Lesson objective: Apply the skill of comparing fractions with unlike denominators using the most appropriate strategy based on the fractions being compared.
This lesson provides an opportunity for students to apply their knowledge and understanding of comparing fractions with unlike denominators to a fictional mathematical situation. Students are asked to determine which real galaxies a group of ficticious martians could travel to given only a fractional amount of fuel in their spaceship.
Key Concept students will use:

there are three possible relationships between two given numbers with the same unit of reference, a and b: a>b, a<b, or a=b

we can compare two numbers indirectly by comparing them both to a common benchmark

a/b = (nxa)/(nxb) because we have n times as many pieces in the whole. Each piece is n times smaller, so we need n times as many of them to cover the same distance or the same area

finding common denominators is helpful in comparing fractions because it enables us to compare samesized pieces
Skills students will use:
 finding equivalent fractions
 comparing fractions with unlike denominators by comparing indirectly to a common benchmark
 comparing fractions with unliked denominators by using the common denominators method
Students engage in Mathematical Practice 2 (reason abstracly and quantitatively) determine which galaxies the group of martians could travel to using the amount of fuel they have left in their spaceship.
Key vocabulary:
 benchmark
 common denominators
 common numerators
 comparison
 denominator
 equivalent
 numerator
 samesized pieces