Thinking%20Rationally%20about%20Decimals%20through%20the%20use%20of%20Base%20Ten%20Blocks

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Thinking Rationally about Decimals through the
use ofBase 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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Decimal Practice

• Whats the value?

One and five hundredths
How do we write that?
1.05
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Decimal Practice

• Whats the value?

Two and thirteen hundredths
How do we write that?
2.13
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Decimal Practice

• Whats the value?

One and fifty one hundredths
How do we write that?
1.51
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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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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
• 1.3 0.2

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
• 0.34 1.01

The sum is 1.35
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Addition

• Add
• 0.04 0.08

The sum is 0.12
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Addition

• Add
• 1.29 0.2

The sum is 1.49
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Addition

• Add
• 1.29 0.02

The sum is 1.31
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Subtraction

• Subtract
• 1.2 - 0.7

The result is 0.5
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Subtraction

• Subtract
• 1.2 - 0.07

The result is 1.13
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Subtraction

• Subtract
• 1.01 - 0.6

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

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

• Lets do 0.8 x 0.4

The answer is 0.32
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Multiplication

• Lets 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 4s does it take to make 36.
• What does 81 3 mean?
• It means how many 3s 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

• What does 1.2 0.1 mean?

The answer is 12
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Division

• What does 1.02 0.1 mean?

It takes ten full rods and two-tenths of another
The answer is 10.2
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Division

• What does 1.02 0.01 mean?

The answer is 102
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Division

• What does 1.2 0.05 mean?

The answer is 24
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Understand decimals better?

• Hope so!