Posted on 03/24/2018 at 09:34 AM by Blog Experts
Fractions, Oh My!
I used to hate fractions. Mostly because I didn’t have a conceptual understanding of them. My experiences with fractions have always been procedural. My recent experiences have been different and I have come to understand how amazing fractions are! Here are few things I have discovered about fractions.
Fractions can be conceptualized for students if read using the unit fraction. Instead of saying 21 fourths compared to 21 one-fourths. SInce 21 pieces of one fourth size creates a better picture, students are also able to conceptually understand fractions.
Fractions and whole numbers are both in our number system. Giving students similar experiences with fractions as whole numbers will help them think of fractions as numbers. For example, finding combinations of 5 (1+4, 2+3) allows student to use the strategy Make Ten when solving the facts: 8+5 = 8+2+3 = 10+3 = 13. This can also be applied to fractions. ½ + ⅝ = ½ + 4/8 + ⅛ = ½ + ½ + ⅛ = 1 + ⅛ = 1 ⅛ WOW, no common denominators needed!
I discovered there is a reason why invert and multiply works when dividing by a fraction. I wonder how many teachers know why this works?
Huge misconceptions are developed if fractions are taught as parts of wholes and sets. In the 3-5 grades, students should ONLY be experiencing fractions as parts of wholes. As they move into middle school, then ratios are introduced and students explore sets which can be parts of wholes but can also be parts of parts. In Marilyn Burn’s recent blog, Can ⅓ + ⅓ = 2/6? It seemed so!, she discusses why intermixing these concepts can be so confusing to students.