modeling)decimals)) with)base)10)blocks)

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

RepresenCng Decimal Numbers

Base 10 blocks Decimal FracCon RepresentaCon RepresentaCon

2.6

€

2 610

RepresenCng Decimal Numbers

Base 10 blocks Decimal FracCon RepresentaCon RepresentaCon

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

1.96

2

Comparing Decimals

1.96

2

2.1

Model Space Ship

Ethan is construcCng 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 soluCon with base 10 blocks.

Model Space Ship -‐ AddiCon

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

RepresenCng Two Ways

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

RepresenCng 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 soluCon with base 10 blocks.

Storing a Model Space Ship -‐ SubtracCon

Subtract 2.18 – 1.62

2.18

Rename 1 as 10 x 0.1



2.18



2.18

2.18 m – 1.62 m = 0.56 m

MulCplying Decimals Using an Understanding of Place Value

Using Place Value Materials (With Renaming)

1.6

x 2

2 groups of 1.6

MulCplying 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

MulCplying a Decimal by a Decimal

1.6

x .2

Find two tenths of each part.


1.6

x .2

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


1.6 x 0.2

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


1.6 x 0.2

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

One MulCplicaCve SituaCon: Two Division Types

Aeisha is cubng 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 quesCons: •  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? (ParCCve 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)



Count groups of (3 x 0.1).



One group of (3 x 0.1).



Two groups of (3 x 0.1).



Three groups of (3 x 0.1).



Four groups of (3 x 0.1).

1.2 meters ÷ by 0.3 = 4

ParCCve (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)



Arrange the blocks in four equal groups.



Four groups of 0.1 m with 0.8 m leg.



Four groups of 0.2 m with 0.4 m leg.

ParCCtve (Sharing) Division


There are four groups with 0.3 meter in each. 1.2 meters ÷ by 4 = 0.3

modeling)decimals)) with)base)10)blocks)

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