Compare without Multiplying

10 min

Narrative

The purpose of this Warm-up is for students to interpret a multiplication expression as a location on the number line. This builds on work students did in the previous lesson, with an emphasis now on precisely locating the expression, using the meaning of multiplication. Students will build on this idea and locate the values of more complex expressions throughout the lesson.

Launch

  • Groups of 2
  • Display the image.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record students’ responses.

Student Task

What do you notice? What do you wonder?

23×5\frac{2}{3} \times 5

Sample Response

Students may notice:
  • There is a number line.
  • Zero and five are the only numbers on the number line.
  • There is a 5 on the number line and in the expression, but there is no 23\frac{2}{3} on the number line.
Students may wonder:
  • Why are there no other numbers on the number line?
  • What is 23×5\frac{2}{3} \times 5?
  • Can we put 23×5\frac{2}{3} \times 5 on the number line?
Activity Synthesis (Teacher Notes)
  • “How can you find the approximate location of 23×5\frac{2}{3} \times 5 on the number line?” (I can find the value and add more tick marks to locate it exactly. I can divide the number line between 0 and 5 into 3 equal parts and 23×5\frac{2}{3} \times 5 will be the second of those tick marks.)
Standards
Addressing
  • 5.NF.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
  • 5.NF.B.5.a·Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

15 min

20 min