Virginia SOL 4.4 a-d: Computation and Estimation using Multiplication and Division

Virginia SOL 4.4 a-d:Computation and Estimation using Multiplication and Division.Austin Mitchellhttp://mrmitchell3.weebly.com [email protected]

By PresenterMedia.com

Important*To advance within the slides click with the mouse or use the arrow keys.

http://mrmitchell3.weebly.com/

http://www.presentermedia.com/mspp.html

Table of Content Use this page to navigate your way around. Click on a section to be taken to the appropriate

area.

•Goals and Expectations•Key Vocabulary

•Basic Multiplication Facts•Multiplication: 2-digit by 2-digit• Practice

•Multiplication: 3-digit by 2-digit• Practice

•Multiplication Quiz•Instructional Video

•Basic Division Facts•Division 3-digit by 1-digit• Practice

•Division Quiz

•Solving Word Problems• Practice

•Unit Test•Websites of Interest•Sources

*To advance within the slides click with the mouse or use the arrow keys.*This button

takes you back a slide

Multiplication Lessons Division Lessons

• Through this PowerPoint you will explore multiplication and division.• You will see step-by-step instructions on how to solve different types

of problems , then you will take what you have learned and solve problems of your own.

• At the end of each lesson you will have a short quiz for you to show what you know.

• At the end of the whole unit you will have an assessment over everything that has been taught.

• The overall goal is for you to become more confident in your ability to solve multiplication and division word problems, including multi-step questions.

• *Use the printout provided by your teacher to show your work, or it can be found at http://mrmitchell3.weebly.com under the important documents tab.

What is expected of you?•GOALS AND EXPECTATIONS


Fill in the blank in your packet, with the correct vocabulary word (use any source available):

_________ A whole number that is multiplied with another factor

to answer a multiplication problem.

_________ The answer to a multiplication problem.

_________ The number being divided in a division problem

_________ A whole number that divides equally into the

dividend

_________ The answer to a division problem

_________ The amount left over after dividing a number

_________ The approximate value you are looking for, usually

found by rounding.

Words you will see•KEY VOCABULARY

Vocabulary Words

DividendDivisorEstimateFactorProductQuotientRemainder

*Answers

Follow this link to work on some flash cards, when you are confident in your

abilities come back to this page and answer the following questions in

your packet.

Multiplication Flash Cards

*When you get to the website, click on the level 3 cards.

7 4 3 9 4 5 8

X3 x9 x3 x7 x3 x8 x2

4 3 5 8 10 6 9

X 7 x10 x7 x3 x 9 x6 x2

Practice your basic facts and then answer the following questions•Basic Multiplication

http://www.factmonster.com/math/flashcards.html

This slide will help you to take the basic facts you know and use them to multiply a 2-digit number by a 2-digit number. On your paper you should be following the steps as they reveal themselves so that you get a better understanding.

Example 1: 45 x 23

The first thing you need to make sure you do with a multiplication problem written horizontally is to rewrite it vertically, making sure to line up the place values.

45

x23

What do I do?

•Multiplication: 2-digit by 2-digit

*To advance within the slides click with the mouse or use the arrow keys.

1

45

x23

5

Step 1: Multiply the ones place of your bottom number by the ones place of your top number.

3 x 5 = 15,

Since you cannot put a two-digit number in the ones place you need to place the 5 in the ones place of your product, and carry the 1 above the tens place of the top number.



1

45

x23

5

Step 2: Multiply the ones place of the bottom number by the tens place of the top number. If you carried from step one you will add this number AFTER you multiply.

3x4=12

12+1=13

since there is not a number in the hundreds place you will place 13 in your answer slot.



13

1

45

x23

135

0



You have multiplied the ones place of your bottom number by each of the top numbers so you are now going to multiply the TENS place of the bottom number by each of the place values of the top number. Step 3: You will multiply the 2 of the bottom number by the

5 of the top number, however, since you are multiplying by tens you need to place a 0 in ones place of your answer. This is the same as multiplying 20 x 5.

I recommend crossing out the numbers you have already used, such as the 1 you carried in step 2, and the ones place of the bottom number.

1

45

x23

135

0



Step 3 continued: You will multiply 2 x 5= 10, but we cannot place a two digit number in one place value. So the 0 goes in the tens place and as in step 1 you need to carry the 1 above the tens place of your top factor. This 1 is different from the one you have already crossed out.

1

0

1

45

x23

135

0



Step 4: Multiply the tens place of the bottom factor by the tens place of the top factor. If you carried from the previous step you will ADD this number AFTER you multiply.

1

0

2 x 4 = 88+1 = 9

This number goes in the hundreds place.

9

1

45

x23

135

0



You have now multiplied 45 x 23 but you are not finished yet. You have two numbers and these numbers need to now be ADDED together to find your total.

What this method of multiplication does is break down the problem into 40 x 3, 5 x 3, 20 x 5 and 3 x 5. These numbers need to be added together to get the total. Step 5: Add the two numbers. 135 + 900

1

0 91,035

1

45

x23

135

0



Your final answer is 1,035

1

0 91,035

Steps to multiplying a 2-digit number by a 2-digit number• Instructional Video

If you are still unsure, you can watch this video for step by step instructions.



• Congratulations!• You have completed the tutorial for multiplying 2-digit by 2-digit

numbers.

• Now take what you know and solve the problems on the next slide in your packet. Make sure to show your work and feel free to use the tutorial to help you find the answers.



• Practice Problems

37 24 28 63 50x83 x21 x45 x39 x19

Click here to go back to beginning of tutorial.

This slide will help you to take the basic facts you know and use them to multiply a 3-digit number by a 2-digit number. On your paper you should be following the steps as they reveal themselves so that you get a better understanding.

Example 1: 312 x 64

The first thing you need to make sure you do with a multiplication problem written horizontally is to rewrite it vertically, making sure to line up the place values.

312

x64

What do I do?





312 x64

When multiplying 3-digit numbers by 2-digit you follow basically the same steps as 2-digit by 2-digit with a couple steps added in.

Since these are related I will shorten up the steps to multiplying 3-digit by 2-digit numbers.



312 x64

Step 1: Multiply the ones place of the bottom factor by each number in the top factor. Remember to carry when needed and you add AFTER you multiply.

4 x 1 = 4

4 x 3 = 12

4 x 2 = 8

8412



312 x64

Step 2: multiply the tens place of the bottom factor by each place value of the top factor.

8412

BEFORE you begin to multiply make sure to cross out any numbers you may have carried, and place a 0 in the ones place of your answer.

0



312 x64

Step 2 continued:

84120

6 x 2 = 12 carry the one

6 x 1 = 6 ADD the 1 you carried 6 + 1 =7

6 x 3 = 18

2

1

718



312 x64

Step 3: Add the products together1,248 + 18,720

841202

1

718

86991



• Congratulations!• You have completed the tutorial for multiplying 3-digit by 2-digit

numbers.





123 274 634 572 337 x21 x11 x52 x48 x66


Answer these problems on the next page of your packet. Page 1 of 2Try to solve these without looking back at the tutorial.

•Multiplication Quiz:


1. Jamie bought 25 boxes of chocolates. In each box of chocolates there were 32 chocolates. How many total pieces of chocolate were there?

2. For his restaurant Brian bought 44 bags of potatoes. In each bag there were 72 potatoes. How many potatoes did Brian buy for his restaurant ?

3. What is the term given to the whole numbers you multiply together in a multiplication problem?

4. A factory makes 742 paper clips in 1 hour. At this rate how many paper clips could the factory make in 32 hours?

Answer these problems on the next page of your packet. Page 2 of 2•Multiplication Quiz:


5. A greeting card company prints 342 cards every day. How many cards could this company make in 24 days?

6. The answer to a multiplication problem is called the________.

7. A college track team went to a track meet. They took 5 vans and 2 buses. If each van had 7 people in it and each bus had 34 people, how many total people were there?

*Before continuing on have theTeacher check your work.

Follow this link to work on some flash cards, when you are confident in

your abilities come back to this page and answer the following

questions in your packet.

Division Flash Cards

When you get to the website, click on the level 3 cards.

Practice your basic facts and then answer the following questions•Basic Division

45 / 9 = 32 / 9 = 56 / 7 =

30 / 3 = 12 / 4 = 49 / 7 =

24 / 6 = 35 / 5 = 28 / 3 =

http://www.factmonster.com/math/flashcard.html?op%5B0%5D=division&level=3

This slide will help you to take the basic facts you know and use them to divide a 3-digit number by a 1-digit number.

On your paper you should be following the steps as they reveal themselves so that you get a better understanding.

Example 1: 3)475

As with multiplication you need to make sure the problem is written in a certain way. The dividend is 375 and goes inside the division symbol, the divisor is 3 and goes on the left of the division symbol. The quotient will go on the top of the division symbol, make sure your quotient has the same number of digits as your dividend, even if one is a zero.

What do I do?

•Long Division: 3-digit by 1-digit


DMSB



The steps to long division follow a pattern of DMSB which is an aconym for Divide Multiply Subtract Bring down. These steps may be difficult to remember so students come up with a mnumonic to remember this.Examples are:1. Dead Monkeys Smell Bad2. Does Mcdonalds Sell Burgers3. Damp Mold Smells Bad

Try and come up with your own, or you can use one of these.

3 )475



I recommend writing DMSB vertically like this, after each step is completed place a check mark next to the letter.

DMSB

Step 1: Divide•Divide 3 into the first number of the dividend (4)•How many 3’s will go into 4?•Write the answer directly above the number you are dividing into (4)•3 goes into 4 only one time

1

3 )475



D MSBStep 2: Multiply

•Multiply the divisor by the first number in the quotient (3x1 = 3)•You can put a multiplication sign at the corner of your division symbol to remind you of this step.•Write your answer directly below the first digit in your quotient.

1x

3

3 )475



D MSBStep 3: Subtract

•Draw a line under the 9•Write your subtraction sign•Subtract vertically (4-3=1)•Write your answer

1x

31

3 )475



D MSBStep 4: Bring Down

•Go to the next number to the right in your dividend and bring this number down to the answer of your subtraction problem.

1x

317

3 )475



D MSB

Step 5: Remainder•This new number is your new dividend. If your divisor can still go into your dividend you need to repeat the steps•If not, this is your remainder•3 can go into 17 so you must repeat the steps.

1x

317

3 )475



D MSB

Step 6: Start back over with division•Divide 17 by 3• See how many times 3 goes

into 17•3 goes into 17 five times, so you would place a 5 above the tens place in your quotient.•Do not forget to check off your steps.

1x

317

5

3 )475



D MSB

Step 7: Multiply•Multiply your divisor by the number you just wrote in the quotient (3 x 5 = 15).•Write the answer (15) directly beneath the number already there (17)

1x

317

5

15

3 )475



D MSBStep 8: Subtract

•Subtract your two numbers• (17-15 = 2)

1x

317

5

15 02

3 )475



D MSBStep 9: Bring Down if

possible•Bring down the next number in your dividend, in this case (5)

1x

317

5

15 02 5

3 )475



D MSB

Step 10: Remainder•If your divisor can divide into this number then you will repeat your division step.•In this case 3 can go into 25 so you will repeat the steps again.

1x

317

5

15 02 5

3 )475



D MSBStep 11: Divide

•3 goes into 25 eight times, so you would place an 8 in the next place value of your quotient, in this case the ones place.

1x

317

5

15 02 5

8

3 )475



D MSB

Step 12: Multiply•Multiply your divisor by the most recent number you placed in your quotient.• 3 x 8 = 24

•This number goes beneath 25 so you can complete your next step.

1x

317

5

15 02 5

8

24

3 )475



D MSBStep 13: Subtraction

•Subtract these two numbers• 25 - 24 = 1

•Write this in the correct spot.

1x

317

5

15 02 5

8

2401

3 )475



D MSB

Step 14: Remainder•Check to see if your divisor can go into this new number.• 3 cannot go into 1 so you

are finished.•1 is what you have left, this is called your remainder, it is written as shown.

1x

317

5

15 02 5

8

2401

R 1

3 )475



D MSB

You will notice on your checklist of DMSB that there is one less check mark on B, this is because you may end up with a remainder, and no other numbers to bring down.

The answer will be 158 R 1

1x

317

5

15 02 5

8

2401

R 1

•Division : 3-digit by 1-digit


• Congratulations!• You have completed the tutorial for dividing 3-digit by 1-digit

numbers.


•Division: 3-digit by 1-digit



• 465 3 723 5 382 4

• 634 4 877 8



•Division Quiz:


1. A children’s soccer league wants to order 374 shirts for the teams. If each box holds 9 shirts, how many boxes will they need?

2. A restaurant needs 472 rolls of toilet paper. If each package has 3 rolls, how many packages would they need?

3. Your school office needs to order 278 labels for the teachers. If the pack of labels has 6 labels in it, what is the number of packs the school office needs to buy?


•Division Quiz:


4. The principal wants to get popsicles for his students. If he has to buy 552 popsicles and they come in boxes of 9, how many boxes does he need to buy?

5. The zookeeper needs to buy 673 fish a month for his penguins. The bags of fish hold 6 fish, how many bags of fish would he need to purchase?

6. Sam’s brother gave him 56 stickers, his mom gave him 124 stickers and his dad gave him 200 stickers. If Sam was going to split the stamps equally between himself and three closest friends, how many stamps would each child have?

Instructional for solving word problems•Solving Word Problems

• When it comes to solving word problems there are certain items you need to focus on.

• What is the question asking you?• What operations are you going to use?• Does the information include the total, or do you need to find the total?


• There is a good website to help you better understand problem solving at http://academic.cuesta.edu/acasupp/as/706.htm

• Step 1 says to find what the problem is asking, what does it tell me that is useful and what is the problem implying.

• Step 2 asks you to draw a picture representing what the question is asking

• Step 3 allows you to make a table to help find the answer

http://academic.cuesta.edu/acasupp/as/706.htm


• One thing you can look for is if the question gives you the total or asks you to find it.

• This can help you determine the operation you will be using.• For example: if you are looking for the total you will be adding or

multiplying, but if you have the total you will be using division or subtraction.

• Be careful, because you may have to use more than one operation. You may have noticed in the quizzes for multiplication and division there was a problem that required you to use more than one operation.

• You can see an example on the next slide

Practice solving word problems•Word Problems

There are 4 third grade classes with 24 students in them and 12 other grades, each with 21 students in them. How many students are there in the school?

1. For this problem you need to first see what the question is asking1. How many students are there in school?2. This helps us to realize that we are looking for the total

1. Do you remember which operations we may be using?

1. Addition or multiplication

2. Next you will notice that there are multiple classes each with a certain number of students.



1. This helps you to understand that you are going to need to multiply as one of your operations. You need to find out what you will multiply for this problem

1. Since there are 4 third grade classes you will need to multiply 4 times 24 to get the number of students.

2. There are 12 other grades with 21 students so you will need to multiply these numbers as well to get the number of students.

3. To find the total number of students you will need to combine both of your products together.



Your operations will look like this:

24 21 252 x4 x12 +96 96 252 348

Practice solving word problems in your packet•Word Problems

Try a couple on your own:

1. Nolan’s mother gave him $180. Nolan bought 8 books, and each cost $12. How much money does Nolan have left?

2. Bob bought some pencils and crayons. If he bought 5 boxes of 24 pencils and 12 boxes of 18 crayons. How many crayons and pencils did he buy?

•Unit Test

To take the final test over this unit click on the link below:

http://www.quia.com/quiz/3731715.html

*You must put your first and last name in the correct field to receive credit. Your score will be reported back to you as soon

as possible.



Websites of Interest



http://mrmitchell3.weebly.com

http://www.amathsdictionaryforkids.com/dictionary.html








SOURCES

http://www.factmonster.com/math/flashcards.html#mul


All Clipart was found through Microsoft PowerPoint Clipart search.

Math definitions were found at:http://www.amathsdictionaryforkids.com/dictionary.html





Fill in the blank with the correct vocabulary word: Factor- A whole number that is multiplied with another,

to answer a multiplication problem.

Product- The answer to a multiplication problem.

Dividend - The number being divided in a division problem

Divisor- A whole number that divides equally into the

dividend

Quotient - The answer to a division problem

Remainder- The amount left over after dividing a number

Estimate- The approximate value you are looking for, usually

found by rounding.

Answers:•KEY VOCABULARY (Answers)

Vocabulary WordsDividend

Divisor

Estimate

Factor

Product

Quotient

Remainder

Documents

Virginia SOL 4.4 a-d: Computation and Estimation using Multiplication and Division