The Brandywine School District
presents
The Singapore Math Series
Session III
Multiplication and
Division
Created by Hester Sutton March 2011
Problem Solving
Words
diagram
Arithmetic
Part-Whole Model (Multiplication and Division)
whole
part
one part x number of parts = whole
whole ÷ number of parts = one part
whole ÷ one part = number of parts
5 children shared the cost of a
present equally. Each of them paid
$6. What was the cost of the present?
?
Cost of the
present
$6
$6 x 5 = $30
whole
one part
number of parts
Part-Whole Model (Multiplication and Division)
whole
part
one part x number of parts = whole
whole ÷ number of parts = one part
whole ÷ one part = number of parts
Four children bought a present for $28.
They shared the costs equally.
How much did each child pay?
28
Cost of the
present
?
$28 ÷ 4 = $7
whole
one part
Each child paid $7
number of parts
Part-Whole Model (Multiplication and Division)
whole
part
one part x number of parts = whole
whole ÷ number of parts = one part
whole ÷ one part = number of parts
A group of children bought a present for
$30. They paid $6 each. How many
children were in the group?
$30
Cost of the
present
$6
30 ÷ 6 = 5
whole
one part
number of
parts
Multiplication with Rebundling
43 x 4 = 172
hundreds
tens
ones
There were 27 desks to clean. 3 boys
shared the work equally. How many
desks did each boy clean?
27
3 units = 27
Desks
27  3  9
1 units = 9
?
Each boy cleaned 9 desks.
27  3
hundreds
tens
= 7
ones
Comparison Model (Multiplication and Division)
larger quantity
smaller quantity
smaller quantity x multiple = larger quantity
larger quantity ÷ multiple = smaller quantity
larger quantity ÷ smaller quantity = multiple
A farmer has 7 ducks. He has 5 times as many
chickens as ducks. How many chickens does the
farmer have?
?
chickens
1 unit = 7
ducks
5 x 7 = 35
7
5 units = 35
The farmer has 35 chickens
Comparison Model (Multiplication and Division)
larger quantity
smaller quantity
smaller quantity x multiple = larger quantity
larger quantity ÷ multiple = smaller quantity
larger quantity ÷ smaller quantity = multiple
A farmer has 35 chickens. He has 5 times
as many chickens as ducks. How many
ducks does the farmer have?
35
chickens
5 units = 35
ducks
35 ÷ 5 = 7
?
1 unit = 7
The farmer has 7 ducks
Comparison Model (Multiplication and Division)
larger quantity
smaller quantity
smaller quantity x multiple = larger quantity
larger quantity ÷ multiple = smaller quantity
larger quantity ÷ smaller quantity = multiple
A farmer has 7 ducks and 35 chickens. How
many times as many chickens as ducks does
the farmer have?
35
chickens
ducks
35 ÷ 7 = 5
7
The farmer has 5 times as many chickens as ducks
Kelly has $16. She has twice as much as her brother. How
much money do Kelly and her brother have together?
16
2 units = $16
Kelly
?
Brother
8
1 units = $8
3 units = 8 x 3
= $24
They have $24 altogether.