Basic Arithmetic
Addition with Regrouping
Addition with regrouping is an essential math skill that helps us add numbers where the sum of the digits in a column is 10 or more. Let’s explore this…
Read lesson →
Author
Professor Orion Hawthorne
Page 7 of 7
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
-
-
Basic ArithmeticBasic addition with algebraic concepts
Algebra is a fascinating branch of mathematics that allows us to solve problems involving unknown numbers. By combining basic addition with algebraic…
Read lesson → -
Basic ArithmeticBasic Addition
Learn basic addition with apples, blocks and number lines — the foundational K-1 lesson that makes finding the sum click for first-time learners.
Read lesson → -
Basic ArithmeticBasic subtraction
Subtraction is one of the four fundamental arithmetic operations, and it plays a crucial role in everyday life. Whether you’re calculating change at the…
Read lesson → -
Basic ArithmeticCounting by Fives
Counting by fives means adding five each time as you count. You land on every fifth number. This method of counting is useful for learning multiplication,…
Read lesson → -
Basic ArithmeticCounting by Tens
Counting by tens means adding ten each time as you count. You land on every tenth number. This method is useful for understanding place value,…
Read lesson → -
Basic ArithmeticCounting by Twos
Counting by twos is a fundamental math skill that helps build a strong foundation for addition, multiplication, and number sense. It’s a simple yet powerful…
Read lesson → -
Basic ArithmeticGreater than, less than or equal comparisons
Understanding how to compare numbers using greater than (>), less than (<), and equal to (=) is a fundamental math skill. These symbols help us determine…
Read lesson → -
Basic ArithmeticSubtraction of two digit numbers
Subtraction is the process of finding the difference between two numbers by removing one quantity from another. When working with two-digit numbers, we need…
Read lesson → -
Basic ArithmeticTelling time
Telling time means being able to read a clock to know what hour and minute it is. This helps us organize our day, from waking up in the morning to going to…
Read lesson → -
Basic ArithmeticThe Metric System
The Metric System is an international measurement system used worldwide for its simplicity and consistency. It uses base units and prefixes to measure…
Read lesson →
