# Comparing Fractions

## Baking

Justin and Annie are baking cakes for a school fundraiser. Annie's recipe calls for 2 2/3 cups of flour. Justin's cake needs 11/12 as much flour as Annie's. How does the amount of flour needed for Annie's cake compare to that of Justin's?

## Student Misconceptions and Mistakes

Oftentimes, students do not know where to begin. Since the problem asks us to compare, the student first needs to identify what they should compare and then how to set the problem up. There are a couple of strategies that the student can use, so they should pick the one that best suits their ability, but also one that they are capable of explaining since that is part of their answer. Students should be able to justify their work.

Students may pick the incorrect operation, or compute incorrectly. For example, subtracting 11/12 from 2 2/3 would show a lesser amount, but the operation would be incorrect. Students who like to stick to steps to solve problems would set the problem up as 11/12 of 2 2/3 ____ 2 2/3. They could do the computation (multiply) the sides and compare. Students who have an understanding of fractions would realize that 11/12 is less than 1, so Justin is using a lesser amount of flour than Annie. This type of learner would not have to actually do the math, but could make inferences about the solution based on their prior knowledge. Visual learners might draw a model.

Another mistake students might make is not answering the question and/or explaining their solution. The explanation is part of the task, so student would have to be able to explain their thinking.