1. Multiplying Multiple Digit Numbers
Graphics/Shape – picture on the slide of a multiplication problem that appears to be on a sheet of paper
Colors – bright colors to attract the attention of a middle school student
Contrast – checkered pattern as the border around the slide and the solid background; the title of the slide, the word multiple uses a different font to appear taller because multiple refers to more
Sixth Grade Remedial Math
Ms. Adams

2. Welcome
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.
Graphics – pictures
ACE – the purpose and overall message is conveyed
Typography elements – chunking
PAT Principles – beginning with a welcome statement
Gestalt Perceptions – the main goal is stated and this will in turn help students be more successful in sixth grade math (multiplying multiple digit numbers)

3. Instructional Goals Identify place value in multiple digit numbers.
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.
ACE – instructional goals are identified and organized in a manner where the learner must learn one objective before moving on the next objective
Hierarchy Perceptions – starting with easiest concept and then moving to the more difficult concept
Space – instructional goals are equally spaced so that it is clearly visible how many instructional goals are there
Color – bright blue and green seem to complement one another in this slide
Graphic – person trying to reach their goal and they are carrying a piece of the puzzle with them; this implies that they help build the bridge to reach the goal

4. 1 2 3 4 5 Table of Contents Vocabulary Lesson 1 Lesson 2 Lesson 3
Multimedia – hyperlinks on the number tabs to go to each lesson
Contrast – color with bright orange and brown tabs; pattern on the slide title contrasts with the border
Shapes – circle tabs
Alignment – center alignment that goes from left to right 4
Lesson 3 5
Lesson 4

5. V O C A B U L R Y Multiplication Multiple Product Factor Place Value
-Repeated addition
of the same number
Example:
Multiple
-The product of the number and any other whole number
Example:
Multiples of 2 _ 2, 4, 6, 8, 10, 12, 14… V O C A B U L R Y
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
Contrast- different colors for each vocabulary word; pattern on the slide title
Multimedia – hyperlinks on multiplication and place value vocabulary words
Fonts – vocabulary words and examples are different fonts to distinguish between the two
Depth – the pictures look close and further away with the tilt
Proximity – the vocabulary words, definitions, and examples are chunked together
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:

6. P L A C E V U E Use the fewest number of blocks to
Place value is the position of a digit within a
number.
How do we represent the number 342?
Typography – the word fewest is smaller than the other words; the numbers are enlarged to reinforce what is in the graphic
Contrast – the pattern and color in the slide title contrasts with the color and solid background of the rest of the slide
Spacing – spacing between the sentences so it is easier to read
Alignment – the slide title is aligned to the center
By using 3 hundred blocks, 4 rows of ten
blocks, and 2 single blocks.
Use the fewest number of blocks to
represent the number.

7. Another way to visualize place value is by making a
chart.
P l a c e V a l u e
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.
Hundreds
Tens
Ones
In order to make the number 342, you need:
Three 100’s = 300
Four 10’s = 40
Two 1’s = 2
Therefore…
= 342
Typography – chunking with the box around the “remember” section
Proximity- the box is close to the chart
Typography – the numbers are in bold to draw your attention
Contrast – the pattern on the slide title and the red box around the “remember” section

8. P L A C E U V Check out the table below. Number Representation 1 7 2 6
Thousands
Hundreds
Tens
Ones
Representation 17 1 7
226 2 6
1,409 4 9
3,400 3 52 5
Contrast- the pattern on the slide title
Alignment – the title is aligned to the “E”;
Typography – the “e” at the end of place and value is larger and in blue and yellow since it goes with both words
PAT principle – repeating the place value chart and representation

9. Let’s Practice Problem 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
Contrast – title slide and typography
Spacing – between the problem
Multimedia - animations

10. NOW IT’S YOUR TURN 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?
5. In 270, which digit is in the hundreds place?
Graphic – picture of a student working
Alignment – aligned to the right
Shape – all information is on the rectangle with the rounded edges

11. How do I multiply? 3 4 4 3 3 x 4 = 3 + 3 + 3 + 3 = 12 3 x 4
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 x 4 = = 12
Number of
groups
Number in
each group
Number of
groups
Number in
each group
Figure/Ground – the pictures and boxes stand out since they give a visual representation of multiplication
Proximity – the pictures are grouped with tabs explaining the groups and how many items are in each group; the multiplication problem at the bottom is between the two visuals

12. Digit Single 3 x 2 = 6 Multiplication Write an addition sentence
for the picture.
___ groups, ____ scissors
in each group
____ +____ + ____ = ____
3 x 2 = 6
Write an addition sentence
for the picture.
___ groups, ____ gummy bears
in each group
___ +___ + ___ + ___ + ___ =____
5 x 8 = 40 5 8 3 2
Shape – shapes are used to separate each of the multiplication problems
PAT Principles – uses shapes, color, and spacing to distinguish between the two problems
Repetition – repeating what is on the previous slide 8 8 8 8 8 40 2 2 2 6

13. S I N G
L E D T
Multiplication
Draw 3 groups of seven sticks.
= 21
Draw 2 groups of six balls.
7 x 3 = 21
PAT Principle – contrast with color; shapes are used to separate the multiplication problems; shapes are also used to show the groups for the multiplication
Multimedia – animations
Repetition – grouping the numbers and repeated addition
6 + 6 = 12
6 x 2 = 12

14. 5 x 5 = ___ 8 x 4 = ____ 32 7 x 4= ____ 28 25 4 x 4 = ___ 16
MULTIPLY ON YOUR OWN
8 x 4 = ____ 32
7 x 4= ____ 28
PAT Principle – contrast with color; shapes are used to separate the multiplication problems; shapes are also used to show the groups for the multiplication
Multimedia – animations
Repetition – grouping the numbers and repeated addition
5 x 5 = ___ 25
4 x 4 = ___ 16

15. Be sure to put the larger or longer number on top.
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: = 40
Remember: 2 groups of 20
To solve this problem by multiplying first, write the
problem vertically as such _ 20
x 2
Contrast – the background color contrasts with the background under the picture
Shape – the cloud conveys that there is an important piece of information that is must be related to the learner
Hierarchy – building onto the knowledge from the previous slides
Alignment – aligned to the right
ACE – purpose is conveyed
Be sure to put the larger or longer number on top.

16. Multiplying By Two Digit Numbers
First, multiply the digits in the ones place value.
2 0
x 2
Last, the product is 40. 20
x 2 40
Second, multiply the single digit
by the digit in the tens place value.
2 0
x 2
4 0
Typography – transition words are in bold and enlarged
Color – various colors
Shape – used for the background and used to show what numbers to multiply

17. Multiplying By Two-Digit Numbers
Here’s another example.
43 x 10
First, set the problem up vertically. 43
x 10
Second, multiply 43 by 0.
x x 0
Next, multiply 43 by the one in the tens place value.
x 10 00
430
Contrast – colors contrast with the bright checkered background and the lighter brown background
Shapes – rectangles to show what numbers to multiply together
Color – show what numbers are being multiplied and the resulting product
Alignment – starts on the right and goes to the left to show order
Put a zero to hold the ones place value before multiplying the number in the tens place value.

18. Be sure to line up the place values after multiplying.
Multiplying By Two-Digit Numbers 43
x 10 00
430
The last step is to add to get the product.
+ 430
Ten sets of 43 is 430.
= 430
Be sure to line up the place values after multiplying.
Spacing – shows the progression of steps in solving the multiplication problem
Color – to show the product
Shape – the rectangle offers a reminder when solving the problem
Repetition – the reminder was on a previous slide

19. Practice
Try these on your own. Multiply.
x 10 00
+ 590
590
The product is 590. 70
x 30 00
+ 2100
2100
The product is
2,100. 90
x 2
180
The product is 180.
Shapes – separate the multiplication problems
Proximity – the numbers are close together in each problem in order to see how to solve the problem
Color – the final answer is in a different color from the problem
Figure/Ground – the problems are the figure and the light brown background with the directions is the ground
Contrast – the pattern on the title slide and the background color contrasts with the checkered border
ACE – evaluate how well the instructional goal was presented and understood

20. 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.
x 4
2448
Multiply 612 and 20.
x 20
000
+12240
x 24 = 14,688
Add the products together.
12240
+ 2448
14688
PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problem
Shape – the rectangle has the last part of the problem and the final answer
Typography – the title slide uses a different font to distinguish that this is a new concept
Multiplying Multiple Digit Numbers

21. 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
Next, multiply 423 by the one in the tens place value.
(We’re basically multiplying 423 and 10)
4230
Then, multiply 423 by the two in the hundreds place value.
Add x 211 = 84,600
84600
PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problem
Shape – the rectangle has the last part of the problem and the final answer
Color – to show the answer and what digit is being multiplied
423
4230
89253

22. Multiplying Multiple Digit Numbers
Let’s work through this problem together.
8,346
x 52
16692
433992
Try this problem on your own.
168
x 95
840
15960 3 6 7 1 2 1 3 4
Multiply 8,346 and 2.
6 x 2 = 12
Carry the digit in the tens place value above the four. Add 1 to the product of 4 and 5.
PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problem
Shape – shows the steps
Multimedia – animations
Multiply 8,346 and 50.
Add

23. NOW MULTIPLY ON YOUR OWN1.
320
x 123
960
6400
+32000
39360 2. 38
x 24
152
+ 380
532 3.
226
x 115
1130
2260
25990
Shapes – separate the problems
Multimedia - animations

24. Let’s Review Thousands Hundreds Tens Ones
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 place
value.
688
Answer: 8
PAT – chunking the words and numbers to understand
Typography – the title slide uses a different font to distinguish that this is a new area

25. Let’s Review
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.
= 81
9 x 9 = 81

26. Let’s Review 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

27. Thank you for your time. Happy Multiplying!
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!

28. Resources http://www.aaamath.com/B/g6_31ax1.htm#section2