Basic Arithmetic
Addition of Two and Three-Digit Numbers with Carrying
Carrying (or regrouping) is a fundamental math technique used when adding numbers where the sum of digits in a column equals 10 or more. The extra value is…
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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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Basic ArithmeticCounting to 10000
You already know how to count up to 100, but what about larger numbers like 1,000 or even 10,000? The good news is that the pattern stays consistent! Let’s…
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Currency MathCurrency Math Up to $1
Learning about currency is an important math skill! Let’s explore the four main denominations and how they work together.
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Basic ArithmeticEstimation and Rounding
Estimation is the process of making a close guess about a number, quantity, or measurement without counting or calculating exactly. It helps us quickly find…
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Basic ArithmeticEven and Odd Numbers
Numbers can be divided into two main categories: even and odd. Knowing the difference helps in math problems, counting, and everyday situations like sharing…
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Currency MathMaking $1 Using Different Amounts
Learning to make $1.00 with different combinations of pennies, nickels, dimes and quarters — an essential currency skill that builds place-value fluency and everyday confidence.
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Basic ArithmeticPlace Value for Multi-Digit Arithmetic
Place value made obvious — why "37" means three tens and seven ones, and how that one idea makes addition with carrying and subtraction with borrowing simple.
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Basic ArithmeticProperties of Addition
The Commutative Property of Addition states that changing the order of the numbers being added does not change the sum. In other words:
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Basic ArithmeticProperties of Subtraction
Subtraction has different rules compared to addition. While addition has properties like commutative, associative, and identity, subtraction behaves…
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Basic ArithmeticRepeated addition
Repeated addition is a fundamental math concept where the same number is added to itself multiple times. It serves as the foundation for understanding…
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Basic ArithmeticSubtraction of Two and Three-Digit Numbers with Borrowing
Subtraction is a fundamental arithmetic operation where we find the difference between two numbers. When subtracting larger digits from smaller ones within…
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Basic ArithmeticAddition of two digit numbers
Addition is one of the most fundamental math operations, and learning to add two-digit numbers confidently opens doors to more advanced math concepts. Let’s…
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