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Grade 5 MatheMaticsGrades 5 to 8 Blackline Masters

BLM 5–8.1: Observation vity:Observation:Possible Actions:Students:Observation:Possible Actions:Students:Observation:Possible Actions:

ExamplesDiagrams/PicturesCharacteristicsBLM 5–8.2: Concept Description Sheet #1Non-Examples

BLM 5–8.3: Concept Description Sheet ptDescriptionExampleDiagramNon-Example

BLM 5–8.4: How I Worked in My GroupNameDateTaskCommentsI took turnsI participatedI encouraged othersI shared materialsI stayed with mygroupI listenedI accomplishedthe task

1605BLM 5–8.5: Number Cards728394

BLM 5–8.6: Blank Hundred Squares

undredsOnestensBLM 5–8.7: Place-Value Chart—Whole Numbersones

Subtraction11, 21, 21, 2,Grade 44.N.4.4.N.5.4.N.6.4.N.11.Grade 55.N.2.5.N.3.5.N.4.Making 10Using one lessUsing onemoreStudents use combinations that add up to tenand can extend this to multiples of ten in latergrades.Starting from a known fact and taking oneaway.Starting from a known fact and adding onemore.Grade 77.N.2.(continued)for 6 – 2think 6 – 1 – 1 is 4;think 6, 5, 4for 8 5 if you know8 4 is 12 and one moreis 13for 8 6 if you know8 7 is 15 and one less is144 is 107 is 10;so 23 is 30Examplefor 3 5think 5 1 1 1 is 8;think 5, 6, 7, 8Grade 66.N.8.MeaningStudents begin with a number and count on toget the sum. Students should begin torecognize that beginning with the larger of thetwo addends is generally most efficient.Counting back Students begin with the minuend and countback to find the difference.Grade 33.N.6.3.N.7.3.N.10.3.N.11.3.N.12.StrategyCounting onGrade 22.N.8.2.N.10.Grade1Grade 11.N.10.The following list compiles mental math strategies as found in the Kindergarten to Grade 8 Mathematics: ManitobaCurriculum Framework of Outcomes. Note: This resource is meant for teacher information, not as a list of strategies thatstudents should memorize.BLM 5–8.8: Mental Math Strategies

onGrade11, 2, 322, 32, 33Building onknowndoublesAdding fromleft to rightThe zeroproperty ofadditionUsing doublesStrategyStarting fromknowndoublesUsingaddition tosubtractUsing place value understanding to add2-digit numerals.doubles minus one (or two)Students learn doubles, and use this to extendfacts.doubles plus one (or two)This is a form of part-part-wholerepresentation. Thinking of addition as:part part wholeThinking of subtraction as:whole – part partKnowing that adding 0 to an addend does notchange its value, and taking 0 from a minuenddoes not change the value.Students learn doubles, and use this to extendfacts:using doublesMeaningStudents need to work to know their doublesfacts.BLM 5–8.8: Mental Math Strategies (Continued)(continued)for 5 7think 6 6 is 12;for 5 7think 5 5 2 is 12for 5 7think 7 7 – 2 is 12for 7 8think 7 7 is 14so 7 8 is 14 1 is 15for 25 33think 20 30 and 5 3is 50 8 or 580 5 5;11 – 0 11for 12 – 5think 5 12so 12 – 5 is 7Example2 2 is 4and 4 – 2 is 2

Multiplication CommutativepropertyMultiplication Skip-countingMultiplication Zero propertyof multiplication34StrategyMaking 10Multiplying a factor by zero will always resultin zero.Using the concept of multiplication as a seriesof equal grouping to determine a product.Switching the order of the two numbers beingmultiplied will not affect the product.MeaningStudents use combinations that add up to tento calculate other math facts and can extendthis to multiples of ten in later grades.AdditionCompensation Using other known math facts andSubtractioncompensating. For example, adding 2 to anaddend and taking 2 away from the sum.AdditionCommutative Switching the order of the two numbers beingpropertyadded will not affect the sum.AdditionCompatibleCompatible numbers are friendly numbersSubtractionnumbers(often associated with compatible numbers to5 or 10).Multiplication ArrayUsing an ordered arrangement to showDivisionmultiplication or division (similar to area).ConceptAdditionSubtraction333, 4(decimals)33Grade3BLM 5–8.8: Mental Math Strategies (Continued)for 4 x 2think 2, 4, 6, 8so 4 x 2 is 830 x 0 is 00 x 15 is 0(continued)Examplefor 8 5think 8 2 3 is10 3 or 13for 25 33think 25 35 – 2 is60 – 2 or 584 3 is the same as3 4for 4 3 students maythink 4 1 is 5 and 2more makes 7for 3 x 4 think for 12 3 think 4 x 5 is the same as5x4

Multiplication Doubling orDivisionhalvingMultiplication Using theDivisionpattern for 9sMultiplication RepeateddoublingDivisionUsingmultiplicationto divideMultiplication Distributiveproperty4, 544, 54, 544. 5StrategyMultiplicativeidentitySkip-countingfrom a onDivisionGrade4This is a form of part-part-wholerepresentation. Thinking of multiplication as:part x part wholeThinking of division as:whole part partIn arithmetic or algebra, when you distribute afactor across the brackets:a x (b c) a x b a x c(a b) x (c d) ac ad bc bdKnowing the first digit of the answer is oneless than the non-nine factor and the sum ofthe product’s digits is nine.Continually doubling to get to an answer.MeaningMultiplying (dividing) a factor (dividend) byone will not change its value.Similar to the counting on strategy foraddition. Using a known fact and skipcounting forward or backward to determinethe answer.Using known facts and doubling or halvingthem to determine the answer.BLM 5–8.8: Mental Math Strategies (Continued)(continued)for 2 x 154think 2 x 100 plus 2 x 50plus 2 x 4 is 200 100 8 or 308Example1 x 12 is 1221 1 is 21for 3 x 8think 3 x 5 is 15 and skipcount by threes 15, 18,21, 24for 7 x 4, think the doubleof 7 x 2 is 28for 48 6, think thedouble of 24 6 is 8for 7 x 9 think one lessthan 7 is 6 and 6 plus 3is nine, so 7 x 9 is 63for 3 x 8, think 3 x 2 is 6,6 x 2 is 12, 12 x 2 is 24for 35 7think 7 x 35so 35 7 is 5

Multiplication Halving anddoublingDivisionDividing bymultiples often56, 7Multiplication onGrade5Examplefor 32 4, think 32 2is 16 and 16 2 is 8 so32 4 is 8When multiplying by a factor of 10 (or a power for 4 x 700, think 4 x 7 isof ten), taking off the zeros to determine the28 and add two zeros toproduct and adding them back on.make 2800Halving one factor and doubling the other.for 24 x 4, think 48 x 2 is96for 76.3 10 think 76.3When dividing by 10, 100, etc., the dividendbecomes smaller by 1, 2, etc. place valueshould become smaller byone place value positionpositions.so 76.3 10 is 7.63MeaningContinually halving to get a number.BLM 5–8.8: Mental Math Strategies (Continued)

BLM 5–8.9: Centimetre Grid Paper

BLM 5–8.10: Base-Ten Grid Paper

BLM 5–8.11: Multiplication Table 0485664729091827364554637281

BLM 5–8.12: Fraction Bars

BLM 5–8.13: Clock Face

BLM 5–8.14: Spinner

BLM 5–8.15: Thousand Grid

Ones.TenthsBLM 5–8.16: Place-Value Mat—Decimal NumbersHundredthsThousandths

04.3BLM 5–8.17: Number Fan5162

789BLM 5–8.17: Number Fan (continued)

WWhat do you WANT to know about?KWhat do you think you KNOW about?BLM 5–8.18: KWL ChartWhat did you LEARN about?L

BLM 5–8.19: Double Number Line

BLM 5–8.20: Algebra Tiles

BLM 5–8.21: Isometric Dot Paper

BLM 5–8.22: Dot Paper

BLM 5–8.23: Understanding Words ChartWhat does it mean?WordPictureWordPictureExampleWhat does it mean?Example

BLM 5–8.24: Number Line

DateHow do I know that I have beensuccessful?to math I already know.others, and try many thingswhen I am trying to answer akind of question that I havenever seen before. I listen to others, talk withProblemSolvinganswers to questions withnumbers by thinking about hownumbers work (and I don’t needto write down my steps). I estimate to make sure myanswer makes sense or when Idon’t need an exact answer ormeasurement. I can quickly figure out theto my life. I connect the math I am learning I connect the math I am learningMentalMathematicsand EstimationConnectionsCommunication I use mathematical language andsymbols that I already know andthat I am learning. I use real things, pictures,symbols, talking, writing, andthinking to communicate.What are themathematicalprocesses?How have I shown my successes?(continued)TaskNameBLM 5–8.25: My Success with Mathematical Processes

Visualizationand link together different picturesand 3-dimensional objects. When thinking about numbers, Iimagine them in my head. When measuring, I know thatsometimes I need an exact numberand sometimes I need one that isclose. I can make up, figure out, explain, other technology toorganize and show my workfigure out patternscheck something of which I amunsurehelp me learn in new ways I use calculators, computers, andTechnologyI use what I know to help mefigure out something that I don’tknow, and I think about myanswers. When doing math, I see patterns,How do I know that I have beensuccessful?ReasoningWhat are themathematicalprocesses?How have I shown my successes?BLM 5–8.25: My Success with Mathematical Processes (continued)

BLM 5–8.26: Percent Circle

Multiplication A nnexing zeros When multiplying by a facto r of 10 (or a power of ten), ta king off the zeros to determine the product and adding them back on. for 4 x 700, think 4 x 7 is 28 and add two zeros to make 2800 5 Multiplication H alving and doubling Halving one factor and doubli

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