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**Thinking Rationally about Decimals through the use of Base Ten Blocks**

Joe Hill

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**Purpose Some lessons build understanding.**

Some lessons build skills which are applied to understanding. Some lessons build speed in applying skills to understanding. The purpose of this lesson is to build understanding.

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**Meet the Base Ten Blocks**

This is a “flat.” It is made up of ten rows and ten columns of small blocks. Its value is 1.

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**Meet the Base Ten Blocks**

This is a “rod.” It is made up of ten rows and one column of small blocks. Ten rods make a flat. Its value is one tenth since ten rods make one flat. We write that 0.1

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**Meet the Base Ten Blocks**

This is a “block.” It is a small cube. There are 10 blocks in a rod. There are 100 blocks in a flat. Its value is one hundredth since one hundred blocks would make one flat. We write that 0.01

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**Multiple Base Ten Blocks**

Three flats would have the value of 3.

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**Multiple Base Ten Blocks**

Four rods would have the value of four tenths. We write that 0.4 Note that its value is also 40 hundredths since there are 40 blocks here. So it could also be written 0.40

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**Multiple Base Ten Blocks**

Six blocks would have the value of six hundredths. We write that 0.06

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**Multiple Base Ten Blocks**

One flat and two rods would have the value one and two tenths. We write that 1.2

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**Multiple Base Ten Blocks**

One rod and two blocks would have the value one tenth and two hundredths. Its value is the same as twelve hundredths. We write that 0.12

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**Multiple Base Ten Blocks**

One flat, three rods and four blocks would have the value one, three tenths and four hundredths. Its value is the same as one and thirty four hundredths. We write that 1.34

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**Multiple Base Ten Blocks**

One flat, one rod and 6 blocks would have the value one, one tenth, and six hundredths. That also equals one and 16 hundredths. How would we write that? 1.16

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**Multiple Base Ten Blocks**

One flat and two blocks would have the value one and two hundredths. How would we write that? 1.02

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**One and five hundredths**

Decimal Practice What’s the value? One and five hundredths How do we write that? 1.05

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**Two and thirteen hundredths**

Decimal Practice What’s the value? Two and thirteen hundredths How do we write that? 2.13

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**One and fifty one hundredths**

Decimal Practice What’s the value? One and fifty one hundredths How do we write that? 1.51

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**One and twenty three hundredths**

Show with blocks: One and twenty three hundredths How do we write that? 1.23

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Show with blocks: One and six tenths How do we write that? 1.6

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**One and eight hundredths**

Show with blocks: One and eight hundredths How do we write that? 1.08

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Show with blocks: 2.3 How do we say that? Two and three tenths

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Show with blocks: 0.46 How do we say that? Forty six hundredths

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Trading Blocks Ten blocks can be traded for a rod.

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Trading Blocks A flat can be traded for ten rods.

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Addition Add: The sum is 1.5

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Addition Add: 1.2 +1.04 The sum is 2.24

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Addition Add: The sum is 1.35

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Addition Add: The sum is 0.12

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Addition Add: The sum is 1.49

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Addition Add: The sum is 1.31

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Subtraction Subtract: The result is 0.5

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Subtraction Subtract: The result is 1.13

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Subtraction Subtract: The result is 0.41

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**Dimensions of Base Ten Blocks**

The height of the flat is 1. The width of the flat is 1. Its area is 1 square unit.

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**Dimensions of Base Ten Blocks**

The height of the rod is 1. The height of the block is one tenth, which we write as 0.1

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**Dimensions of Base Ten Blocks**

The height of a rod is 1. The width of the rod is 0.1 The area of one rod is 0.1 square units since ten of them make a flat.

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**Dimensions of Base Ten Blocks**

The height of the block is 0.1 The width of the block is 0.1 Its area of the block is one hundredth since 100 of them make the flat. We write that 0.01

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**Multiplication Example: 0.4 x 0.2 The answer is 0.08**

To multiply, find the factors on the horizontal and vertical lines then form a rectangle from these points. The answer is 0.08

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Multiplication Another example: 1.2 x 1.1 The answer is 1.32

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Multiplication Let’s do 0.8 x 0.4 The answer is 0.32

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Multiplication Let’s do 1.3 x 0.8 The answer is 1.04

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**Division What does 36 ÷ 4 mean?**

It means how many 4’s does it take to make 36. What does 81 ÷ 3 mean? It means how many 3’s does it take to make 81. What does Hokie ÷ Cav mean? It means many Cavs does it take to make a Hokie.

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**Division How many of these does it take to make The answer is 12**

What does 1.2 ÷ 0.1 mean? How many of these does it take to make The answer is 12

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**Division How many of these does it take to make The answer is 10.2**

What does 1.02 ÷ 0.1 mean? How many of these does it take to make It takes ten full rods and two-tenths of another The answer is 10.2

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**Division How many of these does it take to make The answer is 102**

What does 1.02 ÷ 0.01 mean? How many of these does it take to make The answer is 102

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**Division How many of these does it take to make The answer is 24**

What does 1.2 ÷ 0.05 mean? How many of these does it take to make The answer is 24

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**Understand decimals better?**

Hope so!

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