Introduction
Equivalent Fractions as Same Size 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 equivalent fractions as same size.
What Is Equivalent Fractions as Same Size?
Equivalent Fractions as Same Size 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 Equivalent Fractions as Same Size
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 two circles. Circle A shows \(\frac{1}{2}\) shaded. Circle B shows \(\frac{2}{4}\) shaded. Both circles are the same size. What can you say about these fractions?
- A. They are not related
- B. \(\frac{1}{2}<\frac{2}{4}\)
- C. \(\frac{1}{2}>\frac{2}{4}\)
- D. \(\frac{1}{2}=\frac{2}{4}\)
Why it works: Both circles show the same shaded area. \(\frac{1}{2}\) of one circle equals \(\frac{2}{4}\) of another equal-sized circle. They are equivalent.
Answer: \(\frac{1}{2}=\frac{2}{4}\)
Visual Model 2
Question: Which pair of fractions shows the SAME amount shaded?
- A. \(\frac{1}{2}\) and \(\frac{2}{4}\)
- B. \(\frac{2}{4}\) and \(\frac{2}{8}\)
- C. \(\frac{1}{2}\) and \(\frac{2}{8}\)
- D. \(\frac{2}{4}\) and \(\frac{3}{8}\)
Why it works: Both bars show the same shaded region (one-half of each bar). They are equivalent fractions.
Answer: \(\frac{1}{2}\) and \(\frac{2}{4}\) show the same amount.
Worked Examples
Example 1
Question: Look at the rectangle. It is divided into 6 equal parts, and 2 parts are shaded. Which other fraction is EQUAL to the shaded amount?
- A. \(\frac{3}{8}\)
- B. \(\frac{1}{3}\)
- C. \(\frac{2}{8}\)
- D. \(\frac{1}{4}\)
- \(\frac{2}{6}=\frac{1}{3}\) because both represent one-third of the rectangle.
Answer: \(\frac{1}{3}\)
Example 2
Question: Which two fractions represent the same point on a number line?
- A. \(\frac{2}{4}\) and \(\frac{3}{6}\)
- B. \(\frac{3}{8}\) and \(\frac{4}{8}\)
- C. \(\frac{1}{3}\) and \(\frac{3}{6}\)
- D. \(\frac{1}{2}\) and \(\frac{2}{3}\)
- Both fractions equal one-half and represent the same point on a number line.
Answer: \(\frac{2}{4}\) and \(\frac{3}{6}\)
Example 3
Question: Two identical rectangular gardens are shown. Garden 1 has \(\frac{1}{4}\) planted with flowers. Garden 2 has \(\frac{2}{8}\) planted with flowers. Do the flower sections cover the same area?
- A. The gardens are different sizes.
- B. No, Garden 2 has more.
- C. No, Garden 1 has more.
- D. Yes, same amount.
- \(\frac{1}{4}=\frac{2}{8}\).
- Both sections cover one-quarter of their gardens.
Answer: Yes, same amount.
Real-World Word Problems
Problem 1
Question: Ava has two ribbons. Both ribbons are the same length. She colors \(\frac{3}{6}\) of one ribbon red and \(\frac{1}{2}\) of the other ribbon red. Does she color the same amount on both ribbons?
- A. It depends on the ribbon length.
- B. No, the first ribbon has more.
- C. Yes, both are the same.
- D. No, the second ribbon has more.
Why it works: \(\frac{3}{6}=\frac{1}{2}\) because both represent one-half of the ribbon.
Answer: Yes, both are the same.
Problem 2
Question: A teacher has two identical whiteboards. Board 1 is divided into 3 sections with 2 written on. Board 2 is divided into 6 sections with 4 written on. Are the written sections the same size?
- A. The boards might be different.
- B. No, Board 2 is larger.
- C. Yes, same size.
- D. No, Board 1 is larger.
Why it works: \(\frac{2}{3}=\frac{4}{6}\) because both represent two-thirds of the board.
Answer: Yes, same size.
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
Two fraction bars are shown. Bar 1 shows \(\frac{2}{3}\) shaded. Bar 2 shows \(\frac{4}{6}\) shaded. The shaded regions are the same size. Which statement is true?
- A. \(\frac{2}{3}<\frac{4}{6}\)
- B. \(\frac{2}{3}>\frac{4}{6}\)
- C. \(\frac{2}{3}=\frac{4}{6}\)
- D. Cannot be compared
Question 2
Ben draws two bars. Bar 1 is divided into 4 equal parts with 2 parts shaded. Bar 2 is divided into 8 equal parts with 4 parts shaded. The bars are the same length. Are the shaded regions the same size?
- A. No, Bar 1 is larger.
- B. Cannot tell without measuring.
- C. No, Bar 2 is larger.
- D. Yes, they are the same size.
Question 3
Two pies are the same size. Pie A is cut into 4 slices and 3 are eaten. Pie B is cut into 8 slices and 6 are eaten. How much pie is left in each case?
- A. Cannot tell without tasting.
- B. The same amount left.
- C. Pie B has more left.
- D. Pie A has more left.
Question 4
Sam has two chocolate bars. Bar 1 is split into 3 equal pieces. Bar 2 is split into 6 equal pieces. He eats \(\frac{2}{6}\) of Bar 2. What fraction of Bar 1 equals what he ate?
- A. \(\frac{2}{3}\)
- B. \(\frac{1}{6}\)
- C. \(\frac{3}{6}\)
- D. \(\frac{1}{3}\)
Question 5
Two circles are identical. Circle X shows \(\frac{3}{4}\) shaded gray. Circle Y shows \(\frac{6}{8}\) shaded gray. Are the shaded parts the same size?
- A. They cannot be compared.
- B. No, Circle Y is larger.
- C. Yes, they are equal.
- D. No, Circle X is larger.
Question 6
Lily paints a wall. She paints \(\frac{4}{8}\) of the wall blue. Which fraction shows the same amount?
- A. \(\frac{1}{2}\)
- B. \(\frac{1}{4}\)
- C. \(\frac{3}{8}\)
- D. \(\frac{2}{3}\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(\frac{2}{3}=\frac{4}{6}\)
Two fractions are equivalent if they represent the same-size region. Since both shaded regions are equal, \(\frac{2}{3}=\frac{4}{6}\).
Question 2
Answer: Yes, the shaded regions are the same size.
\(\frac{2}{4}\) and \(\frac{4}{8}\) are equivalent because both show one-half of the bar shaded. When denominator doubles, the numerator also doubles to maintain the same-size region.
Question 3
Answer: The same amount is left.
Pie A has \(\frac{1}{4}\) left. Pie B has \(\frac{2}{8}\) left. These are equivalent: \(\frac{1}{4}=\frac{2}{8}\).
Question 4
Answer: \(\frac{1}{3}\)
\(\frac{2}{6}=\frac{1}{3}\). When Sam eats \(\frac{2}{6}\) of Bar 2, he ate the same amount as \(\frac{1}{3}\) of Bar 1.
Question 5
Answer: Yes, they are equal.
\(\frac{3}{4}=\frac{6}{8}\) because both represent three-fourths of their circles.
Question 6
Answer: \(\frac{1}{2}\)
\(\frac{4}{8}=\frac{1}{2}\). Both represent one-half of the wall.
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
Equivalent Fractions as Same Size 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.
