Pre-K & Kindergarten
Operations and Algebraic Thinking – Sum
Sums and the early-algebra idea of an unknown addend — a Pre-K and Kindergarten lesson on combining quantities and finding what is missing.
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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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FractionsOrder fractions
To order fractions: we start by determining which fraction is smaller and which is larger. We follow this process to determine the sequence we want.
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GeometryParallel, Perpendicular, and Intersecting Lines
Lines are extremely significant to Geometry; the relationships between lines allow us to understand the relationship between shapes, Structural Design…
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GeometryPerimeter
The perimeter is the distance around the outside of a two-dimensional shape. This distance is the length of the shape’s boundary. We measure the perimeter…
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Pre-K & KindergartenPre-Kindergarten Geometry: Matching Objects, Shapes, and Patterns
Young learners’ development begins with matching skills in Mathematics. Matching helps children make sense of what they see, hence building their visual…
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GeometryQuadrilaterals
The complete elementary-school lesson on quadrilaterals — squares, rectangles, rhombuses, parallelograms, trapezoids, and how the family tree of four-sided shapes fits together.
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Pre-K & KindergartenSeasons: Spring, Summer, Autumn, Winter
Do you ever wonder what causes the different weather patterns during various times of the year? And why does it sometimes feel like summertime warmth with…
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Pre-K & KindergartenShapes: square, rectangle, circle, triangle, oval, hexagon, rhombus (diamond)
Recognize and name the basic 2D shapes — square, rectangle, circle, triangle, oval, hexagon, rhombus and diamond — in a Pre-K and Kindergarten lesson with clear diagrams.
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Three, four & five Digit NumbersSkip-counting
Counting in multiples involves the process of advancing through the number line in intervals larger than one unit to arrive at a destination, or counting…
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Three, four & five Digit NumbersSubtraction: four or five digits
Four- and five-digit subtraction (1,000-99,999) is a fundamental arithmetic function that forms the basis of larger sums. Subtracting a number requires…
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GeometrySymmetry
Understand line symmetry with diagrams — find the imaginary fold-line that splits a shape into mirror halves, with worked examples for grades 2-4.
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Basic ArithmeticTime: Day and Night
Have you ever thought about what makes the sunshine during the daytime or the darkness of the night? Or do you think about how, when there’s a full moon,…
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