do You Know about _____? is for students to share what they know about a sum of fractions. The fractions are selected because they represent whole numbers and the whole-number values are visible. Students will work with expressions such as these throughout this lesson.

Launch

  • Display the number.
  • “What do you know about 606+66\frac{60}{6} + \frac{6}{6}?”
  • 1 minute: quiet think time
Teacher Instructions
  • Record responses.

Student Task

What do you know about 606+66\frac{60}{6} + \frac{6}{6}?

Sample Response

Sample responses:

  • There are two fractions being added.
  • One fraction is greater than 1, and one fraction is equal to 1.
  • Both fractions are sixths.
  • It equals 666\frac{66}{6}.
  • 606=10\frac {60}{6} = 10 and 66=1\frac {6}{6} = 1, so it equals 11.

Synthesis

  • “What are some expressions that have the same value as 606+66\frac{60}{6} + \frac{6}{6}?” (10+110 + 1, 11, (60÷6)+(6÷6)(60 \div 6)+ (6 \div 6))
Standards
Building On
  • 5.NF.3·Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <em>For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</em>
  • 5.NF.B.3·Interpret a fraction as division of the numerator by the denominator <span class="math">\((a/b = a \div b)\)</span>. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <span>For example, interpret <span class="math">\(3/4\)</span> as the result of dividing <span class="math">\(3\)</span> by <span class="math">\(4\)</span>, noting that <span class="math">\(3/4\)</span> multiplied by <span class="math">\(4\)</span> equals <span class="math">\(3\)</span>, and that when <span class="math">\(3\)</span> wholes are shared equally among <span class="math">\(4\)</span> people each person has a share of size <span class="math">\(3/4\)</span>. If <span class="math">\(9\)</span> people want to share a <span class="math">\(50\)</span>-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</span>

15 min

20 min