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**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

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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)

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**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

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**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

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**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:

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**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.

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**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

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**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

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**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

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**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

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**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

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**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

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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

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**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

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**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.

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**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

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**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.

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**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

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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

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**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

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**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

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**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

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**NOW MULTIPLY ON YOUR OWN**

1. 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

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**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

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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

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**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

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**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!

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

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