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Modeling Decimals with Base 10 Blocks. Joyce Bishop. Using Familiar Base 10 Blocks to Model Decimal Numbers. flat = 1 l ong = 0.1 small cube = 0.01 small flat = 0.001. Representing Decimal Numbers. Base 10 blocks Decimal Fraction

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Modeling decimals with base 10 blocks

Modeling Decimals with Base 10 Blocks

Joyce Bishop


Using familiar base 10 blocks to model decimal numbers
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
Representing Decimal Numbers

Base 10 blocks Decimal Fraction

Representation Representation

2.6


Representing decimal numbers1
Representing Decimal Numbers

Base 10 blocks Decimal Fraction

Representation Representation

3.217


Comparing decimals
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 decimals1
Comparing Decimals

1.96

2

2.1


Model space ship
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
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
Representing Two Ways

Use your understanding of place value to show two ways to represent 0.18 with base 10 blocks.


Representing two ways1
Representing Two Ways

Use your understanding of place value to show two ways to represent 0.18.

or


Storing a model space ship
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
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 subtraction1
Storing a Model Space Ship - Subtraction

Subtract 2.18 – 1.62

2.18


Storing a model space ship subtraction2
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
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 value1
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
Multiplying a Decimal by a Decimal

1.6

x .2

Find two tenths of each part.


Multiplying a decimal by a decimal1
Multiplying a Decimal by a Decimal

1.6

x .2

Find two tenths of each part (not drawn proportionally.)

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Multiplying a decimal by a decimal2
Multiplying a Decimal by a Decimal

1.6 x 0.2

1.6 x 0.2 = (2 x 0.1) + (12 x 0.01)

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Multiplying a decimal by a decimal3
Multiplying a Decimal by a Decimal

1.6 x 0.2

1.6 x 0.2 = (3 x 0.1) + (2 x 0.01) = 0.32

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xxxxxxx

xxxxxxx


One multiplicative situation two division types
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
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 division1
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 division2
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 division3
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 division4
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 division5
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
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 division1
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 division2
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 division3
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
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


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