# Teaching Fractions Conceptually

In this post I’ve shared some of my favorite lessons for teaching fraction concepts. These lessons are designed to introduce fractions in a conceptual and meaningful way that doesn’t overly rely on rules or procedures.

Most of these teaching fractions lessons can be used for both third and fourth grade students. While many of the concepts taught through these lessons are not explicitly stated in 4th grade standards, it is essential that students have a solid understanding of fractions before moving to more advanced concepts. You can find the 3rd grade lessons here and the 4th grade lessons here.

## Fractional Parts

When introducing and teaching fractions, students need ample experience partitioning shapes into an equal number of parts. To introduce this, I place several pieces of chart paper around the room and label each piece of paper with halves, thirds, fourths, and fifths. Then, I give students a piece of construction paper, and they cut out different shapes and partition them into equal pieces to create halves, thirds, etc. After students partition their shapes, they tape the shape to the corresponding piece of chart paper. This allows us to discuss any misconceptions about equal sized parts.

You can follow the activity with this worksheet that moves students beyond traditional fractions. It forces students to think about the size of the whole and parts, rather than solely count the number of parts.

How long you spend on this concept depends on your students. More than likely, third grade students will need at least two lessons, where a fourth grade students may only need one fractional part lesson.

## Teaching Fraction Concepts: Symbols

The second goal is for students to understand fraction symbols. The way that we write fractions with a top and a bottom number is a convention. This is one of those things you tell students.

• Numerator-This is the counting number. It tells how many shares or parts we have. It tells how many have been counted.
• Denominator-This tells what fractional part is being counted. It tells how many parts are in a whole.

One of my favorite lessons to reinforce equal parts and fraction symbols involves Play-Doh. This activity can be completed with the teacher in a small group rotation or as a whole group activity.

Students use Play-Doh to create circles and rectangles. They partition the shapes into a variety of parts and observe what happens to the size of pieces as the number of parts increases. Students also use this activity to think about how many parts are needed to make a whole.

If you’re teaching fourth grade, the previous two lessons are typically all you need to teach before moving on to parts and wholes. However, if you’re teaching third grade, it’s best to spend a little more time on fraction symbols to allow students to solidify their understanding.

## Parts and Wholes

After teaching equal parts and fraction symbols, the next step in teaching fraction concepts is to introduce parts and wholes. This concept is a big, big deal, so I slow down and teach for deep understanding.

Cuisenaire Rods are by far my favorite fraction manipulative. By using different-length rods as the part and the whole, students develop their understanding that fractions such as 1/2 or 3/4 are not names for specific rods. Instead, they describe the relationship between parts and wholes.

The task below is truly amazing. It really is so powerful for students. Look at the last two problems. That’s not easy, but students CAN do it. I typically have students complete this in their groups (I miss those days). I meet with students who are struggling, and we complete this together in a small group.

This can also be completed digitally. Students use virtual manipulatives (mine used Braining Camp) and copy and paste their creation to the slides.

What site they use for their virtual manipulatives isn’t important. It’s just important that students are using some type of resource to give students the opportunity to explore and manipulate fractional parts.

If I’m teaching third grade, I like to spend a little extra time on parts and wholes to reinforce the idea. You can use lessons like the one shared below to reinforce the concept of fractional parts using pattern blocks.

## Fraction Size

Before teaching fraction comparison, students need time to explore fraction size. For students to develop sound fraction sense, they must begin to reason about the size of fractions and fractional parts, especially in relation to benchmark numbers such as zero, one whole, and one-half.

However, even if students are face-to-face, I prefer the digital version of this lesson. Students can insert pictures of their virtual manipulatives to prove each of their answers.

After students understand parts and wholes, they should begin to relate fractions to the idea of fair shares.

In this pizza task, I intentionally included problems where there would be whole pizzas shared, as well as only fractional parts shared, because I don’t want to isolate mixed numbers into a unit of their own. Instead, I use this lesson to transition us into mixed numbers and fractions greater than one. Some students first share the whole items and distribute the leftovers, and other students slice every piece into equal parts and then distribute the pieces.

This lesson can also be completed digitally. Students will work on Google Slides and don’t need any special manipulatives.

After I’m certain students understand equal parts, fraction symbols, parts and wholes, and sharing, I’m ready to move them to fractions on a number line. As you can see, fourth grade will move through these lessons fairly quickly, while third grade will want to stay on these concepts for a bit longer. Remember, don’t rush it. These concepts are the foundation for everything else they will learn in fractions.

## More Resources for Teaching Fraction Concepts

You can find all the third grade lessons here and all of the fourth grade lessons here.

Additionally, you can return to my Starting Place for Teaching Fractions Post here.

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