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In this lesson, we will learn how to divide multi-digit numbers.
We will learn two concepts of division: fair sharing and repeated subtraction.
We will learn how to relate multiplication and division.
We will learn how to estimate the quotient using different strategies.
We will learn how to divide using the expanded notation method.

### Fair Sharing

One way to look at division is fair sharing.

Example:
A bag has 92 marbles, and Adrian and his three friends want to share them equally. How many marbles will each child get? A rod is traded for 10 units when there are no more rods to pass out. Then the 12 units are distributed, resulting in 23 in each set.
Therefore, each child will receive 23 marbles.

The following video will help students understand division and place value by  modeling distribution of Base Ten Blocks into equal groups. It shows 52 divided by 4.

### Repeated Subtraction

How can you show division as repeated subtraction?
The Dividend is the number being divided.
The Divisor is the number that is dividing another number.
The Quotient is the answer to the division problem.

Examples:
Sophia has 8 sticker sheets and she wants to give 2 sheets to each of her friend. How can you tell the number of friends that will receive stickers?
There are two columns of of 6 stickers on each sheet. I want to give 3 stickers to each student. How many students could I evenly divide the stickers in 2 sheets?
You put 18 people into 3 rows. How many people are in each row?
Rocco is putting 14 drawings into 2 art binders. How many drawings are in each binder? Example:
Jumbo the elephant loves peanuts. His trainer has 625 peanuts. If he gives Jumbo 20 peanuts a day, how many days will the peanuts last?

We need to find out how many 20's there are in 625.
We can try guessing:
- Try 20 (peanuts) × 10 (days) → 200 (not nearly enough)

- Try 20 (peanuts) × 30 (days) → 600 (now there are 25 peanuts left)
- Use 20 more peanuts for 1 more day. That makes 620 peanuts used with just 5 peanuts left over which is not enough for another full day.

Therefore, the peanuts will last 31 days.

### Relating Multiplication and Division

How are multiplication and division related?

Inverse Operations are operations that undo each other.
Fact Families show all related multiplication and division related facts for a set of numbers.

How would you use counters to make an array to show 2 x 6? How many different multiplication and division sentences can you write to represent the array? Relating Multiplication and Division
Watch the video to learn how arrays can be used to link concepts of multiplication and division. Special Quotients: 1 and 0
Four friends want to share 4 books. How many books will each friend get?
There is an empty cookie jar on the counter. Joe and two of his friends want to share the cookies in the jar. How many cookies will each friend get?

### Estimating the Quotient

We will look at three Estimation Strategies for the Quotient

1) Round numbers such that familiar multiplication and division facts can be used. For example:
574 ÷ 9 is about 560 ÷ 8 = 70 or
574 ÷ 9 is about 540 ÷ 9 = 60

2) When dividing round both numbers up or both numbers down. For example:
337 ÷ 8 is about 360 ÷ 9 = 40 or
337 ÷ 8 is about 280 ÷ 7 = 40

3) Round numbers to the nearest multiple of 10 (when the divisor in the problem divides evenly into a multiple of 10 or 25) to be able to divide by 25. For example:
389 ÷ 27 is about 400 ÷ 25 =16 or
612 ÷ 27 is about 600 ÷ 25 = 24

Use rounding and compatible numbers to find estimates of quotients. How to use multiplication and compatible numbers to estimate quotients.

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