Apply Fraction Multiplication

10 min

Narrative

The purpose of this Number Talk is to for students to demonstrate strategies and understandings they have for multiplying fractions. These understandings help students develop fluency and will be helpful later in this lesson when students solve problems involving fraction multiplication.

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.

  • 13×35\frac {1}{3} \times \frac {3}{5}
  • 23×35\frac {2}{3} \times \frac {3}{5}
  • 53×35\frac {5}{3} \times \frac {3}{5}
  • 23×135\frac {2}{3} \times \frac {13}{5}

Sample Response

  • 315\frac {3}{15} or 15\frac {1}{5}: 35\frac {3}{5} is equal to 3×153 \times \frac {1}{5} so 13\frac {1}{3} of that 35\frac {3}{5} is going to be 15\frac {1}{5}.
  • 615\frac {6}{15} or 25\frac {2}{5}: I doubled the answer from the first problem.
  • 1 or 1515\frac {15}{15}: 33×35=35\frac {3}{3} \times \frac {3}{5} = \frac {3}{5} and 23×35=25\frac {2}{3} \times \frac {3}{5} = \frac {2}{5} and 35+25=55\frac {3}{5} + \frac {2}{5} = \frac {5}{5} or 1.
  • 2615\frac {26}{15} or 111151\frac {11}{15}: I multiplied the numerators to get the numerator in the product and I multiplied the denominators to get the denominator in the product.
Activity Synthesis (Teacher Notes)
  • “Did you use the same strategy to find the product of the first and last expressions? Why or why not?” (For the first one, it was easy to think about what 13\frac{1}{3} of 35\frac{3}{5} is. For the last one, I needed to multiply the numerators and then the denominators because it isn’t easy for me to picture in my head.)
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>

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