Teaching Equivalent Fractions | A Framework to Sequence Your Lessons

 

Introducing Equivalent Fractions to 3rd Graders: A Step-by-Step Lesson Plan

Teaching equivalent fractions to 3rd graders can be easier when lessons are thoughtfully structured. Starting with hands-on exploration and progressing toward abstract understanding ensures students build confidence and deepen their fraction sense. Here’s a framework for your first lessons on teaching equivalent fractions. Please note that each stage will likely take multiple days for students to practice and explore.

Stage 1: Explore Fractions with Manipulatives

Begin by introducing students to the concept of fractions as parts of a whole. Use manipulatives such as fraction bars (my personal favorite!) to help students visualize fractions. Even if students need to partner up and share sets, fraction bars provide a consistent and clear representation of fractional parts. For example:

• Show students the one whole, ¼, and ½ pieces of a fraction bar set. Explain that the fraction bars visually show one whole divided into halves and fourths. Show them that it takes two ½ pieces to equal one whole and four ¼ pieces to equal one whole.

• Ask students to use their own pieces to find how many ¼ pieces equal one ½ piece.

Next, guide students to experiment further with these manipulatives. Encourage them to create their own fraction pairs and discover equivalent fractions on their own. Allow students to share their observations, like noticing that two ⅙ pieces cover the same distance as one ⅓ piece.

Let students share their findings either as a whole class or in groups that students might do a gallery walk to visit.

Wrap up the lesson by emphasizing the idea that equivalent fractions represent the same value, even though they may look different.

Stage 2: Build Understanding with Visuals

Once students are comfortable with manipulatives (which will likely take multiple days), transition to creating their own visuals. Provide fraction bars for tracing so students can draw accurate fraction models (e.g., bar diagrams). Encourage them to:

• Trace pieces of fraction bars onto paper to represent fractions such as ½ and ¼.

• Fold paper strips to create their own fraction representations and compare parts visually.

This activity helps students internalize the concept of equivalent fractions. For example, they can see that tracing two ¼ pieces results in the same length as one ½ piece.

To extend this activity, ask students to label their bar diagrams and explain their reasoning. This will naturally lead into creating number lines as they start to recognize consistent patterns.

Stage 3: Introduce Number Lines

Number lines provide a powerful way to show relationships between equivalent fractions and to compare benchmark fractions. Begin by having students trace fraction bars in order to create a number line. Have them start with tracing a line only across the top of the one whole fraction bar and label one end zero and the other end 1. Repeat that same line three times below the original so there are 4 number lines at least one inch apart. 

Next, on the second number line, line up a ½ fraction bar piece at 0 on the number line and mark where it ends on the number line, labeling it ½. Explain that this is a "benchmark" on the number line as ½ is easy to find at the center between 0 and 1. Have students line up two halves and label the right side 2/2, discussing that two halves is equal to one whole.

Next, have students do the same type of marking and labeling with ¼ (along with 2/4 and 3/4) and ⅛ (along with two-eighths, three-eighths, etc.) on the remaining two number lines. Let them explore equivalent fraction pairs using the number lines instead of the fraction bars.

The next day's lesson would be to repeat tracing and labeling the fractions bars to make new number lines for one whole, thirds, and sixths. You may also have students create 3 more number lines with one whole, fifths, and tenths.

As students become more confident, guide them toward creating their own smaller-scale number lines (meaning number lines that don't take up the entire width of a page) without tracing fraction bars.

As they are ready, move students toward including different denominators on the same number line (e.g., thirds and sixths) to emphasize the relationships between fractions. For example:

• Plot ⅓ and ⅙ on the same number line and discuss how the fractions align.

• Use the number lines to compare benchmark fractions like ½, ¼, and ⅓.

Encourage students to find equivalent fractions for a given number. For instance: “What fractions are equivalent to ⅓ on these number lines?” Use discussions to deepen their understanding: “Why do ⅓ and two-sixths align on the number lines?”

To pre-teach comparing fractions, you might place additional emphasis on how number lines can help compare benchmark fractions. For example, discuss how fractions closer to 0, ½, or 1 can be easily identified and compared using number lines.

Stage 4: Connect to Algorithms

Once students have built a strong foundation with visuals and number lines, introduce the algorithm for finding equivalent fractions. Teach them to:

1. Multiply both the numerator and denominator by the same number.

2. Simplify fractions by dividing the numerator and denominator by their greatest common factor.

I teach what I made up and call "The Whiney Kid" rule: I ask students what happens if there are two kids and give candy to only one of them ... the other one whines. I tell them nobody likes whiney kids, so whatever you do for one, you also have to do for the other. The same is true for equivalent fractions ... whatever you multiply/divide the numerator or denominator by, you have to do the same for the other.

Wrap-Up and Extension

By the end of these lessons, students should have a solid understanding of equivalent fractions through hands-on activities, visual models, and number line exploration. 

For additional support, check out our Equivalent Fractions Anchor Chart, which provides clear visuals for finding equivalent fractions. Whether you're teaching equivalent fractions for the first time or reinforcing prior knowledge, this resource can make lessons more engaging and effective.