standard_description: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Task
The fifth grade teachers are in charge of planning the annual Davis Elementary Fun Run.  The teachers decide that each adult should run $\frac{6}{4}$ as far as each student in grade 5 and each student in grade 1 should run $\frac{3}{4}$ as far as each student in grade 5.
Who has to run the longest distance?  Who has to run the shortest distance?  Explain your reasoning.
The fifth grade students decide that they should each run four laps around the track.  How many laps should each adult and each first grade student run?
Peyton, a fifth grader calculates that he will run a$\frac{1}{2}$ mile.  Write two multiplication equations involving $\frac{1}{2}$, one that shows how many miles each adult will run and one that shows how many miles each first grade student will run.
When Peyton showed the adults his calculations, some of them were confused. Some of the adults thought multiplication always makes a number larger, for example $2\times5$ is bigger than 5. When calculating the distance the first graders ran, Peyton used multiplication but got a smaller number. Explain why the product of 5 and another number is not always greater than 5, and write an example to help the adults understand.
Presley, another fifth grade student, wanted to write the distance she ran in eighths.  She noticed that you could write this equation: $\frac{4}{4}\times\frac{1}{2}$miles = $\frac{4}{8}$ miles.  Explain why in this case multiplying by $\frac{1}{2}$ results in a product that is neither larger nor smaller than $\frac{1}{2}$.


aligns: no