# Modeling Decimals with Base 10 Blocks - PowerPoint PPT Presentation

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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

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 Fraction

Representation Representation

2.6

### Representing Decimal Numbers

Base 10 blocks Decimal Fraction

Representation Representation

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

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

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

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

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

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### 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 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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### 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