SOL 4.4c 
Estimate and determine quotients of whole numbers,
​with and without remainders.

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IMPORTANT WORDS TO KNOW:
(Quizlet Flash Cards)

Division

​

​
​Estimate
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Dividend

Divisor

​Quotient

Remainder

Division is the operation of making equal groups or shares.
- When the original amount and the number of shares are known, divide to determine the size of each share.
- When the original amount and the size of each share are known, divide to determine the number of shares. 
- Division is the inverse (or opposite) of multiplication!
​
The act of rounding the dividend or using a compatible number to determine a "reasonable" answer;
​something close to the actual answer.

The number of items you will split into smaller groups.

The number of groups you will divide the dividend into. 

The "answer" to a division problem, sometimes includes a remainder. 

The "leftover" items that did not fit into the smaller groups. The remainder is a part of the quotient.
Sometimes written as a whole number, other times as a fraction. 
Not all division problems have a remainder! (See "Making Sense of the Remainder" at the bottom of this page.)

Parts of division, as seen in common problems:

Estimating Strategies (Division)

Sometimes we are asked to estimate a quotient, which is basically asking us to use mental math.
​There are a few ways to do this:

It's important to remember that Virginia fourth graders are required to solve these problems without using a calculator.

1. Rounding up or down to the nearest 10 or 100.

ROUNDING UP
Example Problem:
Libbey won 386 tokens at the pizza arcade. She wants to share them equally with her 4 friends. After dividing them equally, about how many will each person get?

​We can solve this problem by rounding the 386 tokens UP to the nearest hundred before dividing: 400. We know that there are 5 people in Libbey's group because we have to INCLUDE her as well as her four friends. 

400÷5=80​

So, each person in Libbey's group will have ABOUT 80 TOKENS to spend at the prize center.
​
We know this is a reasonable answer because the actual answer is
77  1/5, which is very close to the estimated answer. 

ROUNDING DOWN
Example Problem:
Damonté collected 654 stamps for his stamp collection. If he wants to store them five binders, about how many stamps will be in each binder?
​

We know this is an estimation problem because it says "about how many." We can solve this problem by rounding the 656 stamps DOWN to the nearest ten before dividing: 650.

650÷5=130



So, each of Damonté's stamp binders will hold
​ ABOUT 130 STAMPS.

We know this is a reasonable answer because the actual answer is
​131  1/5, which is very close to the estimated answer. 

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​2. Front-End Rounding (Highest Place Value)

With this method, you simply round the dividend to the highest place value in the number. 

Watch this video for a demonstration.

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​3. Compatible Numbers (May use multiplication chart)

​The purpose of using compatible numbers is changing one or both parts of the problem to make the operation (+, -, x, or ÷) easier.
The goal is to use "benchmark numbers" such as 5 or 10, which is usually easier for us to work with. 

EXAMPLE PROBLEM:
Peyton, Jamia, and Ashlynn had a jump rope contest. The friends counted a total of 237 jumps.
Write a number sentence to show how you could estimate the number of jumps each friend made during the contest.

We know this is a division problem because it asks us to break 237 jumps into 3 equal groups. Since the directions tell us to estimate,
​we know we can change the numbers to make it easier to solve. 
NOTE: Using compatible numbers gives us flexible answers depending on the type of problem. 

SOLUTION 1: (Closest estimate)
We can change 237 to a number divisible by 3. Look at the highest two place values (237). Now look at the row or column under "3" on the multiplication chart and find another number that is closest to 23. The closest number is 24. So, we can the "23" to "24" and make everything else (the "7") a zero. This gives us 240. Now we can divide:
240÷3=80​
So, each friend jumped about 80 times without messing up.

SOLUTION 2: (Smaller Estimate)
We can change 237 to 250 (nearest 10) and bump 3 up to 5 (nearest benchmark, never use 0!).
250÷5=50​
So, each friend jumped about 50 times without messing up.
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Long Division Strategies

Train Station Method:

In Mr. Price's class, we often use this method to divide because we can use our multiplication chart for each step of the long division process. 

This is best explained using the video to the right.

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Traditional Method:

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Another traditional example:

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Making Sense of the Remainder!

The remainder is the "leftover" part of our quotient. See the chart below to understand when and how to use it. 

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