“Multiplication Movies” For further information contact… Vicki Iliff Roosevelt Academy 115 “E” Street Lake Wales, FL 33853 Route: C 863-678-4252 [email protected] 2008 - 2009 Idea Catalog of Excellence n PROGR AM OVERVIEW n OVER ALL VALUE n MATERIALS “Hey, hey, hey, how many Big Macs does Fat Albert order?” “Which anniversary are Mr. and Mrs. Snowman celebrating?” These are not questions you typically expect to hear in a middle school math class, unless you happen to visit mine when we are learning Multiplication Movies. Multiplication Movies is a fun, effective way for students to master their multiplication facts. It’s appropriate for students of all ages, and can be easily implemented in any classroom. My students love the program, and are disappointed on days when it’s not included in my lesson plans. While necessary materials are readily available in most classrooms, an overall materials list, including pricing and vendors, follows the lesson plans. As a math teacher for 6th - 9th grade ESE and at-risk students, I have tried numerous strategies over the years to help students master their multiplication facts. Multiplication Movies is by far the most successful approach I have used. While increasing access to the calculator in math classes would seem to eliminate the necessity of learning the multiplication tables, this is not really true. Students who are tied to a calculator for the most basic computations have great difficulty with other skills, such as adding and subtracting unlike fractions, identifying patterns, and solving multistep problems. The program is based on research findings that utilizing visual imagery results in increased memory. Students are introduced to a picture and story for each fact. For example, for 8 x 8 = 64, the picture shows Mr. and Mrs. Snowman (who represent the 8’s) holding an anniversary cake with 64 candles on it. Unfortunately for them, those candles put out so much heat that the snow couple melts away, leaving behind only his top hat and her wig. While it seems impossible that a student who is unable to learn a simple fact like 8 x 8 = 64 could remember such a detailed picture and elaborate story, the results are amazing. Within weeks you will see dramatic improvement in student mastery of multiplication facts. Most importantly, though, your students will gain confidence in their ability to learn. n LESSON PLAN TITLES • Introduction to Multiplication Movies • The Remaining Movies • Introduction to Precision Teaching n ABOUT THE DEVELOPER Vicki Iliff has a B.S. in Education from Illinois State University and an M.A. in Administration from the University of Illinois-Springfield. She has 33 years of experience working with students with learning interferences. She currently teaches Intensive Math to 8th/9th graders at Roosevelt Academy. HHH “Multiplication Movies” Vicki Iliff Program Rationale A colleague helped me realize that the premise that students need to memorize all the facts from 0 x 0 to 12 x 12 was faulty. As she convinced me, there are really only 15 facts that require straight memorization. 1. No one needs to memorize facts with 0’s or 1’s; they just need to be taught the rules of 0 and 1 (0 times any number is 0 and any number times 1 is itself). 6. This leaves only 15 facts to memorize: 3x3 3x4 3x6 3x7 3x8 4x4 4x6 4x7 4x8 6x6 6x7 6x8 7x7 7x8 8x8. 2. Even the students with the most serious math impairments are usually able to count by 2’s and 5’s, so I just have them practice those skills until they can perform them quickly, which eliminates the need to memorize the 2’s or 5’s facts. 7. Since most of my students have already learned the facts with answers under 20, I have not developed “movies” for 3x3 3x4 3x6 4x4, but a teacher could certainly develop such “movies”. Students remember better if your picture utilizes color, if it is funny, outlandish or timely, and if the story includes movement. Once students have had practice in the program, they also like to create their own pictures. Encouraging this not only improves their ability to remember the facts, but increases their ability to apply visual imagery as a memory strategy in other settings. 3. There is no need to learn multiplying by two digit numbers like 10, 11, or 12 when we have already established that the students can multiply by 0, 1, & 2. 4. Once a student learns one form of a multiplication fact, such as 2 x 8 =16, it is not necessary for them to learn it again as 8 x 2 = 16. 5. There are many “tricks” students can use for the 9’s facts. I prefer to teach my students to place their hands flat on the desk and assign a number to each finger. The student then folds under the finger corresponding to the number being multiplied by 9. The fingers coming before the folded finger represent the tens digit, and those after the folded finger represent the ones digit. Multiplication Movies works because students are no longer simply relying on one aspect of their memory; the multi-sensory experience provides multiple inputs into different facets of the memory. Students access auditory memory as they listen to the teacher tell the story, visual memory as they see the picture on “the movie screen in their mind , and motor memory when they draw their own version of the picture. All three aspects of memory are linked together, reinforcing each other. It’s really quite exciting to witness. 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Vicki Iliff Lesson Plan No 1: Introduction to Multiplication Movies n SUBJECTS COVERED n DIRECTIONS Math Anticipatory Set: n GR ADES 3rd-12th grade students who have not yet mastered the multiplication facts n OBJECTIVES 4 To obtain student commitments to the program 4 To establish a baseline for each student 4 To introduce visual imagery 4 To introduce the “movies” for 8 x 8 and 8 x 3 4 To have students make note cards for 8 x 8 and 8 x 3 n SUNSHINE STATE STANDARDS MA.4.A.1.1 Use and describe various models for multiplication in problem-solving situations, and demonstrate recall of basic multiplication and related division facts with ease. n MATERIALS • Colored dry erase markers • 2 notecards per student • Colored pencils or markers • 1 Ring per student Give students a 1 minute timing on multiplication problems. Distribute answer sheets and let them grade their own paper, putting the number correct at the top. Ask how many got more than 40 correct; reactions will be disbelief. How many of you would like to be able to answer more than 40 in a minute? Discuss ways they have already tried to learn their facts: flash cards, writing facts over and over, computer programs, etc. Discuss frustration they have felt; how many have been called lazy, or even dumb? Explain you have a totally new way to learn the facts and seek a commitment. Lesson: Explain visualization as seeing pictures on the movie screen in your mind. Have students close their eyes and picture things you describe. (Some students will not be able to actually “see” the picture; but if you ask questions about details of the picture, they will be able to answer them. Assure them this is okay.) Tell students you’re going to describe a little movie to them, and you want them to see it on their screens. I want you to picture two snowmen. The first is Mr. Snowman; he has a bright purple hat, a funny green tie, and a carrot for his nose. Can you see him? What color is his hat? Tell me about his tie. Next to him is Mrs. Snowman. She has curly red hair, and a yellow bead necklace. What color is her necklace? What do you see in her hair? Mr. and Mrs. Snowman are holding a huge cake in between them, and on the cake is the number 64 along with 64 candles, because it’s their 64th wedding anniversary. You decide what color the cake is in your movie. What color did you pick? What color are the candles? You can see all the candles are lit, and Mr. and Mrs. Snowman are so happy. But wait, oh no!! All those candles are making it very hot. Do you know what happens to snowmen when they get too hot? They melt. Watch Mr. and Mrs. Snowman as they’re melting, melting, melting, and all that’s left now is Mr. Snowman’s hat and tie, and Mrs. Snowman’s necklace and her red hair. Open your eyes. I have a picture on the board of what my movie looked like. What number does Mr. Snowman look like? That’s right, an 8. And does Mrs. Snowman also look like an 8? What other number do you see? Yes, there’s a 64 on their cake. Look what happens when we put those 3 numbers together: 8x8=64. If I have Mr. Snowman and Mrs. Snowman, what part of the problem am I missing? And if I have the cake and Mrs. Snowman, what am I missing? Shut your eyes and let’s see if you can answer the same questions from your own multiplication movie. So, from that one movie, you now know 8x8=64 and 64÷8=8. I want you to make a note card to remind you of your first movie. On one side, write 8x8= ______ with your black marker. Put your initials in the corner, so we know whose card it is. On the other side, draw your picture; make it big and colorful, because we remember things better that are in color. Under your picture, use the black marker to write the multiplication and division facts that go with your movie. Would you like to learn a second movie? This one even has sound effects. Teacher draws a yellow 3 on the board. What number is this? If I turn it on its side like this, what restaurant does it make you think of? That’s right; it’s McDonalds’ Golden Arches. This movie takes place at McDonalds. We have an 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Vicki Iliff Lesson Plan No 1: Introduction to Multiplication Movies (cont.) 8 again, but it’s not a snowman this time; it’s Fat Albert. Fat Albert loves McDonalds’ Big Macs; so every day he goes to the drive thru to get some. But he’s SOOO fat, he can’t get in a so he has to walk up to the drive thru to place his order. “Hey, hey, hey, give me 24 Big Macs.” Here’s his bag with a 24 on the outside. Okay, shut your eyes. Can you see the Golden Arches? What number do they look like? Here comes Fat Albert, what number does he look like? Watch his mouth move as he says, “Hey, hey, hey, give me 24 Big Macs.” If you have the Big Macs and Fat Albert, what are you missing? If you have the Golden Arches and Fat Albert, what are you missing? Open your eyes. What are the multiplication facts that go with this movie? Yes, there are 2 this time: 8x3=24 and 3x8=24, and there are also 2 division problems; what are they? 24÷3=8 and 24÷8=3. Okay, take your second card and your black marker and write 8x3 on the front. Remember to put your initials in the corner. On the back, draw Fat Albert at the McDonalds with his bag of 24 Big Macs. Remember to make your picture big and colorful to help you remember. While you’re drawing, hear Fat Albert saying “Give me 24 Big Macs.” Then write your two multiplication facts and your two division facts in black under your picture. While you’re working, I’ll come around and punch a hole in the corner of your cards, and give you a key ring to keep your cards together. From now on, when you come to class, the first thing I want you to do is get your cards, and practice so that you can look at the side with the problem and remember the movie and the facts on the other side. 2008 - 2009 Idea Catalog of Excellence HHH “Multiplication Movies” Vicki Iliff Lesson Plan No 2: Teaching the Remaining Movies n SUBJECTS COVERED n DIRECTIONS Math Review: n GR ADES 3rd-12th grade students who have not yet mastered the multiplication facts n OBJECTIVES 4 To review previous movies 4 To introduce remaining movies 4 To have students make note cards for remaining movies 4 To measure growth on Precision Teaching timing 4 To test mastery of Multiplication Movies n SUNSHINE STATE STANDARDS MA.4.A.1.1 Use and describe various models for multiplication in problem-solving situations, and demonstrate recall of basic multiplication and related division facts with ease. n MATERIALS • Colored dry erase markers • 2 note cards per student • White board Markers • Colored pencils or markers • Newsprint • Precision Teaching materials (student folders, answer sheets, Vis a vis markers, sprayer, paper towels ) • Multiplication Movies rubric Give students a short time each day to review their note cards individually or with a partner. Then conduct a group review of all previously learned “movies” by asking individual students to draw the movies for the group on the whiteboard or blackboard. Review the story for each movie. Twice a week introduce two new movies, for a total of 4 new ones per week. Finish each session with 2 one minute Precision Teaching timings. Once a week (I use Fridays) substitute a mastery test for the timings. Give each student a piece of newsprint; teach students to fold the paper to form enough boxes for all movies learned to date. List the facts (without answers) on the board, and instruct students to draw one movie in each box, and the corresponding multiplication and division facts in the box on the back. Use the rubric on the following page to evaluate student mastery of each movie. like the multiplication facts, the teacher just thought that student wasn’t trying. To shame him, the teacher made him sit on a chair in the corner wearing what was called a dunce cap. This upsidedown four is the chair. This 6 is the student with his dunce cap. And over here we have the other 24 students in the class laughing at him. Can you hear them laughing? 6x6 Scripts for Remaining Multiplication Movies: When developing these scripts, I have tried to choose things I think my students will relate to and remember. My experience has been that students remember better if a picture utilizes color, if it is funny, outlandish or timely, and if the story includes movement. I have taken some liberties (Billy the Kid was not hung; military funerals have 21 gun salutes) to make my stories match the multiplication facts. These scripts are skeletons; the teacher is encouraged to take these basic descriptions and elaborate on them. 6x4 Our movie today takes place when your grandparents were in school. Back then, they didn’t know anything about Learning Disabilities. When a student had trouble learning things, Take a look at these two sixes I’ve drawn on the board. These are telephone receivers. And here we have the faces of two kids who are best friends. Shut your eyes, I want you to picture them as I describe them to you. The boy has a bright green mohawk; the girl has pink hair and a pierced nose. Now you may be wondering why the telephones are in this movie. That’s because these good friends live 36 miles apar t, so the only way they can talk to each other is on the telephone. 6x7 How many of you watch “So You Think You Can Dance”? Today’s movie is about six kids in New York who are hoping to get discovered and hit it big some day. The 7 I’m drawing is a street sign on the corner where they do their dancing. What street is it? You’re right 42nd Street. Here are the six kids. Now, I haven’t told you what kind of dancing they do, because I want you to decide that. Shut your eyes; see the six kids on the corner of 42nd Street. They’re beginning to dance. You decide if they’re break dancing, or clogging, or belly dancing. One of my students said in his movie they were doing the 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Vicki Iliff Lesson Plan No 2: Teaching the Remaining Movies (cont.) hula-hula. They’ll do whatever dance you want. Be sure to give them music to dance to; they’d look pretty silly dancing without music! 7x4 6x8 How many of you like Nascar? Since Talladega was over the weekend, we’ll have a Nascar Movie today. First I’m going to draw this sideways 8; what do you suppose it is? Yes, that’s the track. And here’s our driver, #6. David Ragan. Shut your eyes. I want you to see him climbing into his car and racing around the track. I know you can hear the roar of the race. It’s the 48th lap, and #6 is in first place. Oh no; he spins out and crashes his car. Which lap is it? That’s right; David Ragan, #6, has just spun out in the 48th lap. No trophy for him today. I’ll bet he’ll always remember losing this race in the 48th lap. Will you? Today’s movie takes place in the Old West. Back then, if you broke the law by cattle rustling or robbing banks, your punishment was often a quick hanging; it didn’t matter how young you were. Our story today is about one of the youngest men to be hung: Billy the Kid. Why do you think they called him “the Kid”? You’re right, he was quite young; he was only 21years old. In fact, that’s what he’s saying as they hang him: “I’m only 21.” But we only have two numbers so far: the 7 for the gallows, and the 21 for Billy’s age. Oh, here’s our other number; it’s a 3 high up in the sky. This is a bird called a buzzard; he’s circling around Billy, waiting for him to die so he can pick his bones. Poor Billy, and he was only 21. Since this weekend is homecoming, our first movie today will be about homecoming. Here you have a 4; if I draw an extra line here, what does it look like? That’s right; it’s a goal post. And our 8 is not Fat Albert; he’s the fielder goal kicker. Now shut your eyes, and watch him kick the ball over the goal posts for a field goal. Now look up at the scoreboard, and watch the score change to Lake Wales 32, Bartow 0. Hear the crowd cheering. Lake Wales WINS! Today I’m going to teach you a trick that you can use to solve any 9’s fact. I want you to place your hands flat on your desk. We’re going to give each finger a number, starting with the pinkie on your left hand. Let’s start with the problem 9x4. Fold under your number 4 finger. How many fingers come in front of the folded finger? Yes, 3; that’s the first digit of my answer. How many fingers come after the folded finger. Six is correct; that’s the second digit of the answer. So 9x4=36. Ready for another? I want you to set up for 9x7. How many fingers in front of the folded finger? How many after? What’s the answer? That’s right: 63. Let’s practice some more so you can get your answer quickly. You can use this trick for any of your 9’s. Just remember, the number that is not 9 tells you which finger to fold under. 7x7 7x3 We just celebrated Memorial Day, and today’s movie is about a funeral honoring a soldier. This one is tricky, so watch carefully. Here I have a 7 and right next to it a 4. Can you see what they make? That’s right; it’s a flag: the American flag. And this is a soldier who is going to fire a 28 gun salute to honor the soldier. Shut your eyes so you can picture the flag; what two numbers make the flag? Listen carefully, can you hear the 28 shots of the salute? 8x4 How many of you like football? Today’s movie is about a football team: the San Francisco 49’ers. Here are the two doors of their locker room, and you can see their name proudly posted above the doors. It’s half time, and the players are coming into the locker room. Are any of you 49’ers fans? I want you to picture the players coming in all pumped up and happy because they’re killing the other team. The rest of you, who don’t like the 49’ers, should see them coming in with their uniforms all torn; they’re bleeding and crying, because YOUR team is clobbering them. 7x8 Today’s movie is called “Magic Numbers.” That’s what I’m going to put at the top of my picture. Now I’m writing the problem 7x8 with two blanks in front. When you’re counting, what numbers go in the blanks? That’s right: 5 6, and that’s the answer to our problem, 7x8=56. Magic, don’t you think? 9’s 2008 - 2009 Idea Catalog of Excellence HHH “Multiplication Movies” Vicki Iliff Lesson Plan No 3: Introduction to Precision Teaching This lesson should come after students have had 2 lessons learning Multiplication Movies, so that they will be able to see growth in their scores. • 1 Vis a vis marker per student • 1 ruler per student • Timer • Sprayer n SUBJECTS COVERED n DIRECTIONS Math Anticipatory Set: n GR ADES 3rd-12th grade students who have not yet mastered the multiplication facts n OBJECTIVES 4 To introduce students to Precision Teaching 4 To administer two 1 minute timings 4 To teach students how to begin a double line graph of their results n SUNSHINE STATE STANDARDS MA.4.A.1.1 Use and describe various models for multiplication in problem-solving situations, and demonstrate recall of basic multiplication and related division facts with ease. MA.5.S.7.1 Construct and analyze line graphs and double bar graphs. n MATERIALS • 1 Precision Teaching folder per student (the folder has 2 different laminated multiplication worksheets stapled inside and a Precision Teaching Chart on the front (I get my worksheets from The Mad Minute: A Race to Master the Number Facts by Paul Shoecraft and Terry Clukey.) A source for free worksheets is: http:// math.about.com/od/multiplication/ ig/Times-Tables-Worksheets/ • 1 double sided answer key per student You’re really doing well at learning your Multiplication Movies. When we did our first 1 minute timing, you all thought the time was way too short, and that you’d never be able to do 40 problems in a minute. Today I want to show you how we’re going to keep track of your progress. We’re going to start a Program called Precision Teaching. It’s a scientific way to help students increase their skills. It also lets us draw a graph so that you can really see how much better you’re getting. Here are some graphs from students I’ve had in other years. What’s happening on each of these graphs? Yes, they are going up; some very quickly. This dark line represents 40 problems in a minute. Did most of the students reach that mastery level? Yes, they did, and so will you. Let’s get started. Lesson: Give each student a folder and have them put their name on it. Then explain the routines for the program. Each day, one of you will pass out the Precision Teaching folders, while another student passes out these Vis markers. These markers dry out quickly, so keep yours covered until I tell you to take off the lid. Open your folder; you see you have two different laminated papers; one for timing X and one for timing O. I’ll be using this timer to time one minute. When I tell you to start, you will answer as many questions on the first paper as you can. You don’t have to do them in order; skip problems if you get stuck. Your goal is to answer as many correctly as you can. When the timer goes off, stop and put the lid on your marker. Then you will get ready to use the second paper for timing 2. We’ll follow the same steps for the second timing. When we’ve finished both timings, another student will pass out the answer sheets. (Discuss the importance of using the answer sheet to check their work rather than relying on their memory. You don’t want them to be practicing an incorrect answer. Also discuss the importance of honesty; the only one they cheat is themselves.) When you graph your timing, we’re not interested in how many you missed or skipped; only the number of problems you had correct. You’ll put that number at the top of your paper. Let’s do our first two timings, and then I’ll teach you how to graph your results. (Watch carefully for students not stopping on time or using the answer sheet to change answers. These behaviors usually disappear after the first week) Ready to make your graph? Look on the front of your folder. When you make a graph, you usually need to start by giving each axis a label; but I’ve already done that for you. What is the label on the x axis? That’s right, Date. Look at my example on the board. Each day we have a timing, you will put that date. Do you put dates for days we don’t time or you are absent? No, only dates you have a score for. There is also a label already there on the y axis. What is it? Number correct. This graph already has your scale also; how much does your score have to go up for your graph to go up one box? That’s right, only 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Vicki Iliff Lesson Plan No 3: Introduction to Precision Teaching (cont.) one more correct answer makes your graph go up. We’re ready to start recording your scores. What kind of graphs could we make with this form? Yes, we could do a bar graph, but I think it might be difficult to color in such tiny little bars. And, if we did bar graphs, you could only record the scores for one of your timings each day. I think we should show both scores, so we’re going to do a double line graph. How many of you have ever made that kind of graph? It’s really quite simple, as long as we add one more thing to this form. We need a way to tell the difference between the first and second timing. Sometimes that’s done by different kinds of lines, or by color, but for our graph, we’re going to use X for our first timing, and 0 for our second. To make sure someone else reading this graph knows that, we’re going to put a key on the side like this. use that number for your first X and O score. Go around and tell students their scores, or give them a card with that score) Now, for the second timing, we’ll use today’s scores. Put today’s date in the next space for dates, and put an X for the score you got on the first timing. (Check for accuracy) Now use your second timing for your O score. One last step; we need to connect our X’s with a line, and we always use a ruler so that we have a neat and accurate graph. (Have a student pass out rulers, while you give instruction at the board.) Now everybody use your ruler to connect your X’s. Did you go up from your first score? Use the ruler now to connect your O’s. How many people have an O line that is already going up? Our last routine is clean up. (Choose another student to go from desk to desk to spray water on the laminated sheets; or the teacher can do that in order to maintain control of the water and note student performance and progress. Also establish how answer sheets, folders, and markers are to be returned.) Tomorrow we’ll do another timing, and I’ll expect my helpers to do their jobs quickly and quietly. Let’s try to record scores on my graph on the overhead. (Practice until all seem to have mastered correct placement on the graph) Okay, now you’ll start your graph. We only use pencils on our graphs so that we can erase if we make a mistake. For your first score, we’re going to put the date you did your 1 minute pre-test for me, and you’ll 2008 - 2009 Idea Catalog of Excellence HHH “Multiplication Movies” Vicki Iliff Lesson Plans Materials Budget Materials Budget Supplier Item DescriptionCost Quantity Total Cost Staples 500 index cards (4x6 unruled) $3.28 1 pack $3.28 ___________________________________________________________________________________________________________________________ Pack of Loose-leaf rings (1 inch) $2.98 2 packs $5.96 ___________________________________________________________________________________________________________________________ Box of 12 colored markers $3.79 8 boxes $30.32 ___________________________________________________________________________________________________________________________ Box of 12 vis a vis markers $12.79 2 boxes $25.59 ___________________________________________________________________________________________________________________________ Box of 50 letter-size file folders $12.48 1 box $12.48 ___________________________________________________________________________________________________________________________ Box of 12 colored dry erase markers $14.99 1 box $14.99 ___________________________________________________________________________________________________________________________ Finger Grip Rulers $1.28 15 $10.68 ___________________________________________________________________________________________________________________________ Office Depot Package 500 sheets newsprint $7.99 1 pack $7.99 ___________________________________________________________________________________________________________________________ Ream white copy paper $6.69 1 ream $6.69 ___________________________________________________________________________________________________________________________ Ream colored copy paper $11.49 1 ream $11.49 ___________________________________________________________________________________________________________________________ PCI Education Digitz -The Multiplication Machine $49.95 1 $49.95 ___________________________________________________________________________________________________________________________ Wal Mart Spray bottle $2.00 1 bottle $2.00 ___________________________________________________________________________________________________________________________ Kitchen Timer $5.00 1 timer $5.00 ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________ Subtotal $183.52 ________________________________________________ Vicki Iliff Teacher’s Name___________________________________ Roosevelt Academy School:__________________________________________ Tax if applicable 9.35 ________________________________________________ Shipping if applicable 10.00 ________________________________________________ TOTAL BUDGET AMOUNT 2008 - 2009 Idea Catalog of Excellence $202.87 “Multiplication Movies” Vicki Iliff Additional Information – Precision Teaching Chart 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Rubric Vicki Iliff RUBRIC FOR MULTIPLICATION MOVIES Student Name: ____________________________________ Date:____________ CATEGORY 3 2 1 Correct Movie Picture correctly includes all 3 numbers. Picture correctly includes 2 numbers. Picture is omitted or includes only 1 correct number. Multiplication facts Both multiplication facts are written correctly. 1 multiplication fact is written correctly. No correct multiplication facts are included. Division facts Both division facts are written correctly. 1 division fact is written correctly. No correct division facts are included. TOTAL POINTS: -______________________ 2008 - 2009 Idea Catalog of Excellence “Multiplication Movies” Vicki Iliff Additional Information 2008 - 2009 Idea Catalog of Excellence
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