Division Using Array Model | Visual Guide

Array Model 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?

Array Setup:

Total items: 12 cookies, Number of rows: 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?

Array Setup:

Total items: 18 carrots, Number of columns: 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?

First Arrangement:

Total items: 24 stickers, Number of rows: 4

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bfd

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

Array Model Concepts and Properties

Rows × Columns = Total

Array Structure

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:

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

Array Problem-Solving Steps:

Identify: What is the total? What do you know? What do you need?
Visualize: Draw the array with given information
Calculate: Perform the division operation
Verify: Check by multiplication

Tip 1: Draw arrays to visualize the problem when stuck.

Tip 2: Check your answer by multiplying divisor and quotient.

Tip 3: Remember: rows are horizontal, columns are vertical.

Common errors: Confusing rows with columns, forgetting to count all items.

Memory aid: "Rows go across, columns stand tall."

Detailed Summary: Division Using Array Model

a ÷ b = c if and only if b × c = a

Division-Multiplication Relationship

Core Concepts:

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

Step-by-Step Array Approach:

Read the problem: Identify total, groups, and what to find
Draw the array: Visualize the arrangement
Set up division: Write dividend ÷ divisor
Solve: Count or calculate the quotient
Verify: Multiply divisor × quotient to get dividend

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

Strategy 2: Use skip counting to fill in missing information.

Strategy 3: Break large arrays into smaller, manageable parts.

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

Key insight: Arrays make abstract division concrete and visual.

Connection: Arrays connect division to multiplication and area.

Examples:

Array Model 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

Array Model Benefits

• Visualizes equal groups clearly

• Shows relationship between multiplication and division

• Makes abstract concepts concrete

• Supports understanding of area models

• Builds foundation for larger division problems

Division Using Array Model for Grade 3 Students

Questions & Answers