Mathematics

All Mathematics skills

Foundations

• M1.1 · Signed integers: Overdrawn balances, below-zero temperatures and basement floors are negative integers. When adding, same signs pile up; different signs cancel out.
• M1.2 · Adding and subtracting decimals: Prices and measurements almost always have decimals. The trick is to line up the decimal point and think of the places as cents.
• M1.3 · Order of operations: An expression has a fixed order: parentheses, powers, multiplication and division, then addition and subtraction. Basic calculators sometimes ignore it.
• M1.4 · Powers and roots: A power is repeated multiplication: 5² = 5 × 5. The square root reverses it: √25 = 5. Areas and compound interest rely on this.

Intermediate

• M2.1 · Simplifying fractions: A fraction keeps its value when the top and bottom are divided by the same number. Fully simplified fractions are easier to compare.
• M2.2 · Percent of a number: "Percent" means "per hundred". To find 15% of 200, multiply 200 by 0.15. Shortcut: 10% just moves the decimal point one place.
• M2.3 · Proportions (unit rate): When two quantities grow together at the same rate, find the value of one unit and multiply. It works for price per kilo, hourly rates and consumption.
• M2.4 · Unit conversion: In the metric system, prefixes tell you the factor: kilo = 1000, centi = 1/100, milli = 1/1000. For time, the base is 60.

Applied

• M3.1 · Discounts and increases: A 20% discount means paying 80%: multiply by 0.8. A 20% increase means paying 120%: multiply by 1.2. One factor does the job.
• M3.2 · Linear equations: An equation is a balance: whatever you do to one side, do to the other. Isolate x by undoing operations in reverse order.
• M3.3 · Area and perimeter: Perimeter is the outline (fence, baseboard). Area is the surface (flooring, paint). Rectangle: length × width. Triangle: half of that.
• M3.4 · Arithmetic mean: The mean shares the total equally: add everything and divide by the count. That is how you get average monthly spending or a final grade.