NUMBER SENSE & NUMERATION

TERM 1

MRSTAV

NUMBER SENSE & NUMERATION

Represent whole numbers in expanded form using powers of 10

MRSTAV

CURRICULUM

# SCIENTIFIC NOTATION & NS

EXPANDED FORM USING POWERS OF 10

SCIENTIFIC NOTATION &

EXPANDED FORM USING POWERS OF 10

NS

DO IT NOW

MRSTAV

Good Morning my friend, yesterday at lunch I made a spectacular play on our friend Elijah Austin. I think I will play in the National Basketball Association one day.

Rewrite this message into a shortened version.

Tyree

MRSTAV

How wide is our universe?

210 000 000 000 000 000 000 000 miles

• This number is written in decimal notation
• It is easier to write them in scientific notation.

(22 zeros)

MRSTAV

SCIENTIFIC

NOTATION

10²  =  100                   10 to the power of ²  is One Hundred (2 zero's after the 1)

10³  =  1,000                10 to the power of ³  is One Thousand 

10⁴  =  10,000              10 to the power ⁴  is Ten Thousand (4 zero's after the 1)

10⁵  =  100,000            10 to the power of ⁵  is One Hundred Thousand

10⁶  =  1,000,000         10 to the power of ⁶  is One Million (6 zero's after the 1)

POWERS OF 10

MRSTAV

SCIENTIFIC NOTATION

• A number is expressed in scientific notation when it is in the form:

a x 10ⁿ�

where a is a number between 1 and 9.999999999

and n is how many places you moved the decimal

​

MRSTAV

BASE

2⁵

EXPONENT

INDEX

POWER

MRSTAV

REPEATED MULTIPLICATION

2 x 2 x 2 x 2 x 2

EXPONENTIAL FORM

2⁵

MRSTAV

REPEATED MULTIPLICATION

2¹ = 2

2² = 2 x 2

2³ = 2 x 2 x 2

2⁴ = 2 x 2 x 2 x 2

2⁵ = 2 x 2 x 2 x 2 x 2

MRSTAV

210 000 000 000 000 000 000 000 miles

• Where is the decimal point?
• Where would you move the decimal to make this number be between 1 and 9?
• How many decimal places did you move the decimal?

​

​

MRSTAV

210 000 000 000 000 000 000 000 miles

x 10

a

ⁿ

x 10

2.1

²³

where a is a number between 1 and 9

and n is how many places you moved the decimal

MRSTAV

TRY IT…

MRSTAV

SCIENTIFIC NOTATION

• When the original number is less than 1, the exponent is negative.

​

4 200 000 000

compared to…

0.0000042

MRSTAV

• When the original number is less than 1, the exponent is negative.

0 0000000902

• Where is the decimal point?
• Where would you move the decimal to make this number be between 1 and 10?
• How many decimal places did you move the decimal?

​

​

MRSTAV

• When the original number is less than 1, the exponent is negative.

0 0000000902

x 10

a

ⁿ

x 10

9.02

^-8

where a is a number between 1 and 10

and n is how many places you moved the decimal

MRSTAV

TRY IT

Express in scientific notation

1. Mass of a dust particle: 0.000000000753 kg

​

• Length of the shortest wavelength of visible light (violet): 0.0000004 meter

​

• Mass of an electron: 0.00000000000000000000000000000091093822 kg

= 7.53 x10^-10

= 4.0 x10^-7

= 9.1093822×10^-31

MRSTAV

TRY IT

Express in decimal notation

1. 4.58 x 10⁶
2. 7.0003 x 10¹⁰
3. 1.8 x 10^-4
4. 9.222002 x 10^-8

= 4 580 000

= 70 003 000 000

= 0.00018

= 0.00000009222002

MRSTAV

TRY IT:

Write in Scientific Notation

​

a) 300 000

​

b) 590 000 000

​

c) 93 100 000 000

Write in decimal notation

​

d) 4 x 10^-4

​

e) 3.2 x 10^-6

​

f) 8.3292 x 10⁹

³⁹

JUST KIDDING

MRSTAV

• Exponents (Index, Power)
• Base
• Repeated Multiplication
• Squared
• Cubed

​

​

MRSTAV

WORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALL

WORDWALLWORDWALLWORDWALLWORDWALL

EXPANDED FORM �USING POWERS OF 10

MRSTAV

__ __ __ __ __ __ __ __ __

__ __ __

ONES

__ __ __

THOUSANDS

ONES

TENS

HUNDREDS

ONES

TENS

HUNDREDS

MRSTAV

Standard Form

65 102.00

• The way we usually write numbers.
• They are in groups of 3 starting from the decimal
• Use a SPACE and not a COMMA

​

Written Form

Sixty-Five Thousand One Hundred Two

• Writing a number in words as we would say it
• Don’t use the word “AND”

MRSTAV

Expanded Form Using Powers of 10

• Using “ x 10^#” instead of writing all the zeroes

Expanded Form

60 000 + 5 000 + 100 + 2

• Writing a number as the sum of the value of its digits.
• We split the number up into the separate value of each digit and connect them with addition.

(6 x 10⁴) + (5 x 10³) + (1 x 10²) + (2)

MRSTAV

60 000 + 5 000 + 100 + 2

What does 6 x 10 000 = ______________

60 000 + 5 000 + 100 + 2

(6 x 10 000) + ( ) + ( ) + ( )

5 x 1000

1 x 100

2

MRSTAV

60 000 + 5 000 + 100 + 2

(6 x 10 000) + ( ) + ( ) + ( )

5 x 1000

1 x 100

2

( ) + ( ) + ( ) + ( )

5 x 10

1 x 10

2

6 x 10

⁴

10²  =  100                   10 to the power of ²  is One Hundred (2 zero's after the 1)

10³  =  1,000                10 to the power of ³  is One Thousand 

10⁴  =  10,000              10 to the power ⁴  is Ten Thousand (4 zero's after the 1)

10⁵  =  100,000            10 to the power of ⁵  is One Hundred Thousand

10⁶  =  1,000,000         10 to the power of ⁶  is One Million (6 zero's after the 1)

³

²

MRSTAV

STANDARD FORM

TO

EXPANDED FORM �USING POWERS OF 10

MRSTAV

8 249 405

MRSTAV

8 249 405

1

2

3

4

5

6

8

x 10

6

+

MRSTAV

8 249 405

1

2

3

4

5

8

x 10

6

+

2

x 10

5

+

MRSTAV

8 249 405

1

2

3

4

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

MRSTAV

8 249 405

1

2

3

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

9

x 10

3

+

MRSTAV

8 249 405

1

2

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

9

x 10

3

+

4

x 10

2

+

MRSTAV

8 249 405

1

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

9

x 10

3

+

4

x 10

2

+

0

x 10

1

+

0 multiplied by anything is?

0

MRSTAV

8 249 405

1

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

9

x 10

3

+

4

x 10

2

+

0

Why even write a zero?

MRSTAV

8 249 405

8

x 10

6

+

2

x 10

5

+

4

x 10

4

+

9

x 10

3

+

4

x 10

2

+

5

x 10

NOTHING

NOTHING

MRSTAV

65 102

60 000 + 5 000 + 100 + 2

6 x 10⁴ + 5 x 10³ + 1 x 10² + 2

​

10 325 009

10 000 000 + 300 000 + 20 000 + 5 000 + 9

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

​

MRSTAV

a) 132

​

b) 15 030

​

c) 634 328

​

TRY IT

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EXPANDED FORM �USING POWERS OF 10

TO

STANDARD FORM

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

START FROM THE RIGHT! 🡪

1

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

START FROM THE RIGHT! 🡪

1

__

1

__

2

__

3

__

4

__

5

__

^

3

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

START FROM THE RIGHT! 🡪

1

__

1

__

2

__

3

__

4

__

5

__

^

3

__

1

__

2

__

3

__

4

__

^

2

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

START FROM THE RIGHT! 🡪

1

__

1

__

2

__

3

__

4

__

5

__

^

3

__

1

__

2

__

3

__

4

__

^

2

__

1

__

2

__

3

__

^

5

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

START FROM THE RIGHT! 🡪

1

__

1

__

2

__

3

__

4

__

5

__

^

3

__

1

__

2

__

3

__

4

__

^

2

__

1

__

2

__

3

__

^

5

9

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

__

1

__

2

__

3

__

4

__

5

__

6

__

7

__

^

(SPACE)

(SPACE)

1

__

1

__

2

__

3

__

4

__

5

__

^

3

__

1

__

2

__

3

__

4

__

^

2

__

1

__

2

__

3

__

^

5

9

0

0

0

MRSTAV

1 x 10⁷ + 3 x 10⁵ + 2 x 10⁴ + 5 x 10³ + 9

1

3

2

5

9

0

0

0

MRSTAV

a) 5 x 10³ + 6 x 10² + � 7 x 10¹ + 8

b) 7 x 10⁸ + 2 x 10⁴ + � 9 x 10¹ + 1

c) 5 x 10¹¹ + 9 x 10⁹ + � 7 x 10¹ + 8

​

​

TRY IT

MRSTAV

• Standard Form
• Written Form
• Expanded Form
• Powers of 10

MRSTAV

WORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALLWORDWALL

WORDWALLWORDWALLWORDWALLWORDWALL

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

1. Activity on MrStav.ca

MrStav.ca/JOURNAL

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

TARSAI

PUZZLE

MRSTAV

MRSTAV

Independent Work

Math Journal

Technology

Math Games

EXPECTATIONS

/

/

/

/

• Silent
• Low whisper

• Writing
• Pencil
• Journal
• Working by myslef

Independent Work

Math Journal

Technology

Math Games

• Silent
• Low whisper

• Writing
• Pencil
• Practie Handout
• Working by myslef

• NOT silent
• NOT yelling
• Accountable Math talk
• Word wall words
• Medium volume

• At the table
• Moving Pieces
• Doing the math
• Math journal open
• Playing the game

• Typing
• Not talking
• Silent

• Computer open
• On-screen is the math work
• On-Task
• At the proper desk

EXPECTATIONS

/

/

/

/

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

1. Activity on MrStav.ca

MrStav.ca/JOURNAL

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

1 2 3 4 5

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

1. Activity on MrStav.ca

MrStav.ca/JOURNAL

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

1 2 3 4 5

TECH

INDEPENDENT

WORK

MATH GAME

MATH

JOURNAL

1. Activity on MrStav.ca

MrStav.ca/JOURNAL

MRSTAV

>>

>>

>>

>>

CENTRES

GUIDED

WITH STAV

MRSTAV

MRSTAV

NUMBER SENSE & NUMERATION

Represent whole numbers in expanded form using powers of 10

MRSTAV

CURRICULUM

NUMBER SENSE & NUMERATION

• Express repeated multiplication using exponential notation
• Represent whole numbers in expanded form using powers of 10
• Represent, compare and order rational numbers
• (i.e. positive and negative fractions and decimals to thousandths)
• Translate between equivalent forms of a number
• (i.e. decimals, fractions, percents)
• Determine common factors and common multiples using the prime factorisation of numbers.

MRSTAV

CURRICULUM