Tape
Diagrams
Addition &
Subtraction
Part-Whole Model
Addition & Subtraction: Variation 1
Given 2 parts, find the whole
?
4
5
Jason went on 4 rides at the
carnival on Saturday. On sunday,
he went on 5 rides. How many rides did he
go on altogether?
Part-Whole Model
Addition & Subtraction: Variation 2
Find the missing part when
given 1 part and the whole.
9
4
?
Last weekend, Ryan ran 9 miles. On Saturday,
he ran 4 miles. How many miles did he run on Sunday?
The Comparison Model
Addition & Subtraction
Larger Quantity
Smaller Quantity
difference
larger quantity - smaller quantity = difference
!
smaller quantity + difference = larger quantity
The Comparison Model
Addition & Subtraction
6
?
2
There were 6 dogs at the pet store. There
were 2 more dogs than cats. How many
cats were there in the pet store?
The Comparison Model
Addition & Subtraction
6
4
?
There were 6 dogs at the pet store. If there were 4 cats.
How many more dogs than cats were there?
The Comparison Model
Addition & Subtraction
?
4
2
There were 4 cats in the pet store. If there were
2 more dogs than cats. How many dogs were
there altogether?
Multiplication &
Division
Part - Whole Model
Multiplication & Division
whole
part
one part x number of parts = whole
whole ÷ number of parts = one part
whole ÷ one part = number of parts
Part - Whole Model
Multiplication & Division: Variation 1
whole
5
part
!
!
There were 5 goldfish in each fish tank. If there were 3 fish
tanks, how many goldfish were there altogether?
Part - Whole Model
Multiplication & Division: Variation 2
15
part
If there were 15 goldfish in the pet store and there were 3
tanks, how many goldfish were in each tank?
Part - Whole Model
Multiplication & Division
15
5
part
There were 15 goldfish in the pet store. There
were 5 in each tank. How many tanks
were there altogether?
The Comparison Model
Multiplication & Division
larger
quantity
multiple
smaller
quantity
larger quantity ÷ smaller quantity = multiple
smaller quantity x multiple = larger quantity
larger quantity ÷ multiple = smaller quantity
The Comparison Model
Multiplication
&
Division:
Variation
1
larger quantity ÷ smaller quantity = multiple
35
multiple
7
A farmer has 35 horses. He has
7 cows. How many times more
horses than cows does he have?
The Comparison Model
Multiplication
&
Division:
Variation
2
smaller quantity x multiple = larger quantity
?
5
7
A farmer has 7 cows. He has 5
times as many horses. How
many horses does he have?
The Comparison Model
Multiplication & Division
larger quantity ÷ multiple = smaller quantity
35
7
7
7
7
7
?
A farmer has 35 horses. He has 5 times as
many horses as cows. How many
cows does he have?
Fractions
Part-Whole Model
Showing Fractions
Part
whole
The part is 1/3 of the whole.
Part-Whole Model
Showing Fractions of 1
1 unit
1/4 unit
3/4 unit
3/4 means 1/4 + 1/4 + 1/4
!
or
!
3/4 means 3 x 1/4
Part-Whole Model
Finding Part of a Whole Quantity
12
?
1 unit = 12/4 = 3
3 units = 3 x 3 = 9
The blue portion of the tape diagram is 9.
Part-Whole Model
Finding the Whole from a Partial Quantity
?
9
1 unit = 9/3 = 3
4 units = 4 x 3 = 12
There are 12 altogether.
The Comparison Model
Fractions
A
B
A is 4 times as much as B.
So, B is 1/4 as much as A.
The Comparison Model
Fractions
?
Dogs
Cats
40
There are 3/4 as many dogs
as cats. If there are 40 cats,
how many dogs are there?
The Comparison Model
Fractions
Dogs
?
Cats
40
There are 3/4 as many dogs
as cats. If there are 40 cats,
how many more cats than dogs are there?
The Comparison Model
Fractions
Dogs
70
Cats
There are 3/4 as many dogs
as cats. If there are 70 animals,
how many cats are there?