Use Common Denominators to Compare

5 min

Narrative

The purpose of this Warm-up is to elicit what students know about the numbers 15 and 30, preparing them to work with fractions whose denominators are factors of 15 and 30 later in the lesson. While students may bring up many things about these numbers, relating the two numbers by their factors and multiples is the important discussion point.

Launch

  • Display the numbers.
  • “What do you know about 15 and 30?”
  • 1 minute: quiet think time
Teacher Instructions
  • Record responses.

Student Task

What do you know about 15 and 30?

Sample Response

Sample responses:

  • They are greater than 10.
  • 5×3=155\times3 = 15 and 5×6=305\times6 = 30
  • One is twice the other, or 15×2=3015\times2 = 30.
  • They are both multiples of 3 and 5.
  • One is 15 more than the other.
  • Every other multiple of 15 is a multiple of 30.
Activity Synthesis (Teacher Notes)
  • If no students mentioned factors of 15 and 30, ask them about it.
  • “What are the factors of 15?” (1, 3, 5, 15)
  • “What are the factors of 30?” (1, 2, 3, 5, 6, 10, 15, 30)
  • “What factors do they have in common?” (1, 3, 5, 15)
  • “Do 15 and 30 have any common multiples? What are some of them?” (30, 60, 90)
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.
Building Toward
  • 4.NF.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • 4.NF.A.2·Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols <span class="math">\(&gt;\)</span>, =, or <span class="math">\(&lt;\)</span>, and justify the conclusions, e.g., by using a visual fraction model.

20 min

20 min