This is a strategic problem solving activity that can be conducted in groups. I performed this as a carousel activity and visited the groups to join in on their fruitful discussion.
When we are working on problem solving, it's important for students to correctly identify the operation and apply it correctly to the given figures. When fractions come into the picture, this can become confusing. One strategy students found helpful was to substitute the story with whole numbers to develop the number sentence. Also, it's useful for students to write out the number sentence for each option first and then look at the problem.
It's easier to share an example, I've included how I would discuss with students below:
Problem: Which of the following problems can be solved using the expressions 3 divided by 1/3 ?
Option 1: 3 people equally share 1/3 of pizza. How much pizza does each person eat?
Discussion Point – Each is sharing part of the pizza, one-third of the whole pie that is. So the division story would be one-third divided by one-third. Each person would have one-ninth of the whole pie.
Option 2: A family ate 1/3 of a 3 foot sandwich. How much did they eat?
Discussion Point – The family collectively ate one-third of this three-foot sandwich. The operative word here being “of”. This means the family ate one-third times three meaning they ate one foot of the sandwich.
Option 3: A pie requires 1/3 pounds of apples. How many apples are needed for the 3 pies?
Discussion Point – Each pie needs one-third of a pound of apples. Meaning one-third for Pie One, one-third for Pie Two and one-third for Pie Three. This is repeated addition (or multiplication), one-third plus one-third plus one-third, or one-third times three. Either way, you’ll need one pound of apples to make the three pies.
Option 4: How many 1/3 lbs of bacon can you get from a 3 lb package?
Discussion Point – If we are splitting up a three pound packet of bacon, we want to know how many groups of one-third pounds there are in the three pounds. Therefore, it would be three divided by one-third, and there would be nine segments of the whole package that are one-third pounds each.