Presentation on theme: "Multiplying Multiple Digit Numbers"— Presentation transcript:
1 Multiplying Multiple Digit Numbers Graphics/Shape – picture on the slide of a multiplication problem that appears to be on a sheet of paperColors – bright colors to attract the attention of a middle school studentContrast – 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 moreSixth Grade Remedial MathMs. Adams
2 WelcomeWelcome 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 – picturesACE – the purpose and overall message is conveyedTypography elements – chunkingPAT Principles – beginning with a welcome statementGestalt 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 repeatedaddition.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 objectiveHierarchy Perceptions – starting with easiest concept and then moving to the more difficult conceptSpace – instructional goals are equally spaced so that it is clearly visible how many instructional goals are thereColor – bright blue and green seem to complement one another in this slideGraphic – 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 lessonContrast – color with bright orange and brown tabs; pattern on the slide title contrasts with the borderShapes – circle tabsAlignment – center alignment that goes from left to right4Lesson 35Lesson 4
5 V O C A B U L R Y Multiplication Multiple Product Factor Place Value -Repeated additionof the same numberExample:Multiple-The product of the number and any other whole numberExample:Multiples of 2 _ 2, 4, 6, 8, 10, 12, 14…VOCABULRYProduct-the answer to amultiplication problemExample:Factor-a number that will divideinto another number withouta remainderExample:Factors of 20 _ 1, 2, 4, 5, 10, 20Contrast- different colors for each vocabulary word; pattern on the slide titleMultimedia – hyperlinks on multiplication and place value vocabulary wordsFonts – vocabulary words and examples are different fonts to distinguish between the twoDepth – the pictures look close and further away with the tiltProximity – the vocabulary words, definitions, and examples are chunked togetherPlace 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 numberExample:
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 anumber.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 graphicContrast – the pattern and color in the slide title contrasts with the color and solid background of the rest of the slideSpacing – spacing between the sentences so it is easier to readAlignment – the slide title is aligned to the centerBy using 3 hundred blocks, 4 rows of tenblocks, and 2 single blocks.Use the fewest number of blocks torepresent the number.
7 Another way to visualize place value is by making a chart.P l a c e V a l u eRemember: The value of whole numbersincrease from right to left. For example,the ten place value is greater than theones place value. The hundreds placevalue is greater than the tens and onesplace value.HundredsTensOnesIn order to make the number 342, you need:Three 100’s = 300Four 10’s = 40Two 1’s = 2Therefore…= 342Typography – chunking with the box around the “remember” sectionProximity- the box is close to the chartTypography – the numbers are in bold to draw your attentionContrast – 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 ThousandsHundredsTensOnesRepresentation1717226261,409493,4003525Contrast- the pattern on the slide titleAlignment – 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 wordsPAT 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 ….4Problem 2: Identify the digit in the hundreds place value.1,043*How many hundreds are needed to make the number?Answer : 0Contrast – title slide and typographySpacing – between the problemMultimedia - 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?93. In 627, which digit is in the tens place?24. In 901, which digit is in the hundreds place?5. In 270, which digit is in the hundreds place?Graphic – picture of a student workingAlignment – aligned to the rightShape – 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 43 x 4 = = 12Number ofgroupsNumber ineach groupNumber ofgroupsNumber ineach groupFigure/Ground – the pictures and boxes stand out since they give a visual representation of multiplicationProximity – 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, ____ scissorsin each group____ +____ + ____ = ____3 x 2 = 6Write an addition sentencefor the picture.___ groups, ____ gummy bearsin each group___ +___ + ___ + ___ + ___ =____5 x 8 = 405832Shape – shapes are used to separate each of the multiplication problemsPAT Principles – uses shapes, color, and spacing to distinguish between the two problemsRepetition – repeating what is on the previous slide88888402226
13 SINGL EDTMultiplicationDraw 3 groups of seven sticks.= 21Draw 2 groups of six balls.7 x 3 = 21PAT Principle – contrast with color; shapes are used to separate the multiplication problems; shapes are also used to show the groups for the multiplicationMultimedia – animationsRepetition – grouping the numbers and repeated addition6 + 6 = 126 x 2 = 12
14 5 x 5 = ___ 8 x 4 = ____ 32 7 x 4= ____ 28 25 4 x 4 = ___ 16 MULTIPLY ON YOUR OWN8 x 4 = ____327 x 4= ____28PAT Principle – contrast with color; shapes are used to separate the multiplication problems; shapes are also used to show the groups for the multiplicationMultimedia – animationsRepetition – grouping the numbers and repeated addition5 x 5 = ___254 x 4 = ___16
15 Be sure to put the larger or longer number on top. Multiplying By Two Digit NumbersYou will learn how to multiply a single digitnumber by a number that ends in zero.Let’s take a look at the problem below.20 x 2Using repeated addition: = 40Remember: 2 groups of 20To solve this problem by multiplying first, write theproblem vertically as such _ 20x 2Contrast – the background color contrasts with the background under the pictureShape – the cloud conveys that there is an important piece of information that is must be related to the learnerHierarchy – building onto the knowledge from the previous slidesAlignment – aligned to the rightACE – purpose is conveyedBe 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 0x 2Last, the product is 40.20x 240Second, multiply the single digitby the digit in the tens place value.2 0x 24 0Typography – transition words are in bold and enlargedColor – various colorsShape – used for the background and used to show what numbers to multiply
17 Multiplying By Two-Digit Numbers Here’s another example.43 x 10First, set the problem up vertically.43x 10Second, multiply 43 by 0.x x 0Next, multiply 43 by the one in the tens place value.x 1000430Contrast – colors contrast with the bright checkered background and the lighter brown backgroundShapes – rectangles to show what numbers to multiply togetherColor – show what numbers are being multiplied and the resulting productAlignment – starts on the right and goes to the left to show orderPut 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 Numbers43x 1000430The last step is to add to get the product.+ 430Ten sets of 43 is 430.= 430Be sure to line up the place values after multiplying.Spacing – shows the progression of steps in solving the multiplication problemColor – to show the productShape – the rectangle offers a reminder when solving the problemRepetition – the reminder was on a previous slide
19 PracticeTry these on your own. Multiply.x 1000+ 590590The product is 590.70x 3000+ 21002100The product is2,100.90x 2180The product is 180.Shapes – separate the multiplication problemsProximity – the numbers are close together in each problem in order to see how to solve the problemColor – the final answer is in a different color from the problemFigure/Ground – the problems are the figure and the light brown background with the directions is the groundContrast – the pattern on the title slide and the background color contrasts with the checkered borderACE – evaluate how well the instructional goal was presented and understood
20 Multiplying Multiple Digit Numbers Let’s multiply. 612 x 24When multiplying multiple digit numbers by each other,set the problem up vertically.612x 24Multiply 612 and four.x 42448Multiply 612 and 20.x 20000+12240x 24 = 14,688Add the products together.12240+ 244814688PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problemShape – the rectangle has the last part of the problem and the final answerTypography – the title slide uses a different font to distinguish that this is a new conceptMultiplying Multiple Digit Numbers
21 Multiplying Multiple Digit Numbers Let’s’ try this problem together. 423x 211First, multiply 423 by the one in the ones place value.423Next, multiply 423 by the one in the tens place value.(We’re basically multiplying 423 and 10)4230Then, multiply 423 by the two in the hundreds place value.Add x 211 = 84,60084600PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problemShape – the rectangle has the last part of the problem and the final answerColor – to show the answer and what digit is being multiplied423423089253
22 Multiplying Multiple Digit Numbers Let’s work through this problem together.8,346x 5216692433992Try this problem on your own.168x 958401596036712134Multiply 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.PAT – chunking the words and numbers to understand the steps in solving a multiple digit multiplication problemShape – shows the stepsMultimedia – animationsMultiply 8,346 and 50.Add
23 NOW MULTIPLY ON YOUR OWN 1.320x 1239606400+32000393602.38x 24152+ 3805323.226x 1151130226025990Shapes – separate the problemsMultimedia - animations
24 Let’s Review Thousands Hundreds Tens Ones Place value is the position of a digit within anumber.Think about how many ones, tens, hundreds,or thousands are needed to create a number.Thousands Hundreds Tens OnesProblemFind the digit in the ones placevalue.688Answer: 8PAT – chunking the words and numbers to understandTypography – the title slide uses a different font to distinguish that this is a new area
25 Let’s ReviewMultiplication is repeated addition wherethere are groups of the same size.9 x 9There are 9 groups with 9 in each group.Solve by adding.= 819 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 thetens place value. Add the numbers together. Be sure to line up thenumbers in columns.13x 1339+130169
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!