mted 3109 place value- numeration

8/10/2019 MTED 3109 Place Value- Numeration

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Place Value and Representation

of numbers The numeration system we used is the

Hindu-Arabic System

Has 4 important characteristics- place value: The position of the digit

represents its value.

-Base of ten: base means a collection. 10 isthe value that determine a new collection.The system has 10 digits, 0 through 9


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important characteristics of Hindu

Arabic Numeration Use of zero: A symbol of zero exits and

represents the absence of something.

Example: 508 Additive property: Numbers can be summed

with respect to place value

Once children understand the characteristics,the formation and interpretation of numbersis a natural development


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NumerationBy studying the development of our number

system we begin to understand how a child

feels when faced with the problem of counting

Our number system is based on the 'two

hands' collective unit

We count up to ten and call it one group of

ten


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Grouping

The words for the numbers greater then ten mean

'ten and one', 'ten and two, 'two groups of ten',and

so on In English this is confounded at the start by the use of

the words 'eleven' and 'twelve

These words cause some children problems


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Base 5 Other people used the 'one hand' number unit

Their number words meant 'one', 'two', 'three', 'four','one group of five', 'five and one', 'five and two', etc.

Such a system is called a base five system ofnumeration, while our number system is said to bebase ten


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Base 5

1

2 3

4

1


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Base 5

11

12 13

14

2

Get students to count using base 5 inclass. Go round and round for at least 3

rounds or more;


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Place Value and the Zero

Symbol

The idea that the value of a symbol can varyaccording to its position in relation to other symbolswas an important step in the development of several

number systems Being able to recognise that 36 is different to 63

This idea is called place value


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The Importance of Zero

We use the zero symbol '0' to indicateempty places

Thus, we can tell the differencebetween the numbers 42 and 402though they use the same numerals

Note : 0 , 1 , 2 , 3 ,. are digits;

257, 176 are numerals.


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The Importance of Zero

The idea of a zero symbol came relatively

late in the development of number systems

(at one stage the idea was banned for over acentury)

It is sometimes a difficult concept for children

to grasp.


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Our Decimal

(Base 10) System It is important to realise that our number is not the

only system

We are familiar with our system

Your experience of learning other systems is useful

to remind you what it is like for children in your class

learning our system


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Importance of place value Place value, together with base ten,

enable you to manipulate, read and

symbolised both large and smallnumbers


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How many beads are in each

pile?


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Groups of tens Grouping by tens facilitates counting and

organising larger quantities

The ten-frame provides a convenient modelfor counting, grouping and eventuallyrepresenting two-digit numbers

Model for place value

Provide mental imagery

Pg 169 (Reys)


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Grouping or Trading Children in first three grades need

experience in counting piles of objects;

trading for grouped tens, hundreds, andthousands

Then talking about the results

Models used: ten- frame, bean sticks


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Why practice grouping or

trading? Develop and improve number sense

Provide opportunities for developing mental

computation Develop written computation

How an unknown quantity can be organisedinto a form that can be interpreted by

inspection. The process of grouping by tens is the

framework for place value


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Nature of place value Understanding of place value is

necessary to learn algorithms for

addition, subtraction, multiplication anddivision.

Promote number sense and facilitatesestimation

Sharpens a sense of reasonablenessabout computational results


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Two key ideas of place value Explicit grouping or trading rules

- 10 ones for 1 ten

- 10 tens for 1 hundred

- 10 hundreds for 1 thousand and so

on

Similar trade for numbers less than one

- 1 an be traded for 10 tenths (10 tenths for 1)

- 10 hundredths for 1 tenth and so on


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Two key ideas of place value The position of a digit determines the

number being represented.

Example: 3042 ( 2 is 2 ones)

2403 (2 is 2 thousands)


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Modeling Hands-on experience with manipulatives is essential

in establishing and developing the concept of placevalues

Ten-frames, bean sticks Models may be proportional or nonproportional, but

must be based on groups of 10

Proportional models : decimeter rods, centimeter

cubes, the materials for 10 is ten times the size ofthe material for 1

Nonproportional models: money: 10 one- cent coinsiare the same as one ten-cents coin.; abacus,counters(using different colours)

mted 3109 place value- numeration

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