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 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? • • • • 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 : 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Numbers Numerals had Meaning Egyptian Decode This Number Other Systems 2 count has been superseded by better counting systems and exists only in isolated regions in Africa, Australia and South America. 20 count is found in widely separated regions but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 • • • • • • 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

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# Development of number - Buffalo State College