Multiplication
Two-digit multiplication
The purpose of two-digit multiplication is to solve more complex problems and to build on multiplication facts, thereby developing a strong understanding of…
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Author
Professor Orion Hawthorne
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Professor Orion Hawthorne , Lead lesson writer · K-8 math curriculum specialist
Lead lesson writer for Math Lessons. Former classroom teacher and math-curriculum specialist with a focus on making foundational K-8 math concepts click for first-time learners.
Foundational arithmetic Place value & multi-digit operations Fractions & equivalence Geometry & measurement Word-problem strategies Pre-K & Kindergarten math readiness
Professor Orion Hawthorne is the lead lesson writer at Math Lessons, responsible for the day-to-day structure and clarity of every lesson the site publishes. The "Professor" honorific is informal — it reflects two decades of working with elementary and middle-school learners as a teacher, tutor and curriculum-design consultant rather than a tenured academic appointment. The voice on the page is one human with a deep affection for the subject and a habit of asking "but does it actually make sense?" of every explanation before it ships.
Orion's lessons follow a deliberate template. Each one opens with a plain-English definition that names the concept and makes its purpose obvious — addition is combining quantities to find a sum, division is sharing or grouping. The worked example always grounds the abstraction in something a learner can hold or imagine: apples, blocks, tiles, a number line. Practice problems then escalate from a single-step calculation to multi-step problems and word problems, with full reasoning shown for each, because the goal is for the reader to walk away knowing *why* the answer is right, not merely *what* it is.
Beyond the lessons themselves, Orion is responsible for keeping the site's topical structure coherent. New lessons are written into the existing pillar — Pre-K & Kindergarten, Basic Arithmetic, Multiplication, Division, Fractions, Geometry, Larger Numbers, Currency Math, Financial Math — and refer back to prerequisite lessons inline so a reader who lands on "long division" can trace the path back to "skip counting" or "subtraction with borrowing" if they need to.
When Orion is not writing lessons, the time is spent reviewing reader questions submitted through the contact page (every one is read), updating older lessons whose worked examples could be clearer, and sketching the next batch of topics — currently: place-value beyond 100,000, decimal arithmetic, and the pre-algebra bridge into solving for unknowns. If a topic feels underserved, the most likely path to seeing it covered is to send a note saying so.
Posts by Professor Orion Hawthorne
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DivisionUnderstand division
Understand division through the sharing model and the grouping model — the two real-world meanings of dividing that make every long-division step feel obvious.
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MultiplicationUnderstand multiplication
Understand multiplication as repeated addition and the rectangular-array model — the two mental pictures every later technique, including times tables and long multiplication, depends on.
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FractionsUnderstanding Fractions
Understand fractions as quantities, not symbols — pizza slices, chocolate bars and number lines first, then the notation that shorthand them. The right entry point for grades 2-4.
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Pre-K & KindergartenWeight: what weighs more or less in a balance scale
Compare weights using a balance scale — heavier, lighter and equal in a Pre-K lesson that introduces measurement through hands-on examples.
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Currency MathAdding Up to $100
Add dollar-and-cents amounts up to $100 with worked column-arithmetic examples — bills, cents, and the decimal point made simple for grades 2-4.
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Three, four & five Digit NumbersAddition and Subtraction of Three-Digit Numbers
Add and subtract three-digit numbers with regrouping and borrowing — the foundational multi-digit arithmetic lesson that makes the standard column algorithm intuitive.
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Three, four & five Digit NumbersAddition: four or five digits
Addition of four- and five-digit numbers involves combining numbers ranging from 1,000 to 99,999. This process follows the same fundamental principles as…
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GeometryArea and tiling
Area is the amount of space inside a shape. It tells us how much surface the shape covers. Think of it like how many tiles would fit on a floor or how much…
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Currency Math Up to $100
Count, add and subtract dollars and cents up to $100 — bills, cents, and decimal-point arithmetic explained with full worked examples for everyday situations.
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Basic ArithmeticEstimate differences
Estimating differences means finding an approximate answer to a subtraction problem by rounding numbers first. This valuable skill helps students:
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Basic ArithmeticEstimate sums
stimating sums means finding an approximate total by rounding numbers before adding them. This math skill helps you:
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