Introduction
Equivalence of Fractions is an important Grade 3 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with equivalence of fractions.
What Is Equivalence of Fractions?
Equivalence of Fractions means using equal parts, number lines, and clear fraction language to describe parts of a whole.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Equivalence of Fractions
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Identify the whole before naming a fraction.
- Make sure each part is equal in size.
- Use a number line or model to show where the fraction belongs.
- Explain whether two fractions have the same size or different sizes.
Visual Models
Visual Model 1
Question: Look at the fraction bars. Which fraction is equivalent to \(\frac{1}{3}\)?
- A. \(\frac{1}{4}\)
- B. \(\frac{2}{6}\)
- C. \(\frac{2}{4}\)
- D. \(\frac{1}{2}\)
Why it works: The shaded regions match. \(\frac{1}{3}\) and \(\frac{2}{6}\) are equivalent.
Answer: \(\frac{2}{6}\)
Visual Model 2
Question: Which fraction is equivalent to \(\frac{2}{3}\)?
- A. \(\frac{4}{6}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{2}{4}\)
- D. \(\frac{3}{6}\)
Why it works: \(\frac{2}{3}\) and \(\frac{4}{6}\) represent the same amount. Both show two-thirds.
Answer: \(\frac{4}{6}\)
Worked Examples
Example 1
Question: Look at the bars. Which statement is NOT true?
- A. The first and second are equivalent
- B. The first bar shows \(\frac{1}{2}\)
- C. All three show the same amount
- D. The third bar is smaller
- The first and second bars are equivalent.
- But the third bar shows \(\frac{1}{3}\), which is larger than \(\frac{1}{2}\), so all three do NOT show the same amount.
- Answer C is false.
Answer: All three show the same amount
Example 2
Question: Look at the pies. Which statement is true?
- A. They show the same amount
- B. The left pie is larger
- C. The right pie is larger
- D. They are not equal
- Both pies show the same shaded region. \(\frac{1}{4}\) and \(\frac{2}{8}\) are equivalent.
Answer: They show the same amount
Example 3
Question: Look at the number line. Which fraction equals \(\frac{2}{6}\)?
- A. \(\frac{1}{4}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{3}{6}\)
- On the number line, \(\frac{2}{6}\) and \(\frac{1}{3}\) mark the same point.
Answer: \(\frac{1}{3}\)
Real-World Word Problems
Problem 1
Question: Noah loses \(3\) of \(6\) marbles. What fraction did he lose in simplest form?
Why it works: \(\frac{3}{6}=\frac{1}{2}\).
Answer: \(\frac{1}{2}\)
Problem 2
Question: Which fraction is equivalent to \(\frac{1}{2}\)?
- A. \(\frac{1}{4}\)
- B. \(\frac{2}{4}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{1}{3}\)
Why it works: \(\frac{1}{2}\) and \(\frac{2}{4}\) represent the same amount. Both show half of a whole.
Answer: \(\frac{2}{4}\)
Common Mistakes
- Counting unequal parts as if they were equal.
- Forgetting that the denominator tells how many equal parts make the whole.
- Comparing fractions without first checking the size of the whole.
- Placing a fraction on a number line without counting equal intervals.
Strategy Tips
- Draw the whole first, then divide it into equal parts.
- Use number lines when the question asks about order or location.
- Say the fraction out loud to connect numerator and denominator meanings.
- Check whether the answer should be closer to 0, 1/2, or 1.
Practice Questions
Question 1
Which fraction is equivalent to \(\frac{3}{4}\)?
- A. \(\frac{3}{8}\)
- B. \(\frac{3}{6}\)
- C. \(\frac{6}{8}\)
- D. \(\frac{2}{4}\)
Question 2
Lily has 2 equal pieces of a sandwich. She eats 1 piece. What fraction did she eat?
- A. \(\frac{1}{4}\)
- B. \(\frac{2}{3}\)
- C. \(\frac{1}{2}\)
- D. \(\frac{1}{3}\)
Question 3
Which fraction is equivalent to \(\frac{1}{4}\)?
- A. \(\frac{2}{8}\)
- B. \(\frac{3}{8}\)
- C. \(\frac{1}{3}\)
- D. \(\frac{2}{4}\)
Question 4
Look at the bars. Are \(\frac{1}{2}\) and \(\frac{2}{4}\) equivalent?
- A. Yes, they are equivalent
- B. No, they are not equivalent
- C. The first is larger
- D. The second is larger
Question 5
Sam eats 1 slice from a 3-slice pizza. Which fraction is equivalent to what he ate?
- A. \(\frac{2}{6}\)
- B. \(\frac{1}{2}\)
- C. \(\frac{1}{4}\)
- D. \(\frac{2}{3}\)
Question 6
Which fraction is equivalent to \(\frac{2}{4}\)?
- A. \(\frac{2}{6}\)
- B. \(\frac{3}{8}\)
- C. \(\frac{1}{2}\)
- D. \(\frac{2}{3}\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(\frac{6}{8}\)
\(\frac{3}{4}\) and \(\frac{6}{8}\) both show three-fourths of a whole.
Question 2
Answer: \(\frac{1}{2}\)
Lily ate 1 out of 2 pieces, which is \(\frac{1}{2}\).
Question 3
Answer: \(\frac{2}{8}\)
\(\frac{1}{4}\) and \(\frac{2}{8}\) both show one-quarter of a whole.
Question 4
Answer: Yes, they are equivalent
Both bars show the same amount shaded. \(\frac{1}{2}\) and \(\frac{2}{4}\) are equal.
Question 5
Answer: \(\frac{2}{6}\)
Sam ate \(\frac{1}{3}\), which is equivalent to \(\frac{2}{6}\).
Question 6
Answer: \(\frac{1}{2}\)
\(\frac{2}{4}\) and \(\frac{1}{2}\) both equal half of a whole.
Connection to Standards
This lesson supports Grade 3 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Equivalence of Fractions becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Equal parts first, fraction name second.
