Division Using Arrays 3rd Grade | Visual Learning

Array Division Exercises: Problems 1 to 3

1 Basic Array Division

Exercise 1

Sarah has 12 cookies. She wants to arrange them in an array with 3 rows. How many cookies will be in each row?

3rd Grade Strategy:

Draw 3 rows and distribute 12 cookies equally

Array Setup:

Total items: 12 cookies, Number of rows: 3

Division Equation:

12 ÷ 3 = ?

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Step 1: Identify the total and divisor

Total cookies = 12, Number of rows = 3

Step 2: Draw the array

Create 3 rows and distribute 12 cookies equally

Step 3: Count cookies per row

Row 1: 4 cookies, Row 2: 4 cookies, Row 3: 4 cookies

Step 4: Write the division equation

12 ÷ 3 = 4

12 ÷ 3 = 4 cookies per row

Final answer:

There will be 4 cookies in each row.

Applied rules:

• Division as equal sharing: Distribute items equally among groups

• Array structure: Rows represent groups, columns represent items per group

• Verification: 3 rows × 4 cookies = 12 total cookies

2 Column Array Division

Exercise 2

A farmer has 18 carrots. He plants them in an array with 6 columns. How many rows will he need?

3rd Grade Strategy:

Draw 6 columns and fill with 18 carrots

Array Setup:

Total items: 18 carrots, Number of columns: 6

Division Equation:

18 ÷ 6 = ?

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Step 1: Identify the total and divisor

Total carrots = 18, Number of columns = 6

Step 2: Draw the array

Create 6 columns and fill with 18 carrots

Step 3: Count the number of rows

Row 1: 6 carrots, Row 2: 6 carrots, Row 3: 6 carrots

Step 4: Write the division equation

18 ÷ 6 = 3

18 ÷ 6 = 3 rows needed

Final answer:

The farmer will need 3 rows.

Applied rules:

• Division as grouping: Determine how many groups of a certain size fit into the total

• Array flexibility: Can work with rows OR columns as divisor

• Verification: 3 rows × 6 columns = 18 total carrots

3 Mixed Array Problem

Exercise 3

Emma arranges 24 stickers in an array with 4 rows. Then she rearranges them with 6 rows. How many stickers are in each row in the new arrangement?

3rd Grade Strategy:

Notice the total stays the same, but rows change

First Arrangement:

Total items: 24 stickers, Number of rows: 4

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New Arrangement:

Total items: 24 stickers, Number of rows: 6

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Step 1: Analyze the first arrangement

24 stickers ÷ 4 rows = 6 stickers per row

Step 2: Set up the second arrangement

Total remains 24 stickers, now with 6 rows

Step 3: Calculate stickers per row in new arrangement

24 ÷ 6 = 4 stickers per row

Step 4: Verify the result

6 rows × 4 stickers = 24 total stickers ✓

24 ÷ 6 = 4 stickers per row

Final answer:

There are 4 stickers in each row in the new arrangement.

Applied rules:

• Conservation of quantity: Total items remain constant

• Array flexibility: Same total can have multiple arrangements

• Relationship between factors: More rows means fewer items per row

3rd Grade Array Division Concepts

Total ÷ Groups = Items per Group

Array Division

Division as Sharing

Total ÷ Rows = Items per Row

Equal distribution

Division as Grouping

Total ÷ Columns = Number of Rows

How many groups fit?

Array Structure

Rows × Columns = Total

Visual organization

Key definitions for 3rd Grade:

Array: Items arranged in rows and columns forming rectangles or squares

Rows: Horizontal lines of items (go left to right)

Columns: Vertical lines of items (go top to bottom)

Cells: Individual positions in the array

Dimensions: Number of rows by number of columns

Equal Groups: Same number of items in each row or column

3rd Grade Array Method:

Read the problem: Find total items and number of groups
Draw the array: Make rows or columns as needed
Distribute items: Place items one by one in each group
Count result: How many items are in each group?
Write equation: Total ÷ Groups = Items per group

Tip 1: Draw arrays to see the problem clearly.

Tip 2: Check by multiplying: Groups × Items per group = Total

Tip 3: Rows go across, columns go up and down.

Common errors: Mixing up rows and columns, counting wrong.

Memory trick: "Rows go across, like you're reading."

Detailed Summary: Division Using Arrays for 3rd Grade

a ÷ b = c if and only if b × c = a

Division-Multiplication Relationship

Core Concepts for 3rd Grade:

Division: The process of splitting a total amount into equal parts

Array Model: Visual representation using rows and columns

Rows: Horizontal lines representing groups

Columns: Vertical lines representing items per group

Rectangular Array: Organized grid showing equal groups

Visual Division: Using pictures to understand division

Step-by-Step Array Approach for 3rd Grade:

Read the problem: Find total items and what to find
Draw the array: Make the groups shown in the problem
Put items in groups: Share items equally
Count what's in each group: That's your answer
Check your answer: Multiply to see if you get the total

Strategy 1: Count in one row to find the pattern.

Strategy 2: Use skip counting to fill in groups.

Strategy 3: Make smaller groups if the numbers are big.

Array Properties:

• Identity Property: a ÷ 1 = a

• Zero Property: 0 ÷ a = 0 (when a ≠ 0)

• Undefined: a ÷ 0 is undefined

• Inverse Property: a ÷ b = c means b × c = a

• Commutative Property: Rows × Columns = Columns × Rows

Key insight: Arrays make division clear and easy to see.

Connection: Arrays connect division to multiplication.

Examples:

3rd Grade Array Applications

Simple Array Example

Problem: 12 items in 3 rows

Array: 3 rows × 4 columns = 12 total

Division: 12 ÷ 3 = 4 items per row

Grouping Array Example

Problem: 15 items in groups of 3

Array: 5 rows × 3 columns = 15 total

Division: 15 ÷ 3 = 5 rows needed

Advanced Array Example

Problem: 20 items in 4 rows

Array: 4 rows × 5 columns = 20 total

Division: 20 ÷ 4 = 5 items per row

Why Arrays Help 3rd Graders

• Shows equal groups clearly

• Connects to multiplication facts

• Makes abstract ideas concrete

• Builds understanding of area

• Prepares for bigger division problems

Division Using Arrays for 3rd Grade Students

Questions & Answers