CH04-02 lesson

Equivalent Fractions as Same Size Learning Activity

A focused Grade 3 learning session for Equivalent Fractions as Same Size using visual models, worked examples, strategy guidance, and a short mastery check.

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15
minutes
6
lesson parts
11
practice items
Learning goal

Students will recognize equivalent fractions as the same size or the same point on a number line.

Student goal: I can recognize equivalent fractions that represent the same amount.

Helpful first: Equivalence of Fractions
concept

Learn the Idea

Equivalent Fractions as Same Size means using equal parts, number lines, and clear fraction language to describe parts of a whole.

  • 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 model

See the Math

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?

Grade 3 Equivalent Fractions as Same Size figure 1

  • 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: \(\frac{1}{2}=\frac{2}{4}\)

worked example

Follow a Worked Example

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?

Grade 3 Equivalent Fractions as Same Size figure 3

  • A. \(\frac{3}{8}\)
  • B. \(\frac{1}{3}\)
  • C. \(\frac{2}{8}\)
  • D. \(\frac{1}{4}\)
  1. \(\frac{2}{6}=\frac{1}{3}\) 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?

Grade 3 Equivalent Fractions as Same Size figure 4

  • 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 \(\frac{2}{3}\)
  1. Both fractions equal one-half and represent the same point on a number line.

Answer: \(\frac{2}{4}\) and \(\frac{3}{6}\)

real world

Connect It to a Real Situation

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.

strategy

Avoid Mistakes and Choose a Strategy

  • 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.
  • 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.
summary

Remember the Key Idea

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.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G3-C04-T02-Q001 About 1 min

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?

  1. A \(\frac{2}{3}<\frac{4}{6}\)
  2. B \(\frac{2}{3}>\frac{4}{6}\)
  3. C \(\frac{2}{3}=\frac{4}{6}\)
  4. D Cannot be compared
Check answer and explanation

Answer C: \(\frac{2}{3}=\frac{4}{6}\)

Two fractions are equivalent if they represent the same-size region. Since both shaded regions are equal, \(\frac{2}{3}=\frac{4}{6}\).

G3-C04-T02-Q002 About 1 min

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?

Equivalent Fractions as Same Size visual for G3-C04-T02-Q002
  1. A They are not related
  2. B \(\frac{1}{2}<\frac{2}{4}\)
  3. C \(\frac{1}{2}>\frac{2}{4}\)
  4. D \(\frac{1}{2}=\frac{2}{4}\)
Check answer and explanation

Answer D: \(\frac{1}{2}=\frac{2}{4}\)

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.

guided

1 question
G3-C04-T02-Q003 About 1 min

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?

  1. A No, Bar 1 is larger.
  2. B Cannot tell without measuring.
  3. C No, Bar 2 is larger.
  4. D Yes, they are the same size.
Check answer and explanation

Answer D: Yes, they 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.

practice

5 questions
G3-C04-T02-Q004 About 1 min

Which pair of fractions shows the SAME amount shaded?

Equivalent Fractions as Same Size visual for G3-C04-T02-Q004
  1. A \(\frac{1}{2}\) and \(\frac{2}{4}\)
  2. B \(\frac{2}{4}\) and \(\frac{2}{8}\)
  3. C \(\frac{1}{2}\) and \(\frac{2}{8}\)
  4. D \(\frac{2}{4}\) and \(\frac{3}{8}\)
Check answer and explanation

Answer A: \(\frac{1}{2}\) and \(\frac{2}{4}\)

Both bars show the same shaded region (one-half of each bar). They are equivalent fractions.

G3-C04-T02-Q005 About 1 min

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?

  1. A It depends on the ribbon length.
  2. B No, the first ribbon has more.
  3. C Yes, both are the same.
  4. D No, the second ribbon has more.
Check answer and explanation

Answer C: Yes, both are the same.

\(\frac{3}{6}=\frac{1}{2}\) because both represent one-half of the ribbon.

G3-C04-T02-Q006 About 1 min

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?

Equivalent Fractions as Same Size visual for G3-C04-T02-Q006
  1. A \(\frac{3}{8}\)
  2. B \(\frac{1}{3}\)
  3. C \(\frac{2}{8}\)
  4. D \(\frac{1}{4}\)
Check answer and explanation

Answer B: \(\frac{1}{3}\)

\(\frac{2}{6}=\frac{1}{3}\) because both represent one-third of the rectangle.

G3-C04-T02-Q007 About 1 min

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?

  1. A Cannot tell without tasting.
  2. B The same amount left.
  3. C Pie B has more left.
  4. D Pie A has more left.
Check answer and explanation

Answer B: The same amount left.

Pie A has \(\frac{1}{4}\) left. Pie B has \(\frac{2}{8}\) left. These are equivalent: \(\frac{1}{4}=\frac{2}{8}\).

G3-C04-T02-Q008 About 1 min

Which two fractions represent the same point on a number line?

Equivalent Fractions as Same Size visual for G3-C04-T02-Q008
  1. A \(\frac{2}{4}\) and \(\frac{3}{6}\)
  2. B \(\frac{3}{8}\) and \(\frac{4}{8}\)
  3. C \(\frac{1}{3}\) and \(\frac{3}{6}\)
  4. D \(\frac{1}{2}\) and \(\frac{2}{3}\)
Check answer and explanation

Answer A: \(\frac{2}{4}\) and \(\frac{3}{6}\)

Both fractions equal one-half and represent the same point on a number line.

exit

3 questions
G3-C04-T02-Q009 About 1 min

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?

  1. A \(\frac{2}{3}\)
  2. B \(\frac{1}{6}\)
  3. C \(\frac{3}{6}\)
  4. D \(\frac{1}{3}\)
Check answer and explanation

Answer D: \(\frac{1}{3}\)

\(\frac{2}{6}=\frac{1}{3}\). When Sam eats \(\frac{2}{6}\) of Bar 2, he ate the same amount as \(\frac{1}{3}\) of Bar 1.

G3-C04-T02-Q010 About 1 min

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?

  1. A They cannot be compared.
  2. B No, Circle Y is larger.
  3. C Yes, they are equal.
  4. D No, Circle X is larger.
Check answer and explanation

Answer C: Yes, they are equal.

\(\frac{3}{4}=\frac{6}{8}\) because both represent three-fourths of their circles.

G3-C04-T02-Q011 About 1 min

Lily paints a wall. She paints \(\frac{4}{8}\) of the wall blue. Which fraction shows the same amount?

  1. A \(\frac{1}{2}\)
  2. B \(\frac{1}{4}\)
  3. C \(\frac{3}{8}\)
  4. D \(\frac{2}{3}\)
Check answer and explanation

Answer A: \(\frac{1}{2}\)

\(\frac{4}{8}=\frac{1}{2}\). Both represent one-half of the wall.

Keep the learning path connected
Previous skillEquivalence of Fractions Recommended nextGenerating Simple Equivalent Fractions Same strandUnit Fractions Same strandFractions on a Number Line
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