How to Explain Division to Third Graders

If multiplication is grouping things together, division is taking them apart.

Third graders learn that these operations are partners—two sides of the same coin. Understanding this relationship is the key to mastering both.

What Division Actually Means

Division answers two types of questions:

1. Sharing (Partitive Division)

"12 cookies shared among 3 friends. How many does each friend get?"

12 ÷ 3 = 4

You know the total (12) and the number of groups (3). You're finding how many in each group.

2. Grouping (Measurement Division)

"12 cookies, putting 3 in each bag. How many bags can you fill?"

12 ÷ 3 = 4

You know the total (12) and how many in each group (3). You're finding how many groups.

Same equation, different real-world meaning. Both are division.

Connecting Division to Multiplication

This is the most important concept in third-grade division:

If 4 × 3 = 12, then:

• 12 ÷ 3 = 4
• 12 ÷ 4 = 3

Division "undoes" multiplication. Teach this with fact families:

    12
   /  \
  4 × 3

Facts:
4 × 3 = 12
3 × 4 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3

When a child sees 56 ÷ 8, they should think: "What times 8 equals 56? Seven! So 56 ÷ 8 = 7."

This is why multiplication fluency must come first.

Making Division Concrete

Use Physical Objects

Problem: 15 ÷ 3 = ?

Sharing model: Get 15 counters. "Share these equally among 3 plates."
Deal them out: one to each plate, go around again, again...
Each plate has 5.

Grouping model: "Put 3 counters in each group. How many groups?"
Make a group of 3, another, another...
You made 5 groups.

Draw Pictures

Problem: 20 ÷ 4 = ?

Draw 20 circles. Circle groups of 4:

(○○○○) (○○○○) (○○○○) (○○○○) (○○○○)

5 groups. So 20 ÷ 4 = 5.

Use Arrays

Arrays work for division too:

Problem: 24 ÷ 6 = ?

"If I arrange 24 dots into rows of 6, how many rows?"

● ● ● ● ● ●
● ● ● ● ● ●
● ● ● ● ● ●
● ● ● ● ● ●

4 rows. So 24 ÷ 6 = 4.

Number Lines

Problem: 18 ÷ 3 = ?

Start at 18. Make jumps of 3 backwards until you reach 0:
18 → 15 → 12 → 9 → 6 → 3 → 0

Count the jumps: 6. So 18 ÷ 3 = 6.

Division Vocabulary

Make sure your child knows these terms:

• Dividend: The number being divided (the total)
• Divisor: The number you're dividing by
• Quotient: The answer

In 24 ÷ 6 = 4:

• 24 is the dividend
• 6 is the divisor
• 4 is the quotient

The Special Cases

Dividing by 1

Any number divided by 1 equals itself.
12 ÷ 1 = 12 (putting all 12 in 1 group means 12 in that group)

A Number Divided by Itself

Any number divided by itself equals 1.
12 ÷ 12 = 1 (12 items, 12 groups = 1 in each group)

Zero in Division

0 ÷ 5 = 0 (zero things shared among 5 people = zero each)
5 ÷ 0 = undefined (you can't share among zero people—it doesn't make sense)

Building Division Fluency

Use Multiplication Facts Backwards

If your child knows their times tables, they know division:

If they know...	They can solve...
6 × 7 = 42	42 ÷ 7 = 6 and 42 ÷ 6 = 7
8 × 9 = 72	72 ÷ 9 = 8 and 72 ÷ 8 = 9
5 × 8 = 40	40 ÷ 8 = 5 and 40 ÷ 5 = 8

Practice by giving the product and asking: "What two numbers multiply to make this?"

Fact Family Triangles

        42
       /  \
      6    7

From this: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6

Cover one number and figure out what it must be.

Think-Multiplication Strategy

For 63 ÷ 9:

• Think: "9 times what equals 63?"
• 9 × 7 = 63
• So 63 ÷ 9 = 7

This mental strategy is faster than drawing pictures once facts are solid.

Common Mistakes (And How to Fix Them)

Mistake 1: Confusing Dividend and Divisor

Error: 24 ÷ 6 = ? answered as "What is 6 divided into 24 parts?"

Fix: Use the language consistently. "24 divided by 6" means "24 split into groups of 6" or "24 shared among 6."

Mistake 2: Division as Subtraction

Error: 12 ÷ 3 = 9 (subtracting instead of dividing)

Fix: Go back to concrete models. "Show me 12 cookies shared among 3 friends." Count how many each gets.

Mistake 3: Not Connecting to Multiplication

Signs: Child counts on fingers for every division problem instead of recalling facts.

Fix: Explicitly practice fact families. "Tell me all four facts in this family." Build the automatic multiplication-division connection.

Mistake 4: Struggling with Word Problems

Signs: Can do 15 ÷ 3 but can't solve "15 stickers shared among 3 children."

Fix: Act it out. Get 15 objects and 3 "children" (plates, paper squares). Do the sharing. Then write the equation.

Word Problem Practice

Third graders should solve both types:

Sharing Problems

"24 oranges are packed equally into 4 boxes. How many oranges in each box?"

• Total = 24, groups = 4, find: items per group
• 24 ÷ 4 = 6 oranges per box

Grouping Problems

"There are 24 oranges. Each box holds 6 oranges. How many boxes are needed?"

• Total = 24, items per group = 6, find: number of groups
• 24 ÷ 6 = 4 boxes

Practice identifying: "What do we know? What are we finding?"

Games and Activities

Fact Family Cards

Write fact families on index cards. Child draws a card and says all four facts as fast as they can.

Division War

Players flip cards and divide the larger number by the smaller. (Use cards 1-9.) Highest quotient wins the round.

Fair Share Scenarios

Real-life practice:

• "We have 18 grapes. Share them with your sister."
• "These 20 crayons go in 4 boxes. How many in each?"
• "Put 5 books on each shelf. How many shelves for 35 books?"

Missing Number Puzzles

___ ÷ 6 = 7
48 ÷ ___ = 8
36 ÷ 9 = ___

These reinforce the relationship between multiplication and division.

Introduction to Remainders

While formal remainders are often fourth grade, third graders encounter the concept:

"13 stickers shared among 4 friends. How many does each get?"

13 ÷ 4 = 3 with 1 left over

Each friend gets 3, and there's 1 remaining. This introduces the idea that division doesn't always come out even—an important real-world concept.

Checking Work with Multiplication

Teach your child to verify:

Problem: 56 ÷ 7 = 8
Check: 8 × 7 = 56 ✓

If the check doesn't match the dividend, something went wrong.

Building Understanding Before Speed

The progression:

1. Concrete: Use objects to share and group
2. Pictorial: Draw arrays and groups
3. Abstract: Use symbols and mental math

Don't rush through these stages. A child who truly understands division will become fluent. A child who memorizes answers without understanding will struggle with more complex division later.

The Bottom Line

Division is not a separate skill—it's the partner to multiplication. When your child sees 48 ÷ 6, they should automatically think "6 times what equals 48?"

Build this connection:

• Practice fact families daily
• Use real objects for sharing and grouping
• Connect to multiplication facts
• Check answers using multiplication

When division becomes "multiplication thinking backwards," your third grader has a tool that will serve them through fractions, algebra, and beyond.