Created by Hester Sutton March 2011

The Brandywine School District

presentsThe Singapore Math Series

Session IIIMultiplication and Division

Problem SolvingWords

diagram

Arithmetic

Part-Whole Model (Multiplication and Division)

part

whole

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 x 5 = $30

?

$6

one part

number of parts

whole

Part-Whole Model (Multiplication and Division)

part

whole

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?

Cost of the present

28

?

Each child paid $7

$28 ÷ 4 = $7 whole

number of parts

one part

Part-Whole Model (Multiplication and Division)

part

whole

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?

Cost of the present

$30

$6 whole

one part

30 ÷ 6 = 5 number

of parts

hundreds onestens

Multiplication with Rebundling

43 x 4 = 172

There were 27 desks to clean. 3 boys shared the work equally. How many desks did each boy clean?

Desks

27

?

27 3 9

Each boy cleaned 9 desks.

3 units = 27

1 units = 9

hundreds onestens

= 727 3

Comparison Model (Multiplication and Division)

larger quantity

smaller quantity

larger quantity ÷ smaller quantity = multiple

smaller quantity x multiple = larger quantity

larger quantity ÷ multiple = smaller quantity

A farmer has 7 ducks. He has 5 times as many chickens as ducks. How many chickens does the farmer have?

?

chickens

ducks

7

1 unit = 7 5 x 7 = 355 units = 35

The farmer has 35 chickens

Comparison Model (Multiplication and Division)

larger quantity

smaller quantity

larger quantity ÷ smaller quantity = multiple

smaller quantity x multiple = larger quantity

larger quantity ÷ multiple = smaller quantity

A farmer has 35 chickens. He has 5 times as many chickens as ducks. How many ducks does the farmer have?

35

chickens

ducks

? 1 unit = 7

35 ÷ 5 = 75 units = 35

The farmer has 7 ducks

Comparison Model (Multiplication and Division)

larger quantity

smaller quantity

larger quantity ÷ smaller quantity = multiple

smaller quantity x multiple = larger quantity

larger quantity ÷ multiple = smaller quantity

A farmer has 7 ducks and 35 chickens. How many times as many chickens as ducks does the farmer have?

35chickens

ducks

735 ÷ 7 = 5

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?

Kelly

Brother

16

?

2 units = $16

1 units = $8

3 units = 8 x 3 = $24

8 They have $24 altogether.