# Intro to division

CCSS Math: 3.OA.A.2
Use arrays and word problems to visualize division.

## What is division?

Division lets us separate a number of objects into equal-size groups.
The symbol for division is $\div$ .
To divide, we need to know the total number of objects. We also need to know either the number of groups or the number of objects in each group.

### Equal groups

Let's look at an example:
The Big Pink Bubble Gum Company is holding a bubble blowing contest. They have $\maroonC{18}$ gumballs to share equally between $\blueD{3}$ people.
A division problem always starts with the total number of objects.
The total number of gumballs is $\maroonC{18}$.
The gumballs will be divided equally between $\blueD{3}$ people. So the number of equal groups is $\blueD{3}$.
In this problem, we are dividing $\maroonC{18}$ gumballs into $\blueD{3}$ groups. We can show this with the expression $\maroonC{18}$ $\div$ $\blueD{3}$.

### Let's try another one

The Big Pink Bubble Gum Company decides to use $\maroonC{16}$ gumballs in the competition.
They will have $\greenD{4}$ people blowing bubbles.
Problem 1A
There are a total of
gumballs that will be divided evenly into
groups.
Problem 1B
Which expression can we use to show $\maroonC{16}$ gumballs divided into $\greenD{4}$ equal-size groups?

### Using arrays

We can use arrays to show division.
An array is an arrangement of objects in equal-size rows.
$18$ gumballs shared equally between $3$ people can be shown with this array:
The $18$ gumballs have been divided equally between $3$ rows.
This array shows the expression $18 \div 3$.
When we divide $18$ gumballs into $3$ groups, how many gumballs are in each group?
We can find the answer to the division problem by counting the number of dots in each row.
$18 \div 3 = 6$

### Practice problem 2

Problem 2A
This array shows a total of
dots divided equally into
rows.
Problem 2B
Which expression can be used to represent the array?
Problem 2C
There are
dots in each row.
Problem 2D
${28} \div {7} =$

### Practice problem 3

This array has $\goldD{35}$ dots divided into $\blueD{5}$ equal rows.
Problem 3
$\goldD{35} \div \blueD{5} =$

### Equal shares

This type of problem is similar to the ones we just solved. However, in this case, we know the number of objects in each group instead of the number of equal groups.
Let's look at an example:
Peng's Pony Rides has $\goldD{20}$ ponies. The ponies take kids on rides all day. At the end of the day, the ponies rest in their stables. Each stable holds $\blueD4$ ponies.
We have a total of $\goldD{20}$ ponies.
We also know the number of equal shares in each group. Each stable holds $\blueD{4}$ ponies.
We can use division to figure out how many stables Peng needs for all his ponies.
Problem 4
The expression for $\goldD{20}$ ponies divided into equal groups of $\blueD{4}$ is $\goldD{20}$ $\div$ $\blueD{4}.$

### Let's try another problem

Peng's Pony Rides has a total of $\goldD{20}$ ponies. They built bigger stables. Each stable now holds $\purpleD{10}$ ponies.
Problem 5A
There are a total of
ponies. The ponies will be divided into equal-size groups with
ponies in each group.
Problem 5B
Which expression can we use to show a total of the $\goldD{20}$ ponies divided into groups with $\purpleD{10}$ ponies in each group?
Problem 5C
Which image could we use to show $\goldD{20}$ ponies divided equally into groups with $\purpleD{10}$ ponies in each group?
Problem 5D
$\goldD{20} \div \purpleD{10} =$

## Connecting division and multiplication

The array shows a total of $\purpleD{30}$ dots. The dots have been divided into $\goldD{6}$ equal rows with $\blueD{5}$ dots in each row.
The equation $\purpleD{30}$ $\div$ $\goldD{6}= \blueD{5}$ represents the array.
We could also say the array is made up of $\goldD{6}$ rows of dots with $\blueD{5}$ dots in each row.
The equation $\goldD{6}$ $\times$ $\blueD{5}$ = $\purpleD{30}$ also represents the array.
In both equations, $\purpleD{30}$ is the total number of dots, $\goldD{6}$ is the number of equal-size groups, and $\blueD{5}$ is the number of dots in each group.

### Let's try another one.

Problem 6
Which equations represent the following array?