Modeling decimals with base 10 blocks
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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

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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.)

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx


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)

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx


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

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

xxxxxxx

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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