GED® Math Foundations: Order of Operations, Calculator & Formula Skills Mastery

Course length: 24 sessions

Course purpose: Build reliable order-of-operations, calculator-entry, formula-selection, substitution, unit, and reasonableness skills for GED® Mathematical Reasoning and for quantitative decisions in daily life and work.

Learning cycle used throughout: Each topic moves from a clear worked example to guided practice, error analysis, independent application, and a short cumulative check. Learners explain why a method works, diagnose common traps, and verify calculator results with estimation or inverse operations.

Unit 1 — Expression Structure and Accurate Computation (Sessions 1-4)

• Session 1: Expressions, terms, and grouping symbols
• Session 2: Order of operations from structure
• Session 3: Exponents, roots, and negative bases
• Session 4: Scientific-calculator entry and parentheses

Unit 2 — Formula Foundations (Sessions 5-10)

• Session 5: Formula-sheet mindset, variables, and units
• Session 6: Substitution into formulas
• Session 7: Rearranging simple formulas
• Session 8: Units, conversions, and formula results
• Session 9: Rounding, precision, and money answers
• Session 10: Multi-step formula and calculator strategy

Unit 3 — Error Repair and Calculator Fluency (Sessions 11-16)

• Session 11: Diagnosing order-of-operations errors
• Session 12: Nested groups, fraction bars, and complex numerators
• Session 13: Signed values and absolute value in expressions and formulas
• Session 14: Calculator fractions, decimals, and percents
• Session 15: Calculator powers, roots, and scientific notation
• Session 16: Estimation, inverse operations, and entry debugging

Unit 4 — Applied Formula Mastery (Sessions 17-24)

• Session 17: Selecting formulas from context and units
• Session 18: Perimeter, circumference, and composite boundaries
• Session 19: Area formulas and composite regions
• Session 20: Volume, surface area, and capacity
• Session 21: Rate, distance, time, and unit rate
• Session 22: Percent applications, tax, discount, and simple interest
• Session 23: Multi-step models with conversions and rounding
• Session 24: Cumulative mastery and GED® strategy

Assessment plan: Every session includes a quick self-check. Mixed practice revisits earlier skills so learners must choose a method rather than copy the most recent example. The course practice bank provides explanation-backed questions, and the final session uses a plan-solve-check routine for cumulative review.

By the end of this 24-session course, learners will be able to:

• identify terms, operations, and explicit or implied grouping in numerical and algebraic expressions;
• evaluate expressions accurately using grouping, exponents and roots, left-to-right multiplication/division, and left-to-right addition/subtraction;
• distinguish negative bases from leading negative signs and enter both forms correctly on a scientific calculator;
• translate fraction bars, nested groups, powers, roots, fractions, percents, and scientific notation into reliable calculator keystrokes;
• estimate magnitude before calculating and use inverse operations, units, and context to detect unreasonable answers;
• interpret formula variables and select an appropriate formula from the requested quantity, given information, and units;
• substitute positive, negative, decimal, and fractional values into formulas using parentheses where needed;
• rearrange one-step and multi-step formulas to isolate a requested variable while maintaining equality;
• convert compatible measurement units and report linear, square, cubic, rate, and money units correctly;
• apply formulas for perimeter, circumference, area, volume, surface area, rate, distance, time, percent, and simple interest;
• solve multi-step real-life and workplace problems that combine formula selection, conversion, calculation, and rounding; and
• explain and correct common order-of-operations, calculator-entry, formula-selection, unit, and rounding errors.