Mental Math
Mental Math
Fact Learning Mental Computation
Estimation
Grade 2 Teacher's Guide
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2008
Table of Contents
Mental Math in the Elementary Mathematics Curriculum . . . . . . . . . . . . . 1 Definitions and Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Introducing Thinking Strategies to Students . . . . . . . . . . . . . . . . . . . . . . . 8 Practice and Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Response Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Timed Tests of Basic Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Parents and Guardians: Partners in Developing Mental Math Skills . . . . 13 Pre-operational Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Patterned Set Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Part-Part-Whole Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Ten-Frame Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Other Number Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 One More/One Less and Two More/Two Less . . . . . . . . . . . . . . . 18 Next Number and Counting On and Back . . . . . . . . . . . . . . . . . . . 19 Fact Learning - Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Reviewing Addition Facts and Fact Learning Strategies . . . . . . . . . . . . . 23 Doubles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Plus 1 Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Plus 2, Plus 3 Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Using Five-Frames and Ten-Frames . . . . . . . . . . . . . . . . . . . . . . . 27
Model Numbers on a Five-Frame . . . . . . . . . . . . . . . . . . . . . 27 Visualize Combinations on a Five-Frame . . . . . . . . . . . . . . . 28 Random Numbers on a Five-Frame . . . . . . . . . . . . . . . . . . . 28 Ten-Frame Flash Cards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Ten-Frame Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Empty Ten-Frame Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 New Strategies for Addition Fact Learning Introduced in Grade 2 . . . . . 30 Near Doubles (1-Apart Facts) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2-Apart Facts (Double In-Between Facts) . . . . . . . . . . . . . . . . . . . 30 Plus or Minus 0 (No Change Facts) . . . . . . . . . . . . . . . . . . . . . . . . 31 Relationships for Numbers 10-20 . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Developing the Concept With 2-Part Mats . . . . . . . . . . . . . . 32 Developing the Concept With Ten-Frames . . . . . . . . . . . . . . 33 Reinforcing the Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Make Ten Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Make Ten Flash Cards (example) . . . . . . . . . . . . . . . . . . . . . 35 Addition Facts With Sums to18 . . . . . . . . . . . . . . . . . . . . . . . 37
Fact Learning ? Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Subtraction as "Think Addition" . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Ten-Frame Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Other Ways to Think About Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . 39 Up Through 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Back Down Through 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Subtraction Facts With Minuends to 18 . . . . . . . . . . . . . . . . . . . . . 41
Mental Computation - Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Addition Facts Extended to 2-Digit Numbers (New) . . . . . . . . . . . . 45 Front-End Addition (New) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Finding Compatibles (New) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Compensation (New) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Mental Computation - Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Using "Think Addition" in Subtraction (Extension) . . . . . . . . . . . . . 49
Estimation - Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Rounding in Addition and Subtraction (New) . . . . . . . . . . . . . . . . . 54
Appendixes Thinking Strategies in Mental Math . . . . . . . . . . . . . . . . . . . . . . . . 57 Scope and Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
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