Start with what
everything else uses.
These are the ideas teachers often assume you already know. Review the shaky parts, skip what feels easy, and return whenever a lesson stops making sense.
Number sense before formulas.
Math becomes easier when numbers feel flexible—not like mysterious symbols.
Order of operationsPEMDAS, used correctly
Work from the innermost grouping outward: parentheses, exponents, multiplication or division from left to right, then addition or subtraction from left to right.
Division and multiplication have equal rank, so go left to right: 18 ÷ 3 = 6, then 6 × 2 = 12.
Fractions, decimals, and percentsThree ways to show one value
A fraction is division. A decimal records place value. A percent means “out of 100.” Convert 3/4 by dividing 3 ÷ 4 = 0.75, then multiply by 100 to get 75%.
Negative numbersDirection and distance
The sign tells direction; absolute value tells distance from zero. −8 is less than −3 because it sits farther left on the number line. Subtracting a negative moves right: 5 − (−2) = 7.
Variables and equalityA letter represents a number
An equation is a balanced scale. Whatever operation you perform on one side must also happen on the other. In x + 4 = 11, subtract 4 from both sides, leaving x = 7.
Geometry essentialsMeasure the right thing
Perimeter measures the distance around. Area measures a flat surface in square units. Volume measures space inside a solid in cubic units. Label units before choosing a formula.
Clear sentences carry clear ideas.
Grammar is not decoration. It helps readers understand exactly what you mean.
Complete sentencesWho or what + what happened
A complete sentence needs a subject and a complete predicate. “Because the storm arrived” is a fragment—it leaves the reader waiting. “We went inside because the storm arrived” completes the thought.
Parts of speechJobs words perform
Nouns name. Pronouns replace nouns. Verbs show action or being. Adjectives describe nouns. Adverbs modify verbs, adjectives, or other adverbs. Prepositions show relationships such as under, through, and beside.
Commas and sentence boundariesPrevent run-ons
A comma alone cannot join two complete sentences. Use a period, semicolon, or a comma plus a coordinating conjunction: “I studied, and I felt prepared.”
Subject–verb agreementMatch singular and plural
A singular subject takes a singular verb: “The list is long.” Ignore interrupting phrases: “The list of assignments is long,” not “are long.”
Paragraph structureOne focused idea
Begin with a clear main point, support it with specific evidence or examples, explain the connection, and end by completing—not merely repeating—the thought.
Evidence before conclusions.
Science is a way of asking testable questions and improving explanations.
Claims, evidence, and reasoningHow scientific explanations work
A claim answers the question. Evidence is the relevant observation or data. Reasoning uses a scientific idea to explain why the evidence supports the claim. Data without reasoning is not a full explanation.
Variables and fair testsChange one thing at a time
The independent variable is what you deliberately change. The dependent variable is what you measure. Controlled variables stay the same so the test is fair.
Matter and energyStuff and the ability to change it
Matter has mass and takes up space. Energy is the ability to cause change. Matter can change form, and energy can transfer or transform, but neither simply appears from nowhere.
Scale and systemsParts interact
A system is a group of interacting parts. Scientists use models because many systems are too tiny, enormous, fast, slow, dangerous, or complicated to observe directly.
Measurement and unitsNumbers need meaning
Always record a unit. Length may use meters, mass uses grams or kilograms, volume uses liters or cubic units, and temperature commonly uses degrees Celsius in science.
Context changes the story.
History is not a list of dates—it is an evidence-based explanation of people and change.
Primary and secondary sourcesEvidence versus later explanation
A primary source comes from the time being studied, such as a letter or artifact. A secondary source analyzes the past later. Neither is automatically truthful or unbiased; both must be evaluated.
Chronology and periodizationPlace events in time
Chronology orders events. Periodization groups time into eras to reveal patterns. BCE dates count down toward year 1; CE dates count upward from it.
Cause and effectHistory rarely has one cause
Separate long-term conditions, short-term triggers, and individual choices. Then distinguish immediate effects from consequences that appeared generations later.
Maps and geographyLocation shapes choices
Read the title, legend, scale, direction, and date before using a map. Rivers, climate, resources, and terrain create opportunities and limits, but they do not control every human decision.
Perspective and corroborationCompare before deciding
Ask who created a source, for whom, when, and why. Then corroborate it—compare it with other evidence—to find agreements, contradictions, and missing voices.