![Page 1: Modeling Decimals with Base 10 Blocks Joyce Bishop](https://reader036.vdocuments.net/reader036/viewer/2022062620/551b0989550346cf5a8b4c37/html5/thumbnails/1.jpg)
Modeling Decimals with Base 10 Blocks
Joyce Bishop
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Using Familiar Base 10 Blocks to Model Decimal Numbers
• flat = 1
• long = 0.1
• small cube = 0.01
• small flat = 0.001
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Representing Decimal Numbers
Base 10 blocks Decimal Fraction
Representation Representation
2.6
€
26
10
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Representing Decimal Numbers
Base 10 blocks Decimal Fraction
Representation Representation
3.217€
127
100
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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
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Comparing Decimals
1.96
2
2.1
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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.
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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
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Representing Two Ways
Use your understanding of place value to show two ways to represent 0.18 with base 10 blocks.
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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.
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Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
Rename 1 as 10 x 0.1
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Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
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Storing a Model Space Ship - Subtraction
Subtract 2.18 – 1.62
2.18
2.18 m – 1.62 m = 0.56 m
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Multiplying Decimals Using an Understanding of Place Value
Using Place Value Materials (With Renaming)
1.6x 2
2 groups of 1.6
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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
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Multiplying a Decimal by a Decimal
1.6x .2
Find two tenths of each part.
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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
xxxxxxx
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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)
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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)
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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).
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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).
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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).
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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).
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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
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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)
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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.
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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.
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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.
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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