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Structures for Multiplication Problems B2: Multiply 2-, 3-, 4-digit numbers Set • Mr. Smith put out 4 trays of sandwiches for the party. There were 20 sandwiches on each tray. How many sandwiches were there altogether? 20 • In set problems we create a set of groups of equal size. 20 20 • For these questions it is clear that multiplication is simply 20 repeated addition as we add all group totals together. 20+20+20+20=80 or 4x20=80 Set Jerry displayed all 48 cars in his toy car collection on bookshelves. He put 12 cars on each of the shelves. How many shelves did Jerry use? 12 12 12 12+ 12 = 24 12 12 + 12 + 12 = 36 12 12 + 12 + 12 + 12 = 48 12 x ? = 48 or 48 divided by12 = 4 Comparison • Brian has saved $12 for his new bicycle. Jim has saved three times as much as Brian. How much has Jim saved? • Here we are comparing two or more numbers. • We are always provided with one number and must find either the difference or the other number. Brian $12 Jim more/less $36 Jim has 3 times more 3 X $12 = ___ Comparison • Sara had 75 comic books in her collection. If her brother has a collection of 25 comic books, how many times larger is Sara’s collection? 25 1 time 25 + 25 Sara Brother more/less 75 3 times larger 2 times 25 + 25 + 25 3 times 25 Rate • Rachael worked 5 hours at Happy Joe’s for $9 an hour. How much did she earn? • In rate problems we are dealing with time. • The variables present in these problems include an amount of time, a number per unit of time, and the total. Time # per unit Total 5 hrs $9 per hr $45 $9 9 9 9 or x5 9 $45 +9 $45 Rate • Erin rode 8 km on her bicycle everyday. How long did it take her to ride a total of 32 km? Time # per unit Total 4 8 km per 32 km 32 8 = days day 4 or Day 1 Day 2 Day 3 Day 4 8 km + 8 km + 8 km + 8 km = 32 km Array • The cadet squadron leader lined up the cadets in 3 rows of 12 for their march in the parade. How many cadets marched in the parade? • In array problems we deal with objects or numbers in rows. Row 1 Row 2 Row 3 or 3 x 12 = 36 cadets 12 cadets 12 cadets 12 cadets 36 cadets Array • Mr. Bright ordered a Greco party pizza for supper. The pizza was divided into 4 rows with 6 slices of pizza in each row. How many slices was the pizza divided into? 6 slices 6 slices 6 slices + 6 slices or 4 x 6 = 24 slices 24 slices Combination • The cafeteria staff made up box lunches of one sandwich and one drink. If there were 3 different kinds of sandwiches and 2 different drinks, how many different box lunches could they make? • With combination questions we are provided with various numbers of select objects. These objects come together in many different ways. Box lunches S1 S2 S3 D1 D2 D1 D2 D1 D2 1 lunch 1 lunch 1 lunch 1 lunch 1 lunch 1 lunch or 3 x2 6 Combination • When packing for hockey camp you decide to bring 3 sweaters, 2 pairs of pants, and two pairs of shoes. How many different outfits could you wear? 3x2x2=12 Outfits Shoes 1 Pants 1 Shoes 2 Sweater 1 Shoes 1 Pants 2 Shoes 2 Shoes 1 Pants 1 Shoes 2 Sweater 2 Shoes 1 Pants 2 Shoes 2 Shoes 1 Pants 1 Shoes 2 Sweater 3 Shoes 1 Pants 2 Shoes 2 Area • After an unsuccessful attempt at housebreaking his puppy, Mr. Daigle decided to replace the carpet in his living room with hardwood floors. His living room is 6 meters long and 5 meters wide. How much floor must the hardwood cover? • When dealing with area problems, we try to find the measurement of the total surface in square units. 6m 5m 6m2 5 x 6m2=30m2 5 Area Construction began on the new soccer field that was to be located directly behind John Anderson Elementary School. Now if standard soccer fields are 55 meters wide and 95 meters long, how much space will the builders have to clear before they can begin laying the sod?