Addition Course

Lesson 1 • Concrete Models for Addition

Uses physical objects and drawings to represent addition before abstract symbols. Grounds understanding in tangible, manipulable representations.

Lesson 2 • Addition Symbols and Notation

Covers the plus sign, equals sign, and standard horizontal equation format. Students can read and write basic addition expressions correctly.

Lesson 3 • Numbers and Quantity Basics

Introduces whole numbers, counting, and one-to-one correspondence. Provides the numerical literacy required to perform addition accurately.

Lesson 1 • Making Ten Strategy

Introduces decomposing addends to form groups of ten for easier addition. Lays groundwork for carrying and multi-digit addition later.

Lesson 2 • Fact Fluency Practice

Consolidates all single-digit facts through timed and untimed retrieval practice. Students reach automatic recall across the full fact table.

Lesson 3 • Doubles and Near-Doubles

Draws on doubles facts as anchors for deriving near-double sums quickly. Strengthens fact fluency through pattern recognition.

Lesson 1 • Estimating Two-Digit Sums

Teaches rounding addends to estimate sums before calculating exactly. Develops number sense and the habit of checking reasonableness.

Lesson 2 • Regrouping Ones to Tens

Introduces carrying when the ones column sum exceeds nine. Students understand why regrouping works, not just how to execute it.

Lesson 3 • Place Value in Addition

Explains tens and ones positions and how they govern two-digit addition. Connects place value structure to the column addition procedure.

Lesson 4 • Mental Arithmetic with Two-Digit Numbers

Develops strategies for adding two-digit numbers without pencil and paper. Builds flexibility and speed for practical everyday calculations.

Lesson 1 • Hundreds Place Value

Extends place value knowledge to the hundreds position and its role in addition. Prepares students to manage a third column in written calculations.

Lesson 2 • Regrouping Across Multiple Columns

Addresses carrying from ones to tens and from tens to hundreds in one problem. Students manage cascading regrouping with accuracy and confidence.

Lesson 3 • Three-Digit Addition Without Regrouping

Applies column addition across three positions when no carrying is needed. Reinforces alignment and column-by-column procedure at greater scale.

Lesson 1 • Checking and Verifying Large Sums

Introduces reverse-addition and estimation as verification techniques for large sums. Develops the professional habit of confirming calculated results.

Lesson 2 • Commutative and Associative Properties

Formalises the rules that allow reordering and regrouping addends without changing the sum. Students use these properties to simplify complex additions.

Lesson 3 • Four-Digit Addition Procedures

Applies column addition and regrouping to four-digit numbers systematically. Builds procedural fluency at a scale common in practical contexts.

Lesson 4 • Adding Three or More Addends

Extends the algorithm to problems with three, four, or more addends in a column. Students manage column sums greater than nineteen with accuracy.

Lesson 1 • Adding Fractions with Unlike Denominators

Introduces finding a common denominator to add fractions with different denominators. Students convert, add, and simplify results accurately.

Lesson 2 • Fraction Concepts for Addition

Reviews numerator, denominator, and the meaning of equal parts before adding fractions. Ensures conceptual readiness for fraction addition procedures.

Lesson 3 • Adding Fractions with Like Denominators

Covers adding fractions that share a common denominator by summing numerators. Builds the simplest fraction addition case before tackling unlike denominators.

Lesson 4 • Adding Decimals with Alignment

Teaches decimal-point alignment as the critical step before adding decimal numbers. Students add decimals of varying lengths without errors from misalignment.

Lesson 1 • Multi-Step Addition Problems

Addresses problems requiring two or more sequential addition operations. Students plan solution steps before calculating to avoid procedural errors.

Lesson 2 • Addition in Tables and Charts

Applies addition to data presented in rows, columns, and simple tables. Students sum across categories and verify totals using cross-checking.

Lesson 3 • Reasonableness and Answer Validation

Develops the habit of evaluating whether a computed answer makes sense in context. Students apply estimation and unit checks to validate solutions.

Lesson 4 • Setting Up Addition Equations

Bridges the gap between a word problem narrative and a written equation. Students practise translating language into correct mathematical expressions.

Lesson 1 • Strategic Method Selection

Teaches students to evaluate problem features and choose the most appropriate addition method. Develops metacognitive awareness of when each strategy excels.

Lesson 2 • Column Addition with Mixed Number Types

Combines whole numbers, decimals, and fractions within a single addition problem. Students manage mixed formats by converting to a common representation.

Lesson 3 • Efficiency and Error Reduction Habits

Establishes systematic work habits that minimise addition errors in high-stakes tasks. Students apply structured checking routines as a professional standard.

Lesson 4 • Advanced Mental Arithmetic Techniques

Covers bridging through tens, hundreds, and thousands for rapid mental addition. Students choose and apply the most efficient strategy for each problem type.