# Working with Equivalence

March 13

Hello!

It was so great meeting so many of you at Parent Teacher Conferences last week!  Here’s a look at what we’ve been doing in 4th and 5th grade math and what is coming up.

Fourth graders had a their first fraction test last week.  I was impressed with how well they can use benchmarks to think about the value of fractions.  There was a section where they had to decide whether fractions were closer to 0, ½, or 1.  When the denominators are even numbers, it isn’t very difficult to think about what is equivalent to a half.  However, one question asked them to decide if 4/9 was closer to 0, ½, or 1.  I was impressed with how comfortable the students are with using complex fractions to show their thinking and to think about equivalence.  Many of them were able to write about ½ as being equivalent to 4.5/9 and then stating that 4/9 is half of a ninth away from the halfway point.  Others were able to use pictures or number lines to express their ideas.  Some used explanations and pictures.  Here are some examples of their work.

Fifth graders have been working on adding and subtracting fractions and mixed numbers.  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: