Decimals

How to Write Decimals through a Conceptual Understanding of What

Decimals Are

What is a decimal?

Turn to your partner and explain what you know about decimals.

What is a decimal?

Definition of decimal (link)

When do we use decimals?

Take a few seconds to think aboutwhen you have seen decimals.

When do we use decimals?Temperatures

Percentages

Measurements

Racing Times

Money

Writing DecimalsThere are different ways to represent these numbers.

Flat one whole 1 1.0

Writing DecimalsThere are different ways to represent these numbers.

Flat one whole 1 1.0 Rod one-tenth 0.110

1

Writing DecimalsThere are different ways to represent these numbers.

Flat one whole 1 1.0 Rod one-tenth 0.1 Unit one-hundredth 0.01

10

1

100

1

On your place mat, show one-tenth.

Tenths HundredthsUnits

On your place mat, show one-tenth.

Tenths HundredthsUnitsHow many blocks are in the units column?

On your place mat, show one-tenth.

Tenths HundredthsUnitsHow many blocks are in the units column?

How many tenths are in

the tenths column?

On your place mat, show one-tenth.

Tenths HundredthsUnitsHow many blocks are in the units column?

How many tenths are in

the tenths column?

Can you think of another

way to represent one-tenth?

On your place mat, show one-tenth.

Tenths HundredthsUnitsHow many blocks are in the units column?

How many tenths are in

the tenths column?

Can you think of another

way to represent one-tenth?

Now show two-tenths on your place value mats.

Tenths HundredthsUnits

Now show two-tenths on your place value mats.

Tenths HundredthsUnits

Now show two-tenths on your place value mats.

How do you write two-tenths as a decimal? Write it.

Turn to your partner and explain to her or him how you know that what you wrote means two-tenths.

Tenths HundredthsUnits

Now show two-tenths on your place value mats.

How do you write two-tenths as a decimal? Write it.

0.2

Tenths HundredthsUnits

What does seven-tenths look like?

Represent seven-tenths with the blocks and as a decimal.

What does seven-tenths look like?

Represent seven-tenths with the blocks and as a decimal.

0.7

Writing DecimalsRepresent one-hundredth with your blocks and write it as a

decimal. Flat one whole 1 1.0

Rod one-tenth 0.1

Unit one-hundredth

10

1

100

1

Writing DecimalsRepresent one-hundredth with your blocks and write it as a

decimal. Flat one whole 1 1.0

Rod one-tenth 0.1

Unit one-hundredth 0.01

10

1

100

1

Turn to your partner and explain why the decimal you

wrote represents one-hundredth.

Review of the values of the places.

2, 3 4 6

thousands hundreds tens ones

Review of the values of the places.

2, 3 4 6. ___ ___ ___

thousands hundreds tens ones tenths hundredths thousandths

Review of the values of the places.

2, 3 4 6. ___ ___ ___

thousands hundreds tens ones tenths hundredths thousandths

The decimals follow the same pattern as whole numbers in that each time we move to the right the place is ten times smaller.

Review of the values of the places.

2, 3 4 6. ___ ___ ___

ones

tens tenths

hundreds hundredths

thousands thousandths

Some people see the pattern better whenthey see it this way. Remember each place has a name.

Review of the values of the places.

This can also be organized into a chart.

Think back to fractions…

Remember how thirteen-hundredths

can be represented as

100

13

Think back to fractions…

Remember how thirteen-hundredths can be represented as

100

3

10

1

100

13

Think back to fractions…

Remember how thirteen-hundredths can be represented as

13.0100

3

10

1

100

13

Who can explain why this decimal is correct?

0.10

What does this decimal represent?

Turn and share with your partner.

Who can tell what your partner said?

Do you agree with your partner?

0.20

What does this decimal represent?

Write your explanation in your math notebook. Be prepared to share with the whole class.

Writing DecimalsThere are different ways to

represent this number.

Rod one-tenth 0.1 0.1010

1

Show as many ways as you can to represent this number with the blocks.

Find as many ways as you can to represent each of these numbers

as fractions and as decimals.

Six-hundredths Nine-tenths

Fifteen-hundredths Thirty-five-hundredths

Four-tenths Fifty-hundredths

A Decimal Game to Enjoy!

Builder Ted needs you to put decimals in order to save his dog

Beat the clock to write the decimal

Play against the computer or a partner to make the largest decimal

More Advanced Decimal Games

Add decimals but don't go over 2.0 Play tug-of-war by comparing decimals Race around a track using multiplication, addition,

and subtraction See how decimals and fractions are related

Interactive Place Value Mat

http://www.arcytech.org/java/b10blocks/b10blocks.html

That little point is very important!

Remember that little

dot can mean the

difference between

a penny and a

dollar or more.

$0.01 $1.00