Development of number
May kid can count to 100. He
really understands his numbers!
Understanding Number
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13
Can construct a set with with 16 objects
Can identify a set with 16 objects
Can identify the numeral 16 with a set of 16 objects
Can read and write the numeral 16
Can identify the sixteenth object in sequenced set of objects.
Can tell what comes before and after 16
Can name and show some numbers that are larger and smaller
that sixteen.
• Can express 16 as the sum and difference of other whole
numbers in a variety of ways
• Can show sets that are equal to 16 by 1-1 correspondence
• Can show 16 as 1 ten and 6 ones.
How kids develop the concept
of number.
• Counting
– Rote
– Pattern
• Counting is very important.
• Strategies for addition Counting all,
counting on and counting backwards
1-1 Correspondance
a~a
Relationships
If b ~ a then a ~ b
Symmetry
Reflexsive
a
b
a
a
b
c
if a ~ b and b ~ c then a ~ c
Which do these relations
have?
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You are my sister (no have sisters)
=
>
<
Developing Understanding
number
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Counting Backward and Forward
Pictures
Numberline
Number Charts
True or False?
3
>
5
True?
The numeral (symbol) 3 is
larger than 5.
False?
The number 3 is not larger
than 5.
The numerals:
I : one
V : five
X : ten
L: fifty
C : one hundred
D : five hundred
M : one thousand
Rules for combining the numerals:
Numerals in a string are added: CC = 200 ; CCX = 210.
One numeral to the left of a larger numeral is subtracted from that
number: IX = 9
(Note that a number that is too small to be expressed by the subtraction
of more than one digit is written as a sum of the next smaller numeral, so
8 is not IIX but VIII.)
MCMXXVII :
MCMXCIII:
M = 1000;
CM = 1000 - 100 = 900;
XX = 10 + 10 = 20;
VII = 5 + 2 = 7
-------> 1927
M = 1000;
CM = 900;
XC = 100 - 10 = 90;
III = 3
-----> 1993
MDCCCXIV:
MMV
??????
M = 1000;
D = 500;
CCC = 300;
X = 10;
IV = 5 - 1 = 4
----> 1814.
http://www.saxakali.com/COLOR_ASP/historymaf5.htm
Numbers Numerals had Meaning
Egyptian
Decode This Number
Other Systems
2 count has been superseded by better counting systems and exists only in isolated regions in
Africa, Australia and South America.
20 count is found in widely separated regions but especially in Central America, N.E. Asia
and Africa.
The decimal system has spread over most of the world because of the spread of IndoEuropean languages and because of its efficiency.
The 20 system once prevailed in a large area of Europe but it was replaced although traces
remain in the Basque, Irish and Scottish languages.
Place Value Models
• Place Value Model Types:
• Students do the grouping i.e. sticks, unifix cubes
• The model suggest trades i.e. base ten blocks
• The model has no physical trade suggested. i.e. money,
number tags
• Positional Model i.e. abacus
Introducing a model
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Free play
Establish Relationships
Decode Your disk
Encode Sort Problem
Trade to Standard Representation
Trade to Non-Standard Representation
Abacus
1
Count to 1000 in Base 2
Count to 100 in Base 5
Find The Number
Represented by The following
Numerals
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102
104
105
108
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1002
1004
1005
1008
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1002 -1
1004 -1
1005 -1
1008 -1
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Development of number - Buffalo State College