How to Explain Fractions to Third Graders

Fractions are where math starts to feel different.

Whole numbers make sense: 3 apples, 7 books, 12 eggs. But half an apple? A third of a pizza? This is new territory for third graders—and often frustrating territory.

Here's how to make fractions click.

The Foundation: Equal Parts

Before anything else, your child needs to understand equal parts.

A fraction only makes sense when a whole is divided into equal pieces.

Show the Difference

Equal parts:

[    |    |    ]  ← Three equal parts. Each is 1/3.

Unequal parts:

[  |      |   ]  ← Three parts, but NOT equal. These aren't thirds!

Practice identifying equal parts in real life:

• Is this pizza cut into equal slices?
• Are these pieces of paper the same size?
• Did we share the cookie equally?

Understanding Fraction Notation

A fraction has two numbers:

  1   ← Numerator (how many parts we have)
 ---
  4   ← Denominator (how many equal parts in the whole)

The Denominator Story

Denominator = how many equal parts the whole is cut into

If a pizza is cut into 8 equal slices:

• The denominator is 8
• Each slice is 1/8 of the pizza

If the same pizza were cut into 4 slices:

• The denominator is 4
• Each slice is 1/4 of the pizza

Key insight: The bigger the denominator, the smaller each piece.

• 1/8 is smaller than 1/4 (more pieces = smaller pieces)

This is counterintuitive! Bigger number = smaller piece. Spend time on this.

The Numerator Story

Numerator = how many of those equal parts you have

If you eat 3 slices of a pizza cut into 8:

• You ate 3/8 of the pizza

The numerator counts the pieces. Simple once the denominator makes sense.

Unit Fractions: The Building Blocks

A unit fraction has 1 as the numerator: 1/2, 1/3, 1/4, 1/5, 1/6...

These are incredibly important because:

Every fraction is made of unit fractions.

• 3/4 = 1/4 + 1/4 + 1/4 (three fourths)
• 2/3 = 1/3 + 1/3 (two thirds)
• 5/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 (five eighths)

When your child understands unit fractions, they can understand any fraction.

Comparing Unit Fractions

Which is bigger: 1/3 or 1/6?

Visual approach:

1/3: [████|    |    ]   ← Whole divided into 3 parts
1/6: [██|  |  |  |  |  ] ← Same whole divided into 6 parts

1/3 is bigger because fewer cuts means bigger pieces.

The rule: With unit fractions, bigger denominator = smaller fraction.

• 1/2 > 1/3 > 1/4 > 1/5 > 1/6...

Fractions of Shapes

Third graders work extensively with fractions of shapes.

Circles (Pizza/Pie Model)

    ___
   /   \
  | 1/4 |
   \___/

Easy to visualize, familiar from real life.

Rectangles (Chocolate Bar Model)

┌───┬───┬───┬───┐
│   │ X │ X │   │
└───┴───┴───┴───┘

2 out of 4 parts are shaded = 2/4

Great for connecting to arrays and area.

Number Lines

0         1/4        1/2        3/4         1
|----------|----------|----------|----------|

Number lines show fractions as positions, connecting to measurement. This is crucial for later math.

Comparing Fractions

Third graders learn to compare fractions in specific cases:

Same Denominator

Which is bigger: 2/5 or 4/5?

Same size pieces (fifths). Who has more pieces?

• 2/5 = two fifths
• 4/5 = four fifths
• 4/5 > 2/5

Rule: Same denominator → compare numerators.

Same Numerator

Which is bigger: 2/3 or 2/6?

Same number of pieces. But what size are the pieces?

• 2/3 = two thirds (larger pieces)
• 2/6 = two sixths (smaller pieces)
• 2/3 > 2/6

Rule: Same numerator → smaller denominator means bigger pieces, so bigger fraction.

Comparing to 1/2

Is 3/8 more or less than 1/2?

Half of 8 is 4. So 4/8 = 1/2.
3/8 is less than 4/8.
Therefore 3/8 < 1/2.

This benchmark strategy helps with many comparisons.

Equivalent Fractions

Two fractions can name the same amount:

1/2 = 2/4 = 3/6 = 4/8

Visual Proof

1/2: [████████|        ]

2/4: [████|████|    |    ]

4/8: [██|██|██|██|  |  |  |  ]

All show half the shape shaded.

The Pattern

Multiply both numerator and denominator by the same number:

1/2 × 2/2 = 2/4
1/2 × 3/3 = 3/6
1/2 × 4/4 = 4/8

Third grade introduces this concept; fourth grade develops it fully.

Fractions Greater Than 1

Third graders are introduced to fractions greater than 1:

5/4 means five fourths.

If one whole has 4 fourths, then 5/4 is:

• One whole (4/4) plus one more fourth (1/4)
• Written as the mixed number: 1 1/4

[████|████|████|████] [████|    |    |    ]
       1 whole        + 1/4 extra

Common Misconceptions (And How to Fix Them)

Misconception 1: Bigger Denominator = Bigger Fraction

Error: Thinking 1/8 > 1/4 because 8 > 4.

Fix: Always draw it. Show that 8 pieces from one pizza means smaller slices. Use the same-size whole!

Misconception 2: Adding Tops and Bottoms

Error: 1/2 + 1/3 = 2/5

Fix: Show with pictures that 1/2 + 1/3 is clearly more than 1/2, but 2/5 is less than 1/2. This doesn't work! (Proper addition of unlike fractions comes later.)

Misconception 3: Fractions Aren't Numbers

Signs: Child can shade 3/4 of a shape but can't place 3/4 on a number line.

Fix: Use number lines regularly. Fractions are numbers that live between whole numbers.

Misconception 4: Different Wholes

Error: Comparing 1/2 of a small pizza to 1/4 of a large pizza.

Fix: Emphasize: We can only compare fractions of the SAME whole. 1/2 > 1/4 when we're talking about the same pizza.

Hands-On Activities

Fraction Strips

Cut paper strips into halves, thirds, fourths, sixths, eighths.

Line them up:

• How many fourths make a half?
• Are 2/6 and 1/3 the same?
• Which is bigger, 3/4 or 2/3?

Pattern Blocks

Yellow hexagon = 1 whole
Red trapezoid = 1/2
Blue rhombus = 1/3
Green triangle = 1/6

"How many triangles cover the hexagon?" (6)
"What fraction is one trapezoid?" (1/2)

Cooking

Recipes use fractions constantly:

• "We need 1/2 cup of sugar."
• "Cut this in thirds so we each get an equal piece."
• "The recipe calls for 3/4 teaspoon."

Sharing Fairly

Real division creates fractions:

• 1 cookie ÷ 2 people = 1/2 each
• 3 brownies ÷ 4 people = 3/4 each
• 2 sandwiches ÷ 3 people = 2/3 each

Fraction Vocabulary

Make sure your child knows:

• Fraction: A number representing part of a whole
• Numerator: Top number (how many parts)
• Denominator: Bottom number (how many equal parts in the whole)
• Unit fraction: Fraction with 1 as the numerator
• Equivalent fractions: Different fractions naming the same amount
• Whole: The entire thing being divided

Building Toward Fourth Grade

Third grade fraction work prepares students for:

• Adding and subtracting fractions with same denominators
• Multiplying fractions by whole numbers
• Converting between fractions and decimals
• More complex equivalence

A strong foundation now prevents fraction fear later.

The Bottom Line

Fractions require a different kind of number thinking. The key is always:

1. Start concrete: Use real objects, drawings, manipulatives
2. Equal parts: This is non-negotiable
3. Connect representations: Same fraction shown as picture, number line, symbol
4. Compare carefully: Same whole, different methods for different cases
5. Build from unit fractions: All fractions are made from these building blocks

When your third grader looks at 3/4 and sees "three of the four equal pieces"—not just "3 over 4"—they have true fraction understanding.