Transcript Structures for Multiplication and Division Problems

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?