MAT1236 Final: Addition structures
14 Jun 2018
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Addition'Structures:''
Two$models:$Aggregation:$situation$in$which$two$or$more$quantities$are$combined$into$a$single$
quantity.$‘How$much$altogether’$key$language:$what$is$the$sum,$add$and$combine.$Augmentation:$
refers$to$situations$in$which$a$quantity$is$increased$by$some$amount.$Models$for$addition:$Could$
teach$addition$through$rainbow$facts,$bridging$tens$(8+5=10+3),$using$a$hundreds$grid$(allows$
counting$forwards$or$back$in$10s$or$1s),$using$a$number$line,$counters,$connecting$cubes,$MAB$
blocks.$Properties'of'addition:$Commutative:$the$order$in$which$two$or$more$numbers$are$
added$does$not$affect$the$sum.$Associative:$the$grouping$of$numbers$in$addition$does$not$affect$the$
sum.$Additive:$adding$zero$to$any$number$does$not$change$the$original.$Compensation:$can$be$used$
to$simplify$calculations$by$temporarily$adding$or$subtracting$a$small$number.$(EG:$673+99,$
temporarily$add$1$to$make$99$=$100,$then$do$673+100$and$then$subtract$1.)$Mental$Strategies:$for$
43+48,$adding$from$the$left/partial$sums$(40+40,$3+8,$80+11).$Counting$on$(by$tens,$48,58,$etc)$
Making$compatibles$(43$and$7$make$50$50$plus$40$is$90$90$+$1$=$91)$Bridging$(break$up$a$number$and$
add$the$parts,$43+8$is$51,$add$40$more$is$91).$Extend$basic$facts:$4+59,$so$40+50=90$and$
400+500=900,$practice$counting$on$(forwards$and$backwards$from$any$starting$point$then$skip$
counting),$use$compatible$or$friendly$numbers.$Standard$algorithm:$column$addition,$aid$this$by$
using$MAB$blocks,$language$such$as$grouping$and$exchanging.$Partial$sums.$$
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Document Summary
Two models: aggregation: situation in which two or more quantities are combined into a single quantity. How much altogether" key language: what is the sum, add and combine. Augmentation: refers to situations in which a quantity is increased by some amount. Models for addition: could teach addition through rainbow facts, bridging tens (8+5=10+3), using a hundreds grid (allows counting forwards or back in 10s or 1s), using a number line, counters, connecting cubes, mab blocks. Properties of addition: commutative: the order in which two or more numbers are added does not affect the sum. Associative: the grouping of numbers in addition does not affect the sum. Additive: adding zero to any number does not change the original. Compensation: can be used to simplify calculations by temporarily adding or subtracting a small number. (eg: 673+99, temporarily add 1 to make 99 = 100, then do 673+100 and then subtract 1. ) 43+48, adding from the left/partial sums (40+40, 3+8, 80+11).
