Interpreting Remainders in Division

Stephanie Sharrer

Let’s Look Back…Solve the problem

Label the dividend, divisor, quotient, and remainder.

Try to determine what would happen to the remainder in this problem.

The 7 fifth grade teachers decided to give their students a pizza party on the last day of school to celebrate their

graduation. The teachers ordered 52 pizzas to split evenly among their classes. How much pizza will each

teacher receive for their class?

Stephanie Sharrer

Share your solution, labels, and interpretation of what the remainder means in this problem with your shoulder partner.

Who would like to share their solution with the class?

Let’s Discuss

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As I read aloud A Remainder of One, work through each problem presented in your notebook.

Read Aloud

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Think-Pair-ShareList the choices you can

make regarding the remainder in a division

problem.

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Drop the remainder (Drop It)Add 1 to the quotient (Add It)Use the remainder as the

answer (Use It)Keep the remainder and write

it as a fraction or a decimal (Keep It)

Methods of Interpreting

the Remainder

Stephanie Sharrer

Let’s Take aSusan and Brianna baked 274

cupcakes. They brought the cupcakes to school for their

friends in cupcake trays. If each tray holds 4 cupcakes, how many cupcake trays will they need to

bring all the cupcakes to school?

Stephanie Sharrer

Let’s Take a What operation are we using? How do

you know?

What is the dividend?

What is the divisor?

Division because we are sharing

274 (total number of cupcakes)

4 (number of cupcakes held in each tray)

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Let’s Take a

4)274_____6

24-_____34

8

32-_____2

quotient

remainder

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Let’s Take a What does the quotient (68) mean?

What does the remainder (2) mean?

If I want to know how many trays Susan and Brianna will need to take ALL of the cupcakes to school, what will I do with the remainder?

So how many trays will Susan and Brianna need?

68 trays with 4 cupcakes each

2 cupcakes not in trays

Add It! (add 1 more tray so that the 2 remaining cupcakes will also be packed for school)

68 + 1 more = 69 trays

Let’s Change It Up a LittleSusan and Brianna baked 274 cupcakes.

They brought the cupcakes to school for their friends in cupcake trays. How many

cupcakes will be in the partially full tray?

T-P-S: What are we looking for now? What

are we going to do with the remainder to fi nd

the answer?

USE IT…So there are 2 cupcakes in the

partially full trayStephanie Sharrer

Another ExampleSusan and Brianna baked 274

cupcakes. They brought the cupcakes to school for their friends in cupcake trays.

How many full trays of cupcakes will Susan and Brianna have?

68 trays had 4 cupcakes each and 1 tray had the 2 leftover cupcakes So how many FULL trays will there be?

Stephanie SharrerDROP IT…there are 68 full trays

One More Time Susan and Brianna baked 274 cupcakes.

They brought the cupcakes to school for their friends in cupcake trays.

If Susan and Brianna are splitting the cupcakes between 4 classes, how many cupcakes will each teacher get?

Stephanie Sharrer

One More TimeWhat operation are we using? How do

you know?

What is the dividend?

What is the divisor?

Division because we are sharing

274 (total number of cupcakes)

4 (number of classes the cupcakes are being split between)

Stephanie Sharrer

One More Time

4)274_____6

24-_____34

8

32-_____2

quotient

remainder

Stephanie Sharrer

One More TimeWhat does the quotient (68) mean?

What does the remainder (2) mean?

What is going to be done with the 2 left over cupcakes?

So how many trays will each class get?

68 full cupcakes for each teacher

2 cupcakes left over

They will be cut and split between the classes

68 2/4 cupcakes, or 68 ½ cupcakes (the remainder is used as a fraction over the divisor)

Stephanie Sharrer

Let’s Try One!!

Ken needs athletic socks. They come in packs of 3 for $7. Ken has a twenty dollar bill. How many packs of socks can he buy? How much money will he have left?

•1 pack costs $7•$20 ÷ $7 = 2 r 6

2 packs of socks will cost him $14. That means he has $6 left. Is that enough for another pack?What does this mean?

Let’s Try Another One!!

Marcy buys rulers for the entire 5th grade class. There are 102 students in her grade level. Each box has 8 rulers. How many boxes will Marcy need to buy?

•102 students•8 rulers per box•102 ÷ 8 = 12 r 6

If Marcy only buys 12 boxes of rulers, she would only be able to give a ruler to 96 students. Therefore, she will need to buy 13 boxes.

What does this mean?

How About One More?

Janice has $269 to spend on books. Each book costs $8. How many books can Janice buy?

•$269 to spend• Each book costs $8• $269 ÷ $8 = 33 r 5

Janice can buy 33 books because 33 x $8 = $264.She will have $4 left over after her purchase.

What does this mean?

It’s Your Turn!

There are 149 people in Jared’s class. Jared buys erasers for each of the students. Erasers are sold 4 to a package. How many packages of erasers does Jared need to buy?

It’s Your Turn!

Chloe has $15 to spend on pencils. Each box of pencils costs $2. How many boxes of pencils can Chloe have buy? How much money will she have left after she buys the pencils?

It’s Your Turn!

Kris bakes 85 cookies for her class. There are 26 students in her class. Each student receives the same number of cookies. She promises to give the extra cookies to her little brothers. How many cookies do her brothers get?

It’s Your Turn!

Sam shares stickers with his class. Each sticker sheet has 5 stickers. If Sam’s class has 32 people, how many sheets of stickers does sam need?

It’s Your Turn!

Penny brings candy for the class. Each package of candy has 9 pieces. There are 67 students in her class. How many packages of candy does Penny need to bring?

Let’s ReviewAnd go over some key words and

differences between methods

Stephanie Sharrer

Drop It!Ignore the remainder and only use

the quotient as your answer.

Use this when the question asks for FULL or WHOLE items or when the item cannot easily be split in

real life.

Share It!Include the remainder in your

answer as a fraction or a decimal.

Use this with money, food, or measurements that are easy to

split in real life.

Add It!Take the quotient and add 1 more.

Use this when everything or everyone has to fit and you can’t

leave anything out.

Use It!Use the remainder (and not the

quotient) as your answer.

Use this when the question asks how much is left over or left out or

partially filled.Stephanie Sharrer

On Your OwnBe sure to answer EVERY part of the problem.

192 students want to play football in the Spring Lake League. If 7 people can play on each team, how many

full teams can be made?

How many students will be left out?

How many teams would be necessary in order to allow every

student to play?Stephanie Sharrer