Mental math grade 5 003 - StFX

Mental Math

Mental Computation

Grade 5

Draft ¡ª September 2006

MENTAL MATH

Acknowledgements

The Department of Education gratefully acknowledges the contributions of the following individuals to the

preparation of the Mental Math booklets:

Sharon Boudreau¡ªCape Breton-Victoria Regional School Board

Anne Boyd¡ªStrait Regional School Board

Estella Clayton¡ªHalifax Regional School Board (Retired)

Jane Chisholm¡ªTri-County Regional School Board

Paul Dennis¡ªChignecto-Central Regional School Board

Robin Harris¡ªHalifax Regional School Board

Keith Jordan¡ªStrait Regional School Board

Donna Karsten¡ªNova Scotia Department of Education

Ken MacInnis¡ªHalifax Regional School Board (Retired)

Ron MacLean¡ªCape Breton-Victoria Regional School Board

Sharon McCready¡ªNova Scotia Department of Education

David McKillop¡ªChignecto-Central Regional School Board

Mary Osborne¡ªHalifax Regional School Board (Retired)

Sherene Sharpe¡ªSouth Shore Regional School Board

Martha Stewart¡ªAnnapolis Valley Regional School Board

Susan Wilkie¡ªHalifax Regional School Board

MENTAL COMPUTATION GRADE 5 ¡ª DRAFT SEPTEMBER 2006

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MENTAL MATH

Contents

Introduction....................................................................................................................................................1

Definitions......................................................................................................................................1

Rationale.........................................................................................................................................1

The Implementation of Mental Computational Strategies..............................................................................3

General Approach...........................................................................................................................3

Introducing a Strategy ....................................................................................................................3

Reinforcement ................................................................................................................................3

Assessment ......................................................................................................................................3

Response Time ...............................................................................................................................4

A. Addition ¡ª Fact Learning .........................................................................................................................5

Facts and the Fact Learning Strategies ............................................................................................5

B. Addition ¡ª Mental Calculations ...............................................................................................................7

Quick Addition ¡ª No Regrouping................................................................................................7

Front End Addition ........................................................................................................................8

Finding Compatibles ......................................................................................................................8

Break Up and Bridge ......................................................................................................................9

Compensation ............................................................................................................................. 10

Make 10, 100, or 1000 ................................................................................................................ 11

C. Subtraction ¡ª Fact Learning.................................................................................................................. 12

Review Subtraction Facts to 18 and the Fact Learning Strategies ................................................ 12

D. Subtraction ¡ª Mental Calculations ....................................................................................................... 12

Using Subtraction Facts for 10s, 100s, 1000s, and 10 000s......................................................... 12

Quick Subtraction ....................................................................................................................... 12

Back Through 10/100 ................................................................................................................. 13

Counting on to Subtract.............................................................................................................. 14

Compensation ............................................................................................................................. 15

Balancing For a Constant Difference ........................................................................................... 16

Break Up and Bridge ................................................................................................................... 17

E. Multiplication ¡ª Fact Learning.............................................................................................................. 19

Multiplication Fact Learning Strategies ....................................................................................... 19

F. Multiplication ¡ª Mental Calculations.................................................................................................... 25

Quick Multiplication ¡ª No Regrouping .................................................................................... 25

Division Using the Think Multiplication Strategy ...................................................................... 25

Using Multiplication Facts for Tens, Hundreds, and Thousands ................................................ 25

Division Where the Divisor is a Multiple of 10 ........................................................................... 26

Multiplying by 10, 100, and 1000............................................................................................... 26

Dividing by 0.1, 0.01, and 0.00) ................................................................................................. 27

Multiplying by 0.1, 0.01, and 0.001............................................................................................ 29

Dividing by 10, 100, and 1000.................................................................................................... 30

Front End Multiplication or the Distributive Property................................................................ 30

Compensation ............................................................................................................................. 31

Finding Compatible Factors ........................................................................................................ 32

Open Frames in Addition, Subtraction, Multiplication, and Division ........................................ 32

E. Addition, Subtraction, Multiplication, and Division ¡ª

Computational Estimation........................................................................................................................... 34

Rounding..................................................................................................................................... 34

Rounding with ¡°Fives¡± ................................................................................................................ 35

Front End .................................................................................................................................... 36

Adjusted Front End ..................................................................................................................... 38

Clustering of Near Compatibles For Addition and Mixed Computation .................................... 41

MENTAL COMPUTATION GRADE 5 ¡ª DRAFT SEPTEMBER 2006

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