Introducing Fractions

Fractions are a critical concept for upper elementary students, and it is essential to introduce fractions in a conceptual and meaningful way. When we teach fractions as a series of rules or procedures, students are much more likely to fall behind due to a lack of understanding.

In this post, I’ll share some of my favorite strategies and resources for teaching fractions to third and fourth grade students. While many of these concepts are not explicitly stated in fourth grade fraction standards, it is essential that students have a solid understanding of fractions before moving to more advanced concepts. In fact, I spend a solid two weeks teaching general fraction concepts before I approach my grade level standards.

Introducing Fractions-Fractional Parts

The first goal in introducing fractions is to help students construct the idea of fractional parts of the whole. More than likely, if you ask most third or fourth graders to determine what fraction of the square below is shaded, most students will recognize that one-fourth of the square is shaded. Students may even be able to explain that there are four parts in the whole (denominator) and one part is shaded in (numerator).

However, if you ask the same question with the image below, you may be surprised at the responses you get. Students are simply following the procedure of counting the parts for the denominator are likely to respond with one-third. Students often do not think about the relationship between the part and the whole. Instead, they just count the parts.

When introducing fractions, students need ample experience partitioning a variety of shapes, including irregular 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 use the construction paper to cut out different shapes and partition them into equal pieces to create halves, thirds, etc. Students had to use a variety of shapes, so I didn’t let them cut all squares or even all squares and rectangles. After students partitioned their shapes, they taped the shape to the corresponding piece of chart paper. This allows me to address any misconceptions about equal sized parts.

Third and Fourth Grade Lesson

 

Fourth Grade Worksheet

 

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

Introducing Fractions-Symbols

The second goal is for students to understand fraction symbols. Fraction symbols are often very confusing to students. 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 way to help students develop an understanding is through this Modeling Fractions activity. In this lesson, students take turns drawing a fraction card. After students draw a card, they model that fraction on any of the shapes on their Modeling Fractions worksheet. Students partition the shape into the correct number of equal parts and shade in the appropriate area. Students should also label each fraction to practice using the symbols correctly.

Third Grade Task

 

One of my favorite lessons to reinforce equal parts and fraction symbols involves Play Dough. This lesson is quite a bit different from a traditional math workshop lesson, because it is typically most successful with explicit teacher directions and guidance. This activity can be completed with the teacher in a small group rotation or as a whole group activity.  Students use the Play Dough lid to create a circle. They partition the circle 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.

Third and Fourth Grade Task

 

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.

Introducing Fractions-Parts and Wholes

After teaching equal parts and fraction symbols, it’s time to introduce parts and wholes. This concept is a big, big deal. This will impact all future lessons, so I really slow down and teach for deep understanding.

Cuisenaire Rods are by far my favorite fraction manipulative. I first introduce them when allowing students to explore parts and wholes. 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 the rod designated as the part and the rod designated as the whole.

I have students take out the orange rod and ask which rod is equal to one-half of the rod. Students should identify that the yellow rod is half of the orange rod.  Then, I ask students to find the rod that is one-fifth of the orange rod.  I repeat the process using the brown rod as the whole. When I ask which rod is one-half of the brown rod, some students may respond with the yellow rod, which means they are thinking that the yellow rod is always one-half. It’s important to guide students into finding the rod that has the same relationship with the brown.

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, and I pull students who are really struggling and we complete this together in a small group.

Third and Fourth Grade Task

If I’m teaching third grade, I like to spend a little extra time on parts and wholes to reinforce the idea. In a following lesson, I use pattern blocks to give students the opportunity to see how different wholes can be designated in the same model.

Third Grade Task

Introducing Fractions-Sharing Tasks

After students understand parts and wholes, they should also begin to relate fractions to the idea of fair shares. Students initially perform sharing tasks by distributing items one at a time, and when there are leftover pieces, those items must be subdivided. I love watching how different students approach this differently. 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. When I first started teaching third grade, I thought the brownie task would be too difficult for my students, but I was wrong. It’s true that students may not know how to correctly write a fraction, but I can help with that in the task. My real goal was to get my students thinking about equal parts and equal pieces.

Third Grade Task

In the 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.

Fourth Grade Task

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.

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

You can return to my Starting Place for Teaching Fractions Post here.