Development of number

May kid can count to 100. He really understands his numbers!

Understanding Number 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

Relationships

ReflexsiveSymmetry

a ~ a

If b ~ a then a ~ b

if a ~ b and b ~ c then a ~ c

a

a b

a b c

Which do these relations have?

• You are my sister (no have sisters)

• =

• >

• <

Developing Understanding number

• 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 :

M = 1000; CM = 1000 - 100 = 900; XX = 10 + 10 = 20; VII = 5 + 2 = 7 -------> 1927

MCMXCIII:

M = 1000; CM = 900; XC = 100 - 10 = 90; III = 3 -----> 1993

MDCCCXIV:

M = 1000; D = 500; CCC = 300; X = 10; IV = 5 - 1 = 4 ----> 1814.

MMV

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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2 count has been superseded by better counting systems and exists only in isolated regions in Africa, Australia and South America.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 Indo-European 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

• 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

• 102

• 104

• 105

• 108

• 1002

• 1004

• 1005

• 1008

• 1002 -1

• 1004 -1

• 1005 -1

• 1008 -1