Mental Math Grade 4 Teacher's Guide
Mental Math
Fact Learning Mental Computation
Estimation
Grade 4 Teacher's Guide
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2007
Table of Contents
Mental 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 . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Up 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
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