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Renaming Place Value Whole Numbers to Billions (MKT)
Zozan Ibrahimon 31 October 2012
Transcript of Renaming Place Value Whole Numbers to Billions (MKT)
Numbers To Billions (MKT) Rationale Definitions & Terms Used Conceptual Knowledge (CK) Procedural Fluency & Flexibility (PFF) Procedural Fluency and Flexibility (PFF) Mathematical Connections (MC) Mathematical Connection (MC) Renaming (used to be known as the remainder or 'carry the number'): The quantity left over when one number is divided by another. Renaming is used to maintain whole numbers.
Numbers: are made up of digits in the same way that words are made up of letters
Place Value: The specific column or location of a digit within a numerical system. The place value indicates the specific multiple of the numerical system's base value, or radix.
Base 10 system: The most commonly used number system in everyday life, also known as the decimal system. The base 10 system uses ten digits, 0-9.
Hindu-Arabic System: The system is based upon ten (originally nine) different symbols. The symbols used to represent the system are in principle independent of the system itself. 3 603 512 800 <-- This number is read as "Three Billion, Six hundred and Three Million, Five hundred and Twelve Thousand and Eight Hundred"
The Place value of each of the numbers are as follows: Another Example of renaming this number would be:
3 x 1 000 000 000
OR 3 Lots of 1 Billions
603 x 1 000 000
OR 603 Lots of 1 Millions
512 x 1000
OR 512 Lots of 1Thousands
8 x 100
OR 8 Lots of 1 Hundreds Renaming is used in Addition, Subtraction, Multiplication and Division.
for example: Within subtraction it is also important that 68 can be seen as both 6 tens 8 ones and 5 tens 18 ones, while in division, 6857 may need to be interpreted as 68 hundreds 5 tens 7 ones. S3909217
Zozan.Ibrahim@live.vu.edu.au What is the Hindu-Arabic System? The Hindu-Arabic numeration system evolved around A.D. 800. It is basically the numeration system that is widely used today (The Base-Ten System). The following lists 4 main attributes of this numeration system: First, it uses 10 digits or symbols that can be used in combination to represent all possible numbers. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Second, it groups by tens.
In the Hindu-Arabic numeration system, ten ones are replaced by one ten, ten tens are replaced by one hundred, and ten hundreds are replaced by one thousand, 10 one thousand are replaced by 10 thousands, and so forth...
Third, it uses a place value. starting from right to left; the first number represents how many ones there are
the second number represents how many tens there are; the third number represents how many hundreds there are; the fourth number represents how many thousands there are; and so on...
For example, in the numeral 4687, there are 7 ones, 8 tens, 6 hundreds, and 4 thousands
Place values: thousand hundred ten one
Digits: 4 6 8 7
Numeral value is equal to 4 × 1000 + 6 × 100 + 8 × 10 + 7 × 1 = 4000 + 600 + 80 + 7 = 4687 Al-Khwarizmi References Knowing the concept of place value is essential for every day lives
A lot of students find themselves struggling as they get into the higher levels of mathematics when they don't completely understand the concept of place value
I didn't understand the importance of place value before this course
There are many ways to Rename this number for example, one way could be:
3 Billion + 6 Million + 3 Million+ 500 Thousand + 12 Thousand + 8 Hundred which will equal 3 603 512 800 "In everyday use, numbers often need to be renamed in a variety of ways rather than be simply understood in terms of counting of even place value. At its most Fundamental, a number such as 68 can be viewed not only as 6 tens 8 ones but as 68 ones or 26 tens 8 ones or 268 ones. it is particularly important in computation that a number such as 608 can be renamed as 60 tens 8 ones. these alternative representations can be developed through the use of base-10 materials and then consolidated with a number expander which can be unfolded to see the various ways in which the number can be renamed." (Booker. etl. Teaching Primary Mathematics, 4th ed.) Student Thinking(ST) 'A common misconception with students in regards of Place value and renaming may be numbers that contain zeros pose further difficulties: while 60 represents sixty or 6 tens, 605 signifies 6 hundred 0 tens 5 ones, or six hundred and five rather than the sixty-five that some children see. Similarly, although a number might be said 'six thousand and eight', it is not written 68 but 6008 where the zeros show that there is nothing in the hundreds and tens places.' (Booker, etl. teaching primary mathematics 4th ed.) Booker. etl. "Mathematics Education in the Primary School Victoria University", Pearson Australia, Frenchs Forest, Sydney NSW 2086
Image 1 (MABs)
http://stmarysbowraville.edublogs.org/ (cited on the 15.10.12)
Image 2 (Number expander) http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/structure/st35mentaldiv.htm (cited 15.10.12)`
A-Z famous mathematicians:
Different (cited 15.10.12) Muammad ibn Mūsā al-Khwārizmī (780c-850c) was a Muslim mathematician and astronomer, who made significant contributions within the mathematical field, through his algebraic understanding he managed to revolutionize the way the world processed equations. He was born in a Persian family, but due to the proliferation of the Arabic language, all his work was in Arabic. Khwarizmi can also be accredited for familiarizing the Western World with the decimal positional number system (Hindu-Arabic system or base-ten system); moreover he was the man accountable for the use of Arabic numerals in Mathematics. Till today, people marvel at how he brought about the concept of Algorithm in Mathematics, this explains how the word “algorithm” is a Latin, English distortion of his name. Billions Millions Thousands Hundreds
3 603 512 800