Problem Solving with Line Plots

10 min

Narrative

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

Launch

  • Display the first 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 students’ answers and strategies.
  • Keep the expressions and the work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 13×18\frac{1}{3}\times18
  • 23×18\frac{2}{3}\times18
  • 43×18\frac{4}{3}\times18
  • 53×18\frac{5}{3}\times18

Sample Response

  • 6: 18÷3=618 \div 3=6
  • 12: I doubled the product from the first problem.
  • 24: I doubled the product again.
  • 30: I found 5 times the value of the first product.
Activity Synthesis (Teacher Notes)
  • “What patterns do you notice in the products?” (All have 18 as one factor, and it’s always some number of thirds. Once I know the value of 13×18\frac{1}{3} \times 18, I can find the rest by multiplying by the number of thirds.)
Standards
Addressing
  • 5.NF.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • 5.NF.B.4·Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

25 min