Situations about Multiplying Fractions

10 min

Narrative

The purpose of this Number Talk is for students to demonstrate strategies and understandings they have for multiplying unit fractions. These understandings help students develop fluency and will be helpful later in this lesson when students make sense of a unit fraction multiplied by a non-unit fraction.

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 strategy.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 12×12\frac{1}{2} \times \frac{1}{2}
  • 13×12\frac{1}{3} \times \frac{1}{2}
  • 14×12\frac{1}{4} \times \frac{1}{2}
  • 15×12\frac{1}{5} \times \frac{1}{2}

Sample Response

  • 14\frac{1}{4}: I know half of a half is one fourth.
  • 16\frac{1}{6}: I pictured a diagram that showed 12\frac{1}{2} cut into 3 equal pieces.
  • 18\frac{1}{8}: I multiplied the denominators.
  • 110\frac{1}{10}: I doubled the 5 in the denominator because the pieces will be half the size.

Synthesis

  • “What patterns do you notice?” (The numerators are all 1. The denominators are all even numbers. The fractions are getting smaller. Each time, we find a smaller fraction of 12\frac {1}{2}.)
Standards
Addressing
  • 5.NF.4.a·Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. <em>For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)</em>
  • 5.NF.B.4.a·Interpret the product <span class="math">\((a/b) \times q\)</span> as <span class="math">\(a\)</span> parts of a partition of <span class="math">\(q\)</span> into <span class="math">\(b\)</span> equal parts; equivalently, as the result of a sequence of operations <span class="math">\(a \times q \div b\)</span>. <span>For example, use a visual fraction model to show <span class="math">\((2/3) \times 4 = 8/3\)</span>, and create a story context for this equation. Do the same with <span class="math">\((2/3) \times (4/5) = 8/15\)</span>. (In general, <span class="math">\((a/b) \times (c/d) = ac/bd\)</span>.)</span>

20 min

15 min