Fractions
Fractions
Fractions are numbers that represent parts of a whole. They help us describe situations where something is divided into equal pieces. Fractions are…
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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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GeometryMetric Units of Length
The metric system is a decimal-based system of measurement used worldwide for its simplicity and consistency. One of its most common applications is…
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Currency MathMixed Addition and Subtraction with Currency
You have 50 cents (0.50),andyoufindadime(0.50),andyoufindadime(0.10). Then you buy a pencil for 30 cents ($0.30). How much do you have now?
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Basic ArithmeticOrdering and comparing
Order and compare whole numbers from smallest to largest using place-value comparison — clear rules and worked examples for grades 1-3.
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Three, four & five Digit NumbersPlace Value Up to 1000
Place value is the value of each digit in a number based on its position. In numbers up to 1000, digits can be in the ones, tens, hundreds, or thousands…
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Basic ArithmeticRounding
Rounding means adjusting a number to make it simpler while keeping its value close to the original. We round numbers when we don’t need exact precision –…
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Currency MathSubtracting Currency Math
Subtract small currency amounts in dollars and cents — making change, spending allowances, and worked examples that ground subtraction in actual currency counting.
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Subtracting Up to $100
Subtract dollar-and-cents amounts up to $100 with worked column-arithmetic examples — making change, returning items, and other real-world dollar-and-cents math.
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GeometryTiling
Tiling means covering a flat surface completely with tiles (or unit squares) without leaving any gaps or overlapping them. It’s like putting together a…
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Currency MathAdding Currency Math
Adding dollars and cents is an essential math skill we use every day. Whether you’re saving allowance, counting change, or making purchases, knowing how to add cents…
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Currency MathAdding Up to $1
Add small amounts to make a dollar — pennies, nickels, dimes and quarters with hands-on counting strategies and worked examples for K-2 learners.
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Basic ArithmeticAddition and Subtraction Word Problems
Addition and subtraction are two of the most essential math operations. Word problems help us apply these skills to real-life situations by presenting them…
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