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Mental Math

Mental MathFact LearningMental ComputationEstimationGrade 4 Teacher s Guideb =m ~ ml=_ =OMMM` ~ I=mb=`N^=TkUq W=EVMOF=PSU=QSMMc~ W=EVMOF=PSU=QSOO K K K ~L 2007 Table of ContentsMental Math in the Elementary Mathematics Curriculum ..1 Definitions and Connections ..6 Rationale ..7 Teaching Mental Computation Strategies ..7 Introducing thinking Strategies to Students ..8 Practice and Reinforcement ..10 Response Time ..11 Struggling Students and Differentiated Instruction ..12 Combined Grade Classrooms ..13 Assessment ..14 Timed Tests of Basic Facts ..14 Parents and Guardians: Partners in Developing Mental Math Skills ..15 Fact Learning ..17 Reviewing Addition Facts and Fact-Learning Strategies ..19 Reviewing Subtraction Facts and Fact-Learning Strategies.

Computational estimation refers to using strategies to get approximate answers by doing calculations mentally. Students develop and use thinking strategies to recall answers to basic facts. These are the foundation for the development of other mental calculation …

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Transcription of Mental Math

1 Mental MathFact LearningMental ComputationEstimationGrade 4 Teacher s Guideb =m ~ ml=_ =OMMM` ~ I=mb=`N^=TkUq W=EVMOF=PSU=QSMMc~ W=EVMOF=PSU=QSOO K K K ~L 2007 Table of ContentsMental Math in the Elementary Mathematics Curriculum ..1 Definitions and Connections ..6 Rationale ..7 Teaching Mental Computation Strategies ..7 Introducing thinking Strategies to Students ..8 Practice and Reinforcement ..10 Response Time ..11 Struggling Students and Differentiated Instruction ..12 Combined Grade Classrooms ..13 Assessment ..14 Timed Tests of Basic Facts ..14 Parents and Guardians: Partners in Developing Mental Math Skills ..15 Fact Learning ..17 Reviewing Addition Facts and Fact-Learning Strategies ..19 Reviewing Subtraction Facts and Fact-Learning Strategies.

2 21 Multiplication Fact-Learning Strategies ..22 Multiplication Facts With Products to 81 ..27 Mental Computation ..29 Front-end Addition ..31 Break Up and Bridge ..33 Finding Compatibles ..34 Compensation ..36 Make 10s, 100s or 1000s ..37 Mental Computation Subtraction ..39 Using Subtraction Facts for 10s, 100s and 1000s ..39 Back Down Through 10/100 ..41Up Through 10/100 ..42 Compensation ..43 Break Up and Bridge ..44 Mental Computation Multiplication ..45 Multiplication by 10 and 100 ..45 Estimation Addition and Subtraction ..49 Rounding ..50 Adjusted Front-end ..53 Near Compatibles ..54 Appendixes ..55 thinking Strategies in Mental Math ..57 Scope and Sequence ..61 Mental Math Grade 41 Mental Math in the Elementary Mathematics CurriculumMental math in this guide refers to fact learning, Mental computation, andcomputational estimation.

3 The Atlantic Canada Mathematics Curriculumsupports the acquisition of these skills through the development of thinkingstrategies across grade math refers to fact learning, Mental computation, andcomputational estimation. The Atlantic Canada MathematicsCurriculum supports the acquisition of these skills through thedevelopment of thinking strategies across grade Skills Many children begin school with a limited understanding of number andnumber relationships. Counting skills, which are essential for ordering andcomparing numbers, are an important component in the development ofnumber sense. Counting on, counting back, concepts of more and less,and the ability to recognize patterned sets, all mark advances in children sdevelopment of number facts are mathematical operations for which some studentsmay not be conceptually facts are mathematical operations for which some students may notbe conceptually prepared.

4 As a minimum, the following skills should be inplace before children are expected to acquire basic facts. Students can immediately name the number that comes after a givennumber from 0-9, or before a given number from 2-10. When shown a familiar arrangement of dots # 10 on ten frames, dice,or dot cards, students can quickly identify the number withoutcounting. 2 Mental Math Grade 4 For numbers # 10 students can quickly name the number that isone-more, one-less; two-more, two-less. (the concept of less tends tobe more problematic for children and is related to strategies for thesubtraction facts) Mental mathematics must be a consistent partof instruction in computation from primarythrough the elementary and middle Math Grade 43 Curriculum OutcomesThinking StrategiesGrade 1B7-use Mental strategies to find sumsto 18 and differences from 18 orlessB8-memorize simple addition and/orsubtraction facts from among thosefor which the total is 10 or lessC5-use number patterns to help solveaddition and subtraction sentencesP.

5 28 Doubles Facts for addition andsubtraction factsP. 36 Using patterns to learn the facts Commutative property (3+2 = 2+3)Grade 2B5-develop and apply strategies tolearn addition and subtraction factsB11-estimate the sum or differenceof two 2-digit numbersFact learning is a mentalexercise with an oral and/orvisual prompt; the focus isoral, rather than paper-andpencil; drills should be shortwith immediate feedback over anextended period of 22 Doubles plus 1 Make 10 ( bridging to 10 ) Two-apart facts; double in-between Subtraction as think addition Compensation Balancing for a constant differenceP. 30 (Estimation) Rounding both numbers to thenearest 10 Round one number up and onenumber down Front-end estimationGrade 3B11/12- mentally add and subtracttwo-digit and one-digitnumbers, and roundednumbers.

6 B9- continue to estimate in addition andsubtraction situationsB10-begin to estimate in multiplication and division situationsC3 - use and recognize the patterns in amultiplication tableP. 34 Make 10 Compatible numbers ( partner numbers) Front-end addition Back up through ten ( counting on ) Compensation Balancing for a constant differenceP. 28 Commutative property formultiplication (3x2 = 2x3) Division as think multiplication Helping facts4 Mental Math Grade 4 Curriculum OutcomesThinking StrategiesGrade 4B9 - demonstrate a knowledge of themultiplication facts to 9 x 9B14 - estimate the product or quotient of2- or 3-digit numbers and singledigit numbersB15 - mentally solve appropriateaddition and subtractioncomputationsB16 - mentally multiply 2-digit numbersby 10 or 100C2 - apply the pattern identified whenmultiplying by increasing powersof 10P.

7 32 Doubles Clock-facts for 5 s Patterns for 9 s Helping factsP. 36 (Estimation) Rounding Front-end Clustering of CompatiblesP. 38 Compatibles for divisionP. 40 Front-end addition Compensation Up through 100 (counting on) Back down through 100 (countingback) Compatible numbers Place-value-change strategy formentally multiplying by 10, 100 Mental Math Grade 45 Curriculum OutcomesThinking StrategiesGrade 5B10- estimate sums and differencesinvolving decimals to thousandthsB11- estimate products and quotients oftwo whole numbersB12- estimate products and quotients ofdecimal numbers by single-digitwhole numbersB15- multiply whole numbers by , , and mentallyC2- recognize and explain the patternin dividing by 10, 100, 1000 and inmultiplying by , and perform appropriate mentalmultiplications with facilityBy grade 5, students shouldpossess a variety of strategiesto compute mentally.

8 It isimportant to recognize that thesestrategies develop and improveover the years with 40 to 41 (Estimation) Rounding one up, one down Looking for compatibles that makeapproximately 10, 100, 1000 Front-end P. 44 Place-value-change strategy formentally multiplying by 10, 100, 1000 Halve-double strategy formultiplication Front-end multiplication CompensationP. 46 to 50 Place-value-change strategy formentally dividing by 10, 100, 1000 Place-value-change strategy formentally multiplying by , , 6B9-estimate products and quotientsinvolving whole numbers only,whole numbers and decimals, anddecimals onlyB10-divide numbers by , , mentallyC2-use patterns to explore division , , and calculate sums and differences inrelevant contexts using the mostappropriate methodP.

9 40 (Estimation) Rounding one up, one down formultiplication Front-end method for multiplicationand divisionP. 42 and 50 Place-value-change strategy formentally dividing by , , 44 Compensation in multiplication Front-endStudents should perform Mental computations with facility usingstrategies outlined in the Mental Math Math Grade 4 Definitions and ConnectionsFact learning refers to the acquisition of the 100 number facts relating tothe single digits 0-9 in each of the four operations. Mastery is defined by acorrect response in 3 seconds or less. Mental computation refers to using strategies to get exact answers bydoing most of the calculations in one s head. Depending on the number ofsteps involved, the process may be assisted by quick jottings of sub-stepsto support short term estimation refers to using strategies to get approximateanswers by doing calculations develop and use thinking strategies to recall answers to basicfacts.

10 These are the foundation for the development of other mentalcalculation strategies. When facts are automatic, students are no longerusing strategies to retrieve them from facts and Mental calculation strategies are the foundations forestimation. Attempts at estimation are often thwarted by the lack ofknowledge of the related facts and Mental math Math Grade 47 RationaleIn modern society, the development of Mental computation skills needs tobe a goal of any mathematical program for two important reasons. First ofall, in their day-to-day activities, most people s calculation needs can bemet by having well developed Mental computational processes. Secondly,while technology has replaced paper-and-pencil as the major tool forcomplex computations, people still need to have well developed mentalstrategies to be alert to the reasonableness of answers generated modern society, the development of Mental computation skillsneeds to be a goal of any mathematics being the foundation of the development of number andoperation sense, fact learning is critical to the overall development ofmathematics.


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