MAT1236 Study Guide - Final Guide: Commutative Property, Distributive Property
14 Jun 2018
School
Department
Course
Professor
Multiplication+Structures:++
Repeated'aggregation:'the'idea'that'multiplication'means'‘so'many'sets'of’,'repeated'addition'(if'I'
have'10'sets'of'3'counters,'how'many'counters'altogether'='3x10)'Scaling:'occurs'when'
multiplication'is'used'to'increase'a'quantity'by'a'certain'percentage,'increase'quantity'by'a'scale'
factor.'(multiplying'by'less'than'1'reduces'the'size'of'the'quantity,'EG:'Hannah'spent'$35'on'xmas'
gifts,'Geoff'spent'3'times'as'much,'how'much'did'Geoff'spend).'Models'for'multiplication:'sets'of'
objects,'arrays,'skip'counting'along'a'number'line.''
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Properties+of+Multiplication:'Commutative:'4x3'Is'the'same'as'3x4.'Associative:'factors'may'
be'grouped'in'anyway'without'affecting'the'product.'Distributive:'multiplication'can'be'distributed'
across'addition:'3x(2+4)'is'the'same'as'3x2+3x4'(can'also'be'distributed'across'subtraction)'Property'
of'Zero:'any'number'multiplied'by'0'is'0.'Property'of'One:'any'number'multiplied'by'one'is'the'
number'itself.'Mental'strategies'for'multiplication:'doubling'(times'by'two'is'achieved'by'doubling,'
times'by'4'is'achieved'by'doubling'and'doubling'again),'doubling'and'halving'(EG'25x48,'doubling'
25=50'and'halving'48=24,'doubling'50'and'halving'24'again'gives'100x12=1200),'logical'reasoning'
(calculate'15x120,'that’s'10x120'+'5x120,'but'5x120'is'half'of'10x120,'so'15x120=1200+600=1800),'
extending'basic'facts'(since'10x480=4800,'then'5x480=2400),'factoring'(14x55'='(2x7)x(5x11),'
changing'the'order'of'multiplication'gives'us'10x77=770),'commutative'property'(2x3x4x5x8)'since'
2x5=10'we'calculate'3x4'&'the'double,'double,'and'double'to'multiply'by'8),'partitioning'
(multiplication'by'larger'numbers'can'be'simplified'by'partitioning,'23x8'could'calculate'20x8'and'
3x8,'use'the'rectangle'visual)'&'distributive'property'(397x4,'since'397+3=400,'we'calculate'400x4'&'
subtract'3x4).'Use'a'grid'to'aid'in'teaching'multiplication'facts.'+
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Document Summary
Models for multiplication: sets of objects, arrays, skip counting along a number line. Properties of multiplication: commutative: 4x3 is the same as 3x4. Associative: factors may be grouped in anyway without affecting the product. Distributive: multiplication can be distributed across addition: 3x(2+4) is the same as 3x2+3x4 (can also be distributed across subtraction) property of zero: any number multiplied by 0 is 0. Property of one: any number multiplied by one is the number itself. Mental strategies for multiplication: doubling (times by two is achieved by doubling, times by 4 is achieved by doubling and doubling again), doubling and halving (eg 25x48, doubling. 2x5=10 we calculate 3x4 & the double, double, and double to multiply by 8), partitioning (multiplication by larger numbers can be simplified by partitioning, 23x8 could calculate 20x8 and. 3x8, use the rectangle visual) & distributive property (397x4, since 397+3=400, we calculate 400x4 & subtract 3x4).
