Previously, students worked with fractions whose features encouraged different comparison strategies. For instance, the fractions might:

• Have a common numerator or a common denominator.
• Be noticeably greater or less than a familiar benchmark, and their distance from a benchmark could be discerned.
• Have related denominators, in which one denominator is a factor or a multiple of the denominator of the other, making it intuitive to rewrite one fraction into an equivalent fraction with the same denominator as the second fraction.

In this lesson, students encounter pairs of fractions with different denominators, in which neither denominator is a factor or multiple of the other, and for which other means of comparison are not feasible or intuitive. These fractions motivate students to find another way to compare: by rewriting both fractions as equivalent fractions with a shared denominator.

How did students’ earlier work on factors and multiples support their work in this lesson? What surprised you about the insights students brought forth to help them find common denominators? What challenges did you not anticipate seeing?