Mental Math - Prince Edward Island

Mental Math

Fact Learning Mental Computation

Estimation

Grade 6 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

Fact Learning - Addition, Subtraction, Multiplication and Division . . 19 Reviewing Facts and Fact-Learning Strategies . . . . . . . . . . . . . . . 19

Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Multiplication and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Multiplication Facts With Products to 81 . . . . . . . . . . . . . . . . 23 Division Facts With Products to 81 . . . . . . . . . . . . . . . . . . . . 24 Mental Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Mental Computation - Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Front-End Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Break Up and Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Finding Compatibles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Make 10s, 100s or 1000s . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Mental Computation - Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . 32 Back Down Through 10/100/1000 . . . . . . . . . . . . . . . . . . . . . 32 Up Through 10/100/1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Balancing For a Constant Difference . . . . . . . . . . . . . . . . . . . 35 Break Up and Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Mental Computation - Multiplication and Division . . . . . . . . . . . . . . 38 Multiplying and Dividing by 10, 100 and 1000 Using a Place-Value-Change Strategy . . . . . . . . . . . . . . . . 38 Multiplying by 0.1, 0.01 and 0.001 Using a Place-Value-Change Strategy . . . . . . . . . . . . . . . . 39 Dividing by 0.1, 0.01 and 0.001 Using a Place-Value-Change Strategy . . . . . . . . . . . . . . . . 40 Front End Multiplication - The Distributive Principle . . . . . . . . 42 Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Finding Compatible Factors - Associatve Property . . . . . . . . 44 Halving and Doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Using Division Facts for Tens, Hundreds and Thousands . . . 45 Partitioning the Dividend . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Estimation - Addition, Subtraction, Multiplication and Division . . . . 50 Rounding in Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . 51 Rounding in Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Rounding in Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Appendixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Thinking Strategies in Mental Math . . . . . . . . . . . . . . . . . . . . . . . . 58 Scope and Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

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 6

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