数学加减法方法省公共课一等奖全国赛课获奖课件.pptx

1Operations and Whole Numbers:Developing MeaninglModel by beginning with word problemsReal-world setting or problemModelsConcretePictorialMentalLanguageMathematical World(symbols)第1页2Understanding Addition and SubtractionlThere are four types of addition and subtraction problemsJoinactionSeparateactionPart-part-whole relationships of quantitiesComparerelationships of quantities第2页3Eleven Addition and Subtraction Problem TypeslJoin Result Unknown Peter had 4 cookies.Erika gave him 7 more cookies.How many cookies does Peter have now?Change UnknownPeter had 4 cookies.Erika gave him some more cookies.Now Peter has 11 cookies.How many cookies did Erika give him?Start UnknownPeter had some cookies.Erika gave him 7 more cookies.Now Peter has 11 cookies.How many cookies did Peter have to start with?第3页4Separate Result Unknown Peter had 11 cookies.He gave 7 cookies to Erika.How many cookies does Peter have now?Change UnknownPeter had 11 cookies.He gave some cookies to Erika.Now Peter has 4 cookies.How many cookies did Peter give to Erika?Start UnknownPeter had some cookies.He gave 7 cookies to Erika.Now Peter has 4 cookies.How many cookies did Peter have to start with?第4页5Part-Part-Whole Whole Unknown Peter had some cookies.Four are chocolate chip cookies and 7 are peanut butter cookies.How many cookies does Peter have?Part UnknownPeter has 11 cookies.Four are chocolate chip cookies and the rest are peanut butter cookies.How many peanut butter cookies does Peter have?第5页6Compare Difference UnknownPeter has 11 cookies and Erika has 7 cookies.How many more cookies does Peter have than Erika?Larger UnknownErika has 7 cookies.Peter has 4 more cookies than Erika.How many cookies does Peter have?Smaller UnknownPeter has 11 cookies.Peter has 4 more cookies than Erika.How many cookies does Erika have?第6页7Using Models to Solve Addition and Subtraction ProblemslDirect modeling refers to the process of children using concrete materials to exactly represent the problem as it is written.lJoin and Separate(problems involving action)work best with Direct ModelinglFor example,John had 4 cookies.Jennifer gave him 7 more cookies.How many cookies does John have?(join)第7页8Direct Modeling for Join and SeparatelDavid had 10 cookies.He gave 7 cookies to Sarah.How many cookies does David have now?(separate)lBrian had 10 cookies.He gave some cookies to Tina.Now Brian has 4 cookies.How many cookies did Brian give to Tina?(separate)第8页9Modeling part-part-whole and compare ProblemslMichelle had 7 cookies and Katie had 3 cookies.How many more cookies does Michelle have than Katie?(compare)lMeghan has some cookies.Four are chocolate chip cookies and 7 are peanut butter cookies.How many cookies does Meghan have?(part-part-whole)第9页10Writing Number Sentences for Addition and SubtractionlOnce the children have had many experiences modeling and talking about real life problems,the teacher should encourage children to write mathematical symbols for problems.lA number sentence could look like thisl2+5=?Or 2+?=7第10页11Addition AlgorithmslThe Partial-Sums Method is used to find sums mentally or with paper and pencil.lThe Column-Addition Method can be used to find sums with paper and pencil,but is not a good method for finding sums mentally.lThe Short Method adds one column from right to left without displaying the partial sums(the way most adults learned how to add)lThe Opposite-Change Rule can be used to subtract a number from one addend,and add the same number to the other addend,the sum is the same.第11页12Partial-Sums MethodlExample:348+177=?100s 10s1s 3 48+1 7 7 4 0 0 Add the 100s(300+100)1 1 0 Add the 10s (40+70)1 5 Add the 1s (8+7)5 2 5 Add the partial sums(400+110+15)第12页13Column Addition MethodlExample:359+298=?l100s 10s 1sl 3 5 9l+2 9 8l 5 14 17 Add the numbers in each columnl 5 15 7 Adjust the 1s and 10s:17 ones=1 ten and 7 onesl Trade the 1 ten into the tens column.l 6 5 7 Adjust the 10s and 100s:15 tens=1 hundred and 5 tens.Trade the 1 hundred into the hundreds column.第13页14A Short Methodl248+187=?l 1 1l 2 4 8l+1 8 7l 4 3 5l8 ones+7 ones=15 ones=1 ten+5 onesl1 ten+4 tens+8 tens=13 tens=1 hundred+3 tensl1 hundred+2 hundreds+1 hundred=4 hundreds第14页15The Opposite-Change RulelAddends are numbers that are added.l In 8+4=12,the numbers 8 and 4 are addends.lIf you subtract a number from one addend,and add the same number to the other addend,the sum is the same.You can use this rule to make a problem easier by changing either of the addends to a number that has zero in the ones place.lOne way:Add and subtractl 59 (add 1)60l+26(subtract 1)+25 l 85第15页16The Opposite-Change RulelAnother way.Subtract and add 4.l 59 (subtract 4)55l+26 (add 4)+30l 85第16页17Subtraction AlgorithmslThe Trade-First Subtraction Method is similar to the method that most adults were taughtlLeft-to-Right Subtraction Method lPartial-Differences MethodlSame-Change Rule第17页18The Trade-First MethodlIf each digit in the top number is greater than or equal to the digit below it,subtract separately in each column.lIf any digit in the top number is less than the digit below it,adjust the top number before doing any subtracting.Adjust the top number by“trading”第18页19The Trade-First Method ExamplelSubtract 275 from 463 using the trade-first methodl100s 10s 1s l 4 6 3l-2 7 5lLook at the 1s place.You cannot subtract 5 ones from 3 ones第19页20The Trade-First Method Examplel100s 10s 1s Subtract 463-275l 5 13l 4 6 3 l-2 7 5lSo trade 1 ten for ten ones.Look at the tens place.You cannot remove 7 tens from 5 tens.第20页21The Trade-First Method ExamplelSubtract 463 275l100s 10s 1sl 15l 3 5 13l 4 6 3l-2 7 5l 1 8 8lSo trade 1 hundred for 10 tens.Now subtract in each column.第21页22Left to Right Subtraction MethodlStarting at the left,subtract column by column.l 9 3 2 l-3 5 6lSubtract the 100s 932l -300lSubtract the 10s 632l -50lSubtract the 1s 582l -6l 576第22页23Partial-Differences MethodlSubtract from left to right,one column at a time.Always subtract the larger number from the smaller number.lIf the smaller number is on the bottom,the difference is added to the answer.lIf the smaller number is on top,the difference is subtracted from the number.第23页24Partial-Differences Method Examplel 8 4 6l -3 6 3lSubtract the 100s 800 300 +5 0 0 lSubtract the 10s 60 40 -2 0lSubtract the 1s 6-3 +3 4 8 3第24页25Same-Change Rule Examplel92 36=?lOne way add 4l 92 (add 4)96l-36 (add 4)40l 56lAnother way subtract 6l 92 (subtract 6)86l-36 (subtract 6)-30l 56第25页26Multiplication AlgorithmslPartial-Products MethodslLattice Method第26页27Partial-Products MethodlYou must keep track of the place value of each digit.Write 1s 10s 100s above the columns.l4*236=?lThink of 236 as 200+30+6lMultiply each part of 236 by 4第27页28Partial Products Methodl4*236=?100s 10s 1sl 2 3 6l *4l 4*200 8 0 0l 4*30 1 2 0l 4*6 0 2 4 l Add these three 9 4 4l partial products第28页29Lattice Methodl6*815=?lThe box with cells and diagonals is called a lattice.l 8 1 54 80 63 06第29页30Types of Multiplication and Division ProblemslEqual GroupinglPartitive Division Size of group is unknownlExample:lTwenty four apples need to be placed into eight paper bags.How many apples will you put in each bag if you want the same number in each bag?第30页31Types of Multiplication and Division ProblemslRatelPartitive Divison size of group is unknownlExample:lOn the Mitchells trip to NYC,they drove 400 miles and used 12 gallons of gasoline.How many miles per gallon did they average?第31页32Types of Multiplication and Division ProblemslNumber of equal groups is unknownlQuotative DivisionlExample:lI have 24 apples.How many paper bags will I be able to fill if I put 3 apples in each bag?第32页33Types of Multiplication and Division ProblemslNumber of equal groups is unknownlQuotative DivisionlExample:lJasmine spent$100 on some new CDs.Each CD cost$20.How many did she buy?第33页34Partial Quotients Method lThe Partial Quotients Method,the Everyday Mathematics focus algorithm for division,might be described as successive approximation.It is suggested that a pupil will find it helpful to prepare first a table of some easy multiples of the divisor;say twice and five times the divisor.Then we work up towards the answer from below.In the example at right,1220 divided by 16,we may have made a note first that 2*16=32 and 5*16=80.Then we work up towards 1220.50*16=800 subtract from 1220,leaves 420;20*16=320;etc.第34页35The End第35页