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Transcript of Welcome to sixth grade math. Today you will learn how to multiply multiple digit numbers. I am your...
Multiplying
Multiple
Digit NumbersSixth Grade Remedial Math
Ms. Adams
Welcome to sixth grade math. Today you will learn how to multiply multiple digit numbers. I am your tutorial guide Miss Adams. I currently teach sixth grade math at Jane Macon Middle School. I hope that you will learn a lot today so that you can successfully master the objectives presented in this lesson.
Please take note of the guide tabs on each page. This will help you navigate through the tutorial. Please feel free to go back and review any of the pages. Good luck with successfully completing this tutorial.
Instructional Goals
1. Identify place value in multiple digit numbers.
2. Represent multiplication with single digit numbers by modeling repeated addition.
3. Multiply a two digit number by a multiple of 10.
4. Multiply a multiple digit number by a multiple digit number.
Table of Contents
1 Vocabulary
2Lesson 23
Lesson 1
4 Lesson 3
5 Lesson 4
VOCABULARY
Multiplication-Repeated addition of the same numberExample:
Multiple-The product of the number and any other whole numberExample: Multiples of 2 _ 2, 4, 6, 8, 10, 12, 14…Product
-the answer to a multiplication problem
Example:
Factor-a number that will divide into another number without a remainder
Example: Factors of 20 _ 1, 2, 4, 5, 10, 20
Place Value-the value of a digit as determined by its position in a number; the name of the place or location of a digit in a number
Example:
PLACE
VALUE
Place value is the position of a digit within a number.
How do we represent the number 342?
By using 3 hundred blocks, 4 rows of ten
blocks, and 2 single blocks.
Use the fewest number of blocks to represent the number.
PlaceValue
Another way to visualize place value is by making a chart.
3 4 2
Hun
dred
sTe
ns
One
s
In order to make the number 342, you need:
•Three 100’s 100 + 100 + 100 = 300
•Four 10’s 10 + 10 + 10 + 10 = 40
•Two 1’s 1 + 1 = 2
Therefore…
300 + 40 + 2 = 342
Remember: The value of whole numbers increase from right to left. For example, the ten place value is greater than the ones place value. The hundreds place value is greater than the tens and ones place value.
P L A C
E U L AV
Check out the table below.
NumberThousands
Hundreds
Tens
Ones Representation
17 1 7
226 2 2 6
1,409 1 4 0 9
3,400 3 4 0 0
52 5 2
Let’s PracticeProblem 1: Identify the digit in the tens place value.
941*Think about how many sets of ten are needed to display this number.
The answer is ….4
Problem 2: Identify the digit in the hundreds place value.
1,043*How many hundreds are needed to make the number?
Answer : 0
NOW IT’S YOUR TURN
1. In 265, which digit is in the ones place?
5
2. In 397, which digit is in the tens place?
9
3. In 627, which digit is in the tens place?
2
4. In 901, which digit is in the hundreds place?
9
5. In 270, which digit is in the hundreds place?
2
Multiplication is repeated addition that is symbolized by the
operation symbol “x”.
Multiplication means to have groups of the same size.
3 x 4
3 4 4 3
3 x 4 = 3 + 3 + 3 + 3 = 12
Number of groups
Number in each group
Number of groups
Number in each group
Single
Digit
Multiplication
Write an addition sentence for the picture.
___ groups, ____ scissors in each group
____ +____ + ____ = ____
3 x 2 = 6
3 2
2 2 2 6
Write an addition sentence for the picture.
___ groups, ____ gummy bears in each group
___ +___ + ___ + ___ + ___
=____
5 x 8 = 40
5 8
8 8 8 8 8 40
SINGLE
DIGIT
MULTIPLICATION
7 + 7 + 7 = 21
7 x 3 = 21 Draw 2 groups of six balls.
6 + 6 = 12
6 x 2 = 12
MULTIPLY ON YOUR OWN
7 x 4= ____28
8 x 4 = ____32
4 x 4 = ___165 x 5 = ___25
Multiplying By Two Digit Numbers
You will learn how to multiply a single digit number by a number that ends in zero.
Let’s take a look at the problem below.20 x 2
Using repeated addition: 20 + 20 = 40
Remember: 2 groups of 20
To solve this problem by multiplying first, write the problem vertically as such _ 20
x 2
Be sure to put the
larger or longer
number on top.
Multiplying By Two Digit NumbersFirst, multiply the digits in the ones place value.
2 0 x 2
0Second, multiply the single digit by the digit in the tens place value.
2 0 x 2
4 0
Last, the product is 40.
20 x 2
40
Multiplying By Two-Digit NumbersHere’s another example.
43 x 10
First, set the problem up vertically. 43 x 10
Second, multiply 43 by 0.43 43
x 0 x 0 0 00
Next, multiply 43 by the one in the tens place value. 43 x 10 00 430
Put a zero to hold the
ones place value before multiplying the number in the tens
place value.
43 x 10
00 430
The last step is to add to get the product.43
x 1000
+ 430 430
Ten sets of 43 is 430. 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 + 43 = 430
Multiplying By Two-Digit Numbers
Be sure to line up the
place values after
multiplying.
Practice
Try these on your own. Multiply.
1. 59 x 10 00 + 590 590
The product is 590.
2. 70 x 30 00 + 2100 2100
The product is2,100.
3. 90 x 2 180
The product is 180.
Multiplying Multiple Digit Numbers
Let’s multiply. 612 x 24
When multiplying multiple digit numbers by each other, set the problem up vertically.
612 x 24
Multiply 612 and four. 612
x 4 2448
Multiply 612 and 20. 612
x 20 000 +12240
12240 612 x 24 = 14,688
Add the products together.12240+ 244814688
Multiplying Multiple Digit Numbers
Let’s’ try this problem together.423 x 211
First, multiply 423 by the one in the ones place value. 423 x 211 423
Next, multiply 423 by the one in the tens place value. (We’re basically multiplying 423 and 10). 423
x 211 4234230
Then, multiply 423 by the two in the hundreds place value. 423 x 211 423 4230 Add 423 x 211 = 84,600
84600
423 4230+ 84600 89253
Multiplying Multiple Digit NumbersLet’s work through this problem together.
8,346 x 52 16692+417300 433992
Multiply 8,346 and 2.
6 x 2 = 12Carry the digit
in the tens place value
above the four. Add 1 to the product of 4
and 5.
1
Multiply 8,346 and
50.
321
Add
Try this problem on your own.
168 x 95 840
+ 15120 15960
4376
Click icon to add picture
NOW MULTIPLY ON YOUR OWN
320 x 123 960 6400 +32000 39360
1. 2. 38 x 24 152 + 380 532
3. 226 x 115 1130 2260 + 22600 25990
Place value is the position of a digit within a number.
Think about how many ones, tens, hundreds, or thousands are needed to create a number.
Thousands Hundreds Tens Ones
Problem
Find the digit in the ones placevalue.
688
Answer: 8
Multiplication is repeated addition where there are groups of the same size.
9 x 9 There are 9 groups with 9 in each group.
Solve by adding.
9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 81
9 x 9 = 81
When multiplying by more than one digit, place value is
important.
Start by multiplying by the digit in the ones place. Carry the digits, if needed, and continue multiplying by the digit in the tens place value.
Don’t forget to put a zero to hold the ones place value before multiplying by the tens place value. Add the numbers together. Be sure to line up the
numbers in columns. 13
x 13 39 +130 169
IN CONCLUSION…
• Take your time.
• Ask yourself questions to help you along the way.
• Multiplication is repeated addition.
• Remember to carry over, if necessary, when multiplying.
Thank you for your time. Happy Multiplying!
RESOURCES
• http://www.aaamath.com/B/g6_31ax1.htm#section2
• http://www.mathsisfun.com/numbers/multiplication-long.html
• http://www.homeschoolmath.net/teaching/md/multiplication-repeated-addition.php
• http://mathatube.com/tables-charts-placevalue-chartshtml.html
• http://www.helpingwithmath.com/by_subject/multiplication/mul_by_10_3nbt3.htm