Modeling Decimals
with Base 10 Blocks
Joyce Bishop
Using Familiar Base 10 Blocks to Model Decimal
Numbers
• flat = 1
• long = 0.1
• small cube = 0.01
• small flat = 0.001
Representing Decimal Numbers
Base 10 blocks
Decimal
Representation
Fraction
Representation
2.6
6
2
10

Representing Decimal Numbers
Base 10 blocks
Decimal
Representation
Fraction
Representation
27
1
100

3.217
Comparing Decimals
Represent each of the following numbers with
base 10 blocks and put them in order from
smallest to greatest:
2.1
1.96
2
Comparing Decimals
1.96
2
2.1
Model Space Ship
Ethan is constructing a model of a space ship. The
first stage is 2.34 meter tall. The second stage is
1.031 meters tall. What is the total height?
Model the solution with base 10 blocks.
Model Space Ship - Addition
Add 2.34 + 1.031:
2.34
1.031
= (3 x 1) + (3 x 0.1) + (7 x 0.01) + (1 x 0.001)= 3.371
Representing Two Ways
Use your understanding of place value to show two
ways to represent 0.18 with base 10 blocks.
Representing Two Ways
Use your understanding of place value to
show two ways to represent 0.18.
or
√
Storing a Model Space Ship
Ethan has another model space ship that is 1.62
meters tall. If he stores it in a cabinet that is 2.18
meters tall, how much taller is the cabinet than the
model space ship?
Model your solution with base 10 blocks.
Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
Rename 1 as 10 x 0.1
Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
2.18 m – 1.62 m = 0.56 m
Multiplying Decimals Using an Understanding of
Place Value
Using Place Value Materials (With Renaming)
1.6
x 2
2 groups of 1.6
Multiplying Decimals Using an Understanding of
Place Value
Using Place Value Materials (With Renaming)
1.6
x 2
Trade to make another unit.
1.6 x 2 = 3.2
Multiplying a Decimal by a Decimal
1.6
x .2
Find two tenths of each part.
Multiplying a Decimal by a Decimal
1.6
x .2
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Find two tenths of each part (not drawn
proportionally.)
Multiplying a Decimal by a Decimal
1.6 x 0.2
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1.6 x 0.2 = (2 x 0.1) + (12 x 0.01)
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Multiplying a Decimal by a Decimal
1.6 x 0.2
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1.6 x 0.2 = (3 x 0.1) + (2 x 0.01) = 0.32
One Multiplicative Situation: Two Division Types
Aeisha is cutting ribbon for a hair bow. She has 1.2
meters of ribbon. Each piece of ribbon must be 0.3
meters long. She can cut 4 pieces of ribbon.
Two division questions:
• You know how long each piece of ribbon must be.
How many pieces can you cut? (Measurement
Division)
• You know how many pieces of ribbon you need. How
long is each piece? (Partitive or Sharing Division)
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
Rename 1.0 as (10 x 0.1)
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
Count groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
One group of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
Two groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
Three groups of (3 x 0.1).
Measurement Division
Aeisha has 1.2 meters of ribbon to use for a
hair bow. Each piece of ribbon must be 0.3
meters long. How many pieces can she cut?
Four groups of (3 x 0.1).
1.2 meters ÷ by 0.3 = 4
Partitive (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into
a hair bow. If she wants to cut it into 4 pieces,
how long will each piece be?
Rename 1.0 as (10 x 0.1)
Partitive (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a
hair bow. If she wants to cut it into 4 pieces, how
long will each piece be?
Arrange the blocks in four equal groups.
Partitive (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a
hair bow. If she wants to cut it into 4 pieces, how
long will each piece be?
Four groups of 0.1 m with 0.8 m left.
Partitive (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a
hair bow. If she wants to cut it into 4 pieces, how
long will each piece be?
Four groups of 0.2 m with 0.4 m left.
Partititve (Sharing) Division
Aeisha has 1.2 meters of ribbon to make into a
hair bow. If she wants to cut it into 4 pieces, how
long will each piece be?
There are four groups with 0.3 meter in each.
1.2 meters ÷ by 4 = 0.3