Unit 1 of 6

Essential Skills

  • 6 lessons
  • Parts 1 to 12

The SAT expects quick, accurate work with fractions, signs, ratios, percents and units, because nearly every question uses them somewhere. This unit makes those steps reliable, from the order of operations and negative numbers to proportions, percent change and converting rates between units.

It then turns to reading expressions and formulas precisely and translating a situation described in words into an equation, the step that most word problems hinge on.

Every lesson is a pair of videos. The theory part explains the idea and the practice part works through problems. Each lesson page has the definitions and an example for every key term.

Numbers and Proportional Reasoning

  1. Fractions, Signs and Order of Operations

    How to read a numerical expression exactly as written, with fractions, negative numbers, parentheses and powers, so that every later equation starts from the right value.

    Theory part 1Practice part 2

  2. Ratios and Proportions

    What a ratio says about two quantities, how to scale both parts consistently, how to split a total in a given ratio, and how to tell whether a relationship is a direct proportion.

    Theory part 3Practice part 4

  3. Percentages and Percent Change

    How to find a percentage of any amount, measure percent change against the right original value, use multipliers forward and backward, and tell percentage points from percent change.

    Theory part 5Practice part 6

  4. Units, Rates and Conversions

    How to convert lengths, rates, areas and volumes by multiplying by conversion factors, keeping the units attached at every step so that they show whether the answer is right.

    Theory part 7Practice part 8

Expressions and Word Problems

  1. Expressions, Substitution and Mathematical Language

    What variables, constants, coefficients, terms and factors are, how an expression differs from an equation, and how to substitute values, negative ones included, without sign errors.

    Theory part 9Practice part 10

  2. Turning Word Problems into Equations

    How to name the unknown with its unit, translate each stated relationship into an equation or inequality, and check the solution against what the situation allows.

    Theory part 11Practice part 12