Fifth Grade Math: Mixed Numbers and the Distributive Property. Is That Possible?

Fifth graders have been working operations with fractions.  In fourth grade, they only added fractions with like denominators.  Now, the expectation is to add and subtract with unlike denominators.  They have been using their understandings of equivalence from fourth grade to create common denominators.  Most have been successful with this.

The difficulty comes when we encounter something like this: 5 1/3 – 2 ⅝.  Once we create common denominators, our fractions are 5 8/24 – 2 15/24. It is not easy to subtract 15/24 from 8/24.  We shared a number of strategies in class, which included converting to improper fractions, counting up or back and representing it on a number line, and regrouping by borrowing a whole from the whole number and renaming the fraction.  Most students found the last strategy to be the most manageable for them, but they can use whatever they feel most comfortable with. If they find they are having some difficulty with the concept, here is the link to a video that explains it very clearly:

https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-add-sub-mix-num-w-unlike-den/v/subtracting-mixed-numbers-with-regrouping

Fifth graders have also been working diligently on multiplying fractions and mixed numbers.  I’ve been making the students hungry by looking at problems that involve sharing brownies and square pizzas!  Not only have we been looking at multiplying proper fractions, but also thinking about mixed numbers. We have worked with a number of scenarios to find area using mixed numbers.  Some students were surprised to realize that we can use the distributive property (which they have been using since 3rd grade for whole number multiplication) and apply it to mixed numbers.  Below is an example of how it works. We can split up our numbers into the wholes and the parts and then multiply. This would be a way to multiply 5 2/8 by 2 ⅓.

Once all of the sections of the array have been multiplied, all you need to do is add up the partial products.

Have a wonderful Spring Break and enjoy any holidays you may be celebrating!