Compare and Order Fractions

10 min

Narrative

This Number Talk encourages students to think about multiples of 5, 6, and 12—numbers that students will see as denominators later in the lesson. It also prompts students to rely on doubling and on properties of operations to mentally solve multiplication problems. The reasoning elicited here will be helpful later in the lesson when students compare fractions by finding equivalent fractions with a common denominator.

To find products by doubling or by using properties of operations, students need to look for and make use of structure (MP7).

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 answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 5×65 \times 6
  • 5×125 \times 12
  • 6×126 \times 12
  • 11×1211 \times 12

Sample Response

  • 30: I know the fact by heart.
  • 60: I know that 12 is twice 6, so 5×125 \times 12 is 10×610 \times 6.
  • 72: Six times 12 is 12 more than 5 times 12.
  • 132: I added 5×125 \times 12 and 6×126 \times 12 to get 11×1211 \times 12.
Activity Synthesis (Teacher Notes)
  • “How do the first three expressions help you find the value of the last one?”
Standards
Building On
  • 4.OA.4·Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.
  • 4.OA.B.4·Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

20 min

15 min