The Landmark Method for Teaching Arithmetic

Introduction

Part I: Teaching Methods

Chapter 1: Principles of Good Teaching

• Move From the Concrete to the Abstract
• Microunit Instruction
• Spiral Back
• Put Multiple Modalities to Work
• Reflect Learning Styles
• Formal Testing

Chapter 2: Math as a Language

• Complete Sentences
• The Grammar of Math Sentences

Chapter 3: Readiness Skills for Multidigit Computation

• Group Theory and Large Number Comprehension
• Visual Clustering
• Bones
• Establishing Icons for Familiar Quantities
• Woodmark Numeric Icons
• Subtraction Using Woodmark Icons
• Multiplication Using Woodmark Icons
• Place Value
• Estimation and Comparison
• Base (Ten) Ball
• Big Number
• Handwriting Skills
• Alignment of Numbers
• Vertical Alignment within Multidigit Computation
• Graph Paper Versus Vertical or Horizontal Lines

Part II: Number Facts

Chapter 4: Strategies for Teaching Math Facts

• Learn the Basic Facts
• Teach Facts Efficiently
• Use Existing Images to Define Facts
• Fact Twister
• Fact Mosaics
• Rhythmic and Tonal Patterns
• Help All Students to Respond
• Pattern Recognition: Append Structure to the Guessing Game
• Correct Paired Associations
• Success-Oriented Rehearsal Strategies
• Patterning Versus Rote Memorization

Chapter 5: Order of Multiplication Fact Instruction

• The Cadenced Facts: One, Two, Five, and Ten Families
• Motor Memory
• Linking Cadenced Facts to Fact Sentences
• Geoboards
• Semantic Memory Associations
• The Two Family
• The Divisibility Rule for Two
• Divisibility Rule Fish
• The Five Family
• The Ten Family
• Another Column on the 1-100 Chart
• Board Games
• Rule Oriented Families
• The One and Zero Families
• The Nine Family
• The Nine Times Finger Calculator
• The Three Family
• Finding Higher Facts By Adding Combinations of Lower Ones
• The Commutative and Associative Properties
• The Six Family
• Six Family Patterns
• Finger Calculation of the Six Family
• Use Madsion Avenue's Selling Power
• Save Those Six-Pack Rings
• The Four Family
• The Divisibility Rule for Four
• The Last Two Families: Seven and EightsPart III: Multidigit Computation

Chapter 6: Multidigit Multiplication

• Multiplying Multidigit Numbers
• If Billy Told You to Add a Zero to the Second Row, Would You Do It?
• "Eye" Remember the Zero!
• The Place-Holding Icon
• Get to Know the Area

Chapter 7: Multidigit Division

• Teaching Long Division
• The Division Icon and Microunited Instruction
• Compare
• Divide
• Multiply
• Subtract
• Check Subtraction
• Bring Down
• Repeat the Process
• What About the Remainder?
• Ladder Charts
• The Touch Method
• Motor Memory
• Using the Division Icon in Conjunction with the Problem

Part IV: Math in Context

Chapter 8: Applications

• The Real World
• Story Problems
• Scaffolding
• Word Problems
• Visualization
• Visual Memory

Appendix