MAE2240 Lecture Notes - Lecture 4: Commutative Property, Number Sense, Telephone Numbers In The United Kingdom
29 May 2018
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!WEEK!4!
Basic!facts!and!mental!strategies:!
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Number!sense:!"a#view#of#numbers#as#meaningful#entities#and#the#expectation#that#
mathematical#manipulations#and#outcomes#make#sense.#Those#who#view#mathematics#in#
this#way#continually#utilise#a#variety#of#internal#'checks#and#balances'#to#judge#the#
reasonableness#of#numerical#outcomes"#(McIntosh,#Reys,#Bana,#and#Farrell,#1997)#
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Encourage#students#to#explore#mental#computation#as#a#first#resort,#mental#computation#is#
teaching#not#testing#so#focus#on#mental#strategies.##
Two#approaches#to#mental#strategies:#
• Mental#strategies#emerge#from#counting#
• Mental#strategies#and#basic#facts#are#intertwined#
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Doubling)and)near)double:#8+7,#8+8-1,#7+7+1#
Bridging)ten:#8+7,#8+2+5#(relies#on#breaking#7#up)##
Relate)to)a)known)fact)or)compensation:#8+9,#9+10-1#
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Properties!of!the!number!system:!#
• Commutative#property:#8+4=4+8,#7x3=3x7#
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