Ally's Love of Learning — Basics of Every Core School Subject

Mathematics

Mathematics is the study of numbers, patterns, and relationships: a toolkit for solving problems and describing the world with precision.

Place value: Each digit's position gives it a different value: the 3 in 30 means three tens, while the 3 in 300 means three hundreds.
Fractions and decimals: Two ways to write a part of a whole. One-half can be written as 1/2 or as 0.5 — they mean exactly the same amount.
Order of operations: Work through parentheses first, then exponents, then multiplication and division, then addition and subtraction.
Variables: A letter like x stands in for a number you don't know yet. Solving an equation means figuring out what it has to be.
Area and perimeter: Perimeter is the distance around a shape's edge; area is the amount of space inside it.

Science is less a subject than a method: a disciplined way of asking questions about the natural world and testing the answers against evidence.

The scientific method: A repeatable process: ask a question, form a hypothesis, test it, look at the results, and draw a conclusion.
States of matter: Solid, liquid, and gas describe how tightly particles are packed and how freely they move. Adding or removing heat can change one into another.
Cells: The basic unit of life. Every living thing is made of at least one cell, and most are made of trillions.
Conservation of energy: Energy can change form, from motion to heat to light, but the total amount never increases or disappears.
Gravity: A force that pulls any two objects with mass toward each other. On Earth, it's why a dropped ball falls instead of floating.

Language arts is about moving ideas from one mind to another: reading closely, writing clearly, and choosing words on purpose.

Parts of speech: Nouns, verbs, adjectives, adverbs, and the rest are the building blocks that combine to form a sentence.
Subject-verb agreement: A singular subject needs a singular verb ("she runs"), and a plural subject needs a plural verb ("they run").
Thesis statement: The single sentence that states the main claim an essay or paper will spend the rest of its length supporting.
Context clues: The words and sentences surrounding an unfamiliar word, often enough on their own to guess what it means.
Figurative language: Tools like simile and metaphor that compare two unlike things to make writing more vivid.

History asks what happened and why it mattered. Social studies widens the lens to how people organize their communities, governments, and economies.

Primary vs. secondary sources: A primary source, like a letter or photo, comes from the time itself; a secondary source, like a textbook, analyzes it afterward.
Cause and effect: Historical events rarely stand alone. One development usually sets off, or grows out of, another.
Forms of government: Democracy, monarchy, and dictatorship differ mainly in who holds power, and how much say ordinary people have in choosing them.
Supply and demand: Prices tend to rise when something is scarce and wanted, and fall when it's plentiful or wanted less.
Civic rights and responsibilities: Freedoms like speech and voting come paired with responsibilities, like following the law and serving on a jury if called.

Geography maps the relationship between people and place, from continents and coastlines down to a single city block.

Latitude and longitude: An invisible grid over the globe: latitude measures distance north or south of the equator, longitude measures east or west of the Prime Meridian.
Continents and oceans: Earth's landmasses are grouped into seven continents, surrounded by four or five oceans depending on how you count.
Weather vs. climate: Weather is what's happening right now, like today's rain. Climate is the long-term pattern a region typically sees.
Physical vs. political maps: A physical map shows natural features like mountains and rivers; a political map shows human-drawn borders, cities, and capitals.
Natural resources: Materials from the earth, like water, timber, and minerals, that people rely on and sometimes compete over.

Computer science looks at how machines process information step by step. Digital literacy is knowing how to use that power safely and well.

Algorithms: A precise, step-by-step set of instructions for completing a task. A recipe is an algorithm just as much as a computer program is.
Binary: Computers store and process everything, text, images, and sound, as combinations of just two digits: 0 and 1.
Hardware vs. software: Hardware is the physical machine you can touch; software is the set of instructions that tells the hardware what to do.
Debugging: The process of finding and fixing an error, or "bug," in a program. A normal and expected part of writing code.
Digital privacy: Using long, unique passwords and thinking twice before sharing personal information are two of the simplest ways to stay safe online.

Art and music give feeling a shape. Color, line, rhythm, and melody are their own kind of vocabulary, with rules worth knowing before you break them.

The color wheel: Red, blue, and yellow are primary colors. Mixing pairs of them creates the secondary colors orange, green, and purple.
Elements of art: The basic vocabulary of visual art: line, shape, color, texture, space, form, and value.
Rhythm and tempo: Rhythm is the pattern of long and short beats in music; tempo is simply how fast or slow those beats go.
Melody and harmony: Melody is the main tune you hum along to; harmony is the supporting notes played underneath it.
Perspective: A drawing technique that uses converging lines and relative size to make a flat surface look like it has depth.

Health basics cover how the body works day to day, and the small habits, like sleep, food, movement, and hygiene, that keep it running well.

The food groups: Fruits, vegetables, grains, protein, and dairy each support the body in a different way. Variety matters more than any single food.
Sleep needs: Most school-age children need about 9 to 12 hours of sleep a night; most adults need 7 to 9.
The five senses: Sight, hearing, smell, taste, and touch are how the body constantly gathers information about the world around it.
Hygiene: Simple habits like handwashing are among the most effective ways to stop the spread of illness.
Naming feelings: Putting a specific word to an emotion, like frustrated, nervous, or relieved, is often the first step toward managing it well.