Any 5th-grade teacher knows that Mastering the Conversion of Improper Fractions to Mixed Numbers and vice versa is the foundation of adding and subtracting fractions that require regrouping. Some educators call regrouping fractions, or borrowing but in this article, I’ll refer to it as regrouping.
If your students struggle with this important skill, I have a proven method to get them to be successful. I’ll walk you through the teaching strategies that make this math concept easier for your students to grasp. The answer is to use visual models.
Why Visual Fraction Models Simplify Improper Fractions and Mixed Numbers for 5th Graders
Visual models simplify and make abstract concepts like improper fractions and mixed numbers easier for 5th grade students to grasp. Before you teach your students the procedural method of changing a mixed number to an improper fraction, you will want to develop their conceptual understanding.
Your students need to have a true understanding of how to rename fractions so take it slow and sequence your lessons for mastery.
Step-by-Step Guide: Sequencing Lessons on Improper Fractions and Mixed Numbers
Do not, I repeat DO NOT teach all these concepts in one day. You are asking for trouble! Here is how to sequence your lessons.
- Decomposing Fractions (1-2 days)
- Improper Fractions to Mixed Numbers
- Mixed Numbers to Improper Fractions
Always start your lesson with visual models (or what I call “pictures” for my students) and then move on to solving with numbers.
Teach Decomposing Fractions for 5th Graders (1-2 Days)
Use Visual Models First to Teach Decomposing Fractions
Before I teach my students how to change mixed numbers to improper fractions we review the concept of decomposing fractions. We decompose or “break down” fractions greater than 1 with visual models so students can see how mixed numbers are built.
When you show your students the first example, teach them the proper vocabulary. This builds familiarity with key terms like numerator and denominator. I know it’s tempting but do not call the numerator the “top number”.
Create an anchor chart and have your students copy the terms in their math notebooks or glue a mini-anchor chart in their notebooks like the one below. During the lesson, I also remind my students how to read fractions and that improper fractions are also called “fractions greater than one”.
Move on to the Algorithm of Decomposing Fractions
Now that your students have seen multiple examples with visual models, it’s time to drop the visual models and move on to using only numbers to represent how fractions are decomposed or “broken down”. Detail the concept of decomposing improper fractions into sums of fractions with the same denominator.
Remind students that you have a whole number when the numerator and the denominator are the same. Put a rectangle around the entire fraction since the rectangle looks like a one. Watch the video below to see what I mean.
Using Visual Models to Rename Mixed Numbers to Improper Fractions
Students need to see how mixed numbers are equivalent to improper fractions. In the example below, teach your students how 2 wholes and ¾ are colored in. We want to know how many fourths there are. So we count the total amount.
To get the answer faster, we multiply 2 x 4 and then add the remaining ¾. We do more examples and I ask students if they see a pattern. It is crucial that you get them to notice the pattern. Let them notice the pattern of the steps they need to take to get the answer.
You can get this worksheet HERE.
The pattern is to multiply, add, and then write the denominator. An acronym to help them remember this is MAD. Have your students draw the MAD emoji and remind them that they might get “mad” when you ask them to change a mixed number to an improper fraction.
How to Teach Converting Improper Fractions to Mixed Numbers on Day 2
Teach your students how to change an improper fraction to a mixed number on a different day. Refer them back to the example you did on Day 1 when you decomposed the fractions 10/4 like the example below. Remind them that 10/4 can be read at 2 and 2/4.
There are two ways to name fractions. Ask: When we color 10/4, do we see whole numbers? After we color more examples and determine the mixed numbers, I teach my students that there is a shortcut to drawing and that’s dividing.
The mnemonic device I use is that the numerator is the king and kings have decadent meals and eat as much food as they want so they tend to be “big”, just like the numerator is always bigger than the denominator.
The king lives in a castle so we place him in the castle and put the poor man outside the castle. The poor man works outside and wears a visor, therefor he is called a divisor.
Check out the video below to see what I mean!
Get the Mixed Numbers and Improper Fractions Worksheets
I’ve created worksheets to help students practice changing improper fractions to mixed numbers through step-by-step visual guides. All of these strategies can be done by just using paper and a pencil but I find that having these worksheets takes away the laborious task of students having to keep drawing the fraction bars over and over again.
Also, if you teach this skill whole-class, you will know that your students are coloring the correct fractions. If they draw the fraction bars themselves, sometimes they draw the fractions incorrectly. This happens often with students who struggle in math. My worksheets are aligned with curriculum standards and are Common Core focused. They are sequenced in a logical order that makes sense and builds upon previous skills. You can find them HERE.
Final Thoughts
Mastering fractions in 5th grade is critical and the best way to do this is with conceptual understanding through visual models. Always start every fraction lesson with visual models and you will be golden!
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