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

€

2 610

Representing Decimal Numbers

Base 10 blocks Decimal Fraction

Representation Representation

3.217€

1 27100

Comparing Decimals

Represent each of the following numbers with base 10 blocks and put them in order from smallest to greatest:

2.1 1.962

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

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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)

1.6x 2

2 groups of 1.6

Multiplying Decimals Using an Understanding of Place Value

Using Place Value Materials (With Renaming)

1.6x 2

Trade to make another unit.1.6 x 2 = 3.2

Multiplying a Decimal by a Decimal

1.6x .2

Find two tenths of each part.

Multiplying a Decimal by a Decimal

1.6x .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