Mental Math - Prince Edward Island
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
Mental Math in the Elementary Mathematics Curriculum
Mental math in this guide refers to fact learning, mental computation, and computational estimation. The Atlantic Canada Mathematics Curriculum supports the acquisition of these skills through the development of thinking strategies across grade levels.
Mental math refers to fact learning, mental computation, and computational estimation. The Atlantic Canada Mathematics Curriculum supports the acquisition of these skills through the development of thinking strategies across grade levels.
Pre-Operational Skills Many children begin school with a limited understanding of number and number relationships. Counting skills, which are essential for ordering and comparing numbers, are an important component in the development of number sense. Counting on, counting back, concepts of more and less, and the ability to recognize patterned sets, all mark advances in children's development of number ideas.
Basic facts are mathematical operations for which some students may not be conceptually prepared.
Basic facts are mathematical operations for which some students may not be conceptually prepared. As a minimum, the following skills should be in place before children are expected to acquire basic facts.
? Students can immediately name the number that comes after a given number 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 without counting.
Mental Math ? Grade 2
1
? For numbers # 10 students can quickly name the number that is one-more, one-less; two-more, two-less. (the concept of less tends to be more problematic for children and is related to strategies for the subtraction facts)
Mental mathematics must be a consistent part of instruction in computation from primary through the elementary and middle grades.
2
Mental Math ? Grade 2
Curriculum Outcomes
Thinking Strategies
Grade 1
B7- use mental strategies to find sums to 18 and differences from 18 or less
B8- memorize simple addition and/or subtraction facts from among those for which the total is 10 or less
C5- use number patterns to help solve addition and subtraction sentences
P. 28 ? Doubles Facts for addition and
subtraction facts P. 36 ? Using patterns to learn the facts ? Commutative property (3+2 = 2+3)
Grade 2
B5- develop and apply strategies to learn addition and subtraction facts
B11- estimate the sum or difference of two 2-digit numbers
Fact learning is a mental exercise with an oral and/or visual prompt; the focus is oral, rather than paper-and pencil; drills should be short with immediate feedback over an extended period of time.
P. 22 ? Doubles plus 1 ? Make 10 ("bridging to 10") ? Two-apart facts; double in-between ? Subtraction as "think addition" ? Compensation ? Balancing for a constant difference
P. 30 (Estimation) ? Rounding both numbers to the
nearest 10 ? Round one number up and one
number down ? Front-end estimation
Grade 3
B11/12- mentally add and subtract two-digit and one-digit numbers, and rounded numbers.
B9- continue to estimate in addition and subtraction situations
B10- begin to estimate in multiplication and division situations
C3 - use and recognize the patterns in a multiplication table
P. 34 ? Make 10 ? Compatible numbers ("partner"
numbers) ? Front-end addition ? Back up through ten ("counting on") ? Compensation ? Balancing for a constant difference
P. 28 ? Commutative property for
multiplication (3x2 = 2x3) ? Division as "think multiplication" ? Helping facts
Mental Math ? Grade 2
3
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