GED® Math Basics
A comprehensive 24-session foundation in GED® mathematical reasoning. The course develops number sense, fractions, decimals, ratios, percent, measurement, algebra, linear relationships, geometry, data, probability, and mixed problem solving. Every session contains more than 1,000 words of instruction, multiple representations, misconception analysis, ten fully solved examples, and fifteen aligned practice questions with explanations. A separate 46-question cumulative final exam uses original, non-repeated items.
📚 Course Curriculum
1. Whole-Number Sense, Place Value, Rounding, and Estimation. Learning goals. Read and write multi-digit whole numbers in standard and expanded form. Compare, order, and round …
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2. Integers, Absolute Value, and Signed Operations. Learning goals. Locate, compare, and order positive and negative integers. Interpret absolute value as distance from zero. Add, …
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3. Numerical Expressions and Order of Operations. Learning goals. Evaluate expressions containing grouping symbols, exponents, and all four operations. Treat multiplication and division as equal-priority …
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4. Factors, Multiples, Prime Numbers, Exponents, and Roots. Learning goals. List factors and classify numbers as prime or composite. Find greatest common factors and least …
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5. Fraction Meaning, Equivalence, Comparison, and Mixed Numbers. Learning goals. Interpret fractions with area, set, and number-line models. Generate and simplify equivalent fractions. Compare and …
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6. Adding, Subtracting, Multiplying, and Dividing Fractions. Learning goals. Add and subtract fractions and mixed numbers. Multiply fractions using cancellation and unit reasoning. Divide fractions …
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7. Decimal Place Value and Decimal Operations. Learning goals. Read, compare, order, and round decimals. Convert terminating decimals and fractions. Add, subtract, multiply, and divide …
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8. Ratios, Unit Rates, and Proportions. Learning goals. Write and simplify ratios without reversing their order. Calculate and interpret unit rates. Solve proportions using scaling …
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9. Percent Meaning, Conversion, and Basic Percent Problems. Learning goals. Convert among fractions, decimals, and percentages. Find a percent of a quantity. Find what percent …
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10. Discounts, Tax, Tips, Markup, Percent Change, and Simple Interest. Learning goals. Calculate discounts, taxes, tips, and markups. Distinguish the amount of change from the …
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11. Measurement, Unit Conversion, and Dimensional Reasoning. Learning goals. Convert within common metric and customary units. Convert rates and compound units. Distinguish linear, square, and …
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12. Algebraic Expressions, Substitution, and Formulas. Learning goals. Translate verbal descriptions into algebraic expressions. Evaluate expressions by substitution and order of operations. Combine like terms …
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13. One-Step and Two-Step Linear Equations. Learning goals. Solve one-step equations with all four operations. Solve two-step equations with signed and decimal coefficients. Check solutions …
Open trial session →14. Multi-Step Equations, Identities, No-Solution Cases, and Inequalities. Learning goals. Solve equations with distribution and variables on both sides. Recognize one-solution, identity, and no-solution outcomes. …
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15. Proportional Relationships, Slope, and Rate of Change. Learning goals. Identify proportional relationships in tables and graphs. Calculate slope from two points or a context. …
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16. Linear Equations, Graphs, Intercepts, and Line Relationships. Learning goals. Interpret slope and y-intercept in y = mx + b. Graph a line from an …
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17. Functions, Systems of Equations, and Algebraic Modeling. Learning goals. Determine whether a relation is a function. Evaluate function notation and write rules from tables. …
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18. Perimeter, Circumference, and Boundary Problems. Learning goals. Find perimeter of polygons and regular figures. Use C = pi d and C = 2pi r. …
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19. Area, Circles, Composite Figures, and Coverage. Learning goals. Calculate area of rectangles, triangles, parallelograms, trapezoids, and circles. Identify perpendicular base-height pairs. Decompose composite shapes …
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20. Pythagorean Theorem and Coordinate Geometry. Learning goals. Find a missing leg or hypotenuse in a right triangle. Use the converse to test whether a …
Open trial session →21. Volume, Surface Area, and Three-Dimensional Measurement. Learning goals. Find volume of prisms, cubes, and cylinders. Find surface area from face inventories and formulas. Solve …
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22. Data Displays, Mean, Median, Mode, Range, and Weighted Reasoning. Learning goals. Calculate and interpret mean, median, mode, and range. Find missing values and combined …
Open trial session →23. Probability, Experimental Data, and Counting Principles. Learning goals. Find probabilities from equally likely outcomes. Use complements and experimental probabilities. Multiply probabilities for multi-stage events. …
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24. Cumulative GED®-Style Modeling, Strategy, and Mixed Review. Learning goals. Select methods in mixed, multi-step situations. Combine percent, rate, algebra, geometry, and data reasoning. Use …
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Course Syllabus
GED® Math Basics: 24-Session Syllabus
Course structure
- Length: 24 sessions
- Recommended pace: 3 sessions per week for 8 weeks, with an extra review day each week
- Session design: retrieval warm-up, an explanatory visual with accessible guidance, explicit concepts, a repeatable method, multiple representations, 10 fully solved examples, misconception analysis, transfer, and spaced review
- Practice: 15 lesson-linked multiple-choice questions per session, each with a worked explanation and an easy-to-hard progression
- Final exam: 46 original cumulative multiple-choice questions that do not repeat the session bank
- Mastery target: at least 80% plus correction of every missed item
Session outline
| Session | Topic | First essential outcome |
|---|---|---|
| 1 | Whole-Number Sense, Place Value, Rounding, and Estimation | Read and write multi-digit whole numbers in standard and expanded form. |
| 2 | Integers, Absolute Value, and Signed Operations | Locate, compare, and order positive and negative integers. |
| 3 | Numerical Expressions and Order of Operations | Evaluate expressions containing grouping symbols, exponents, and all four operations. |
| 4 | Factors, Multiples, Prime Numbers, Exponents, and Roots | List factors and classify numbers as prime or composite. |
| 5 | Fraction Meaning, Equivalence, Comparison, and Mixed Numbers | Interpret fractions with area, set, and number-line models. |
| 6 | Adding, Subtracting, Multiplying, and Dividing Fractions | Add and subtract fractions and mixed numbers. |
| 7 | Decimal Place Value and Decimal Operations | Read, compare, order, and round decimals. |
| 8 | Ratios, Unit Rates, and Proportions | Write and simplify ratios without reversing their order. |
| 9 | Percent Meaning, Conversion, and Basic Percent Problems | Convert among fractions, decimals, and percentages. |
| 10 | Discounts, Tax, Tips, Markup, Percent Change, and Simple Interest | Calculate discounts, taxes, tips, and markups. |
| 11 | Measurement, Unit Conversion, and Dimensional Reasoning | Convert within common metric and customary units. |
| 12 | Algebraic Expressions, Substitution, and Formulas | Translate verbal descriptions into algebraic expressions. |
| 13 | One-Step and Two-Step Linear Equations | Solve one-step equations with all four operations. |
| 14 | Multi-Step Equations, Identities, No-Solution Cases, and Inequalities | Solve equations with distribution and variables on both sides. |
| 15 | Proportional Relationships, Slope, and Rate of Change | Identify proportional relationships in tables and graphs. |
| 16 | Linear Equations, Graphs, Intercepts, and Line Relationships | Interpret slope and y-intercept in y = mx + b. |
| 17 | Functions, Systems of Equations, and Algebraic Modeling | Determine whether a relation is a function. |
| 18 | Perimeter, Circumference, and Boundary Problems | Find perimeter of polygons and regular figures. |
| 19 | Area, Circles, Composite Figures, and Coverage | Calculate area of rectangles, triangles, parallelograms, trapezoids, and circles. |
| 20 | Pythagorean Theorem and Coordinate Geometry | Find a missing leg or hypotenuse in a right triangle. |
| 21 | Volume, Surface Area, and Three-Dimensional Measurement | Find volume of prisms, cubes, and cylinders. |
| 22 | Data Displays, Mean, Median, Mode, Range, and Weighted Reasoning | Calculate and interpret mean, median, mode, and range. |
| 23 | Probability, Experimental Data, and Counting Principles | Find probabilities from equally likely outcomes. |
| 24 | Cumulative GED®-Style Modeling, Strategy, and Mixed Review | Select methods in mixed, multi-step situations. |
Recommended study cycle
Read the learning goals, attempt the entry retrieval prompt, study the core explanation, and pause before each worked example to write a plan. Complete the linked practice without notes. Correct every miss from a blank page, then revisit selected problems after a delay and in mixed order. Keep an error log organized by interpretation, setup, operation, sign, unit, calculation, graph reading, and final communication.
Evidence-informed learning design
This course uses four recurring design choices.
- Worked examples require active explanation. Each solution includes a plan, calculation, verification, and a prompt asking the learner to explain why the method works. Davenport (2019) describes worked examples as expert guides and emphasizes prompts that make learners explain steps and confront misconceptions.
- New skills begin clearly, then become mixed. The early examples in a session concentrate on the new method; later examples require method selection. In a cluster randomized classroom trial, a higher dose of interleaved mathematics practice improved performance on a delayed, unannounced test, while the authors also caution that learners may need a small amount of blocked practice when first meeting a skill (Rohrer et al., 2020).
- Important ideas return after a delay. Entry retrieval, cumulative examples, and the capstone revisit earlier skills rather than leaving them in a single chapter. Hopkins et al. (2018) describe mathematics retrieval spread across weeks and report evidence favoring spaced over massed practice for long-term retention.
- Adult numeracy is contextual and representational. Examples use work, household, financial, measurement, graphical, and civic situations. Gal and Tout (2014) frame adult numeracy as accessing, using, interpreting, and communicating mathematical information represented in multiple ways in real situations.
References
Davenport, C. E. (2019). Using worked examples to improve student understanding of atmospheric dynamics. Bulletin of the American Meteorological Society, 100(9), 1653-1664. https://doi.org/10.1175/BAMS-D-18-0226.1
Gal, I., & Tout, D. (2014). Comparison of PIAAC and PISA frameworks for numeracy and mathematical literacy. OECD Education Working Papers, No. 102. https://doi.org/10.1787/5jz3wl63cs6f-en
Hopkins, R. F., Lyle, K. B., & Ralston, P. (2018). Retrieval practice and spacing: Effects on long-term learning among engineering precalculus students. 2018 ASEE Annual Conference & Exposition Proceedings. https://doi.org/10.18260/1-2--29900
Rohrer, D., Dedrick, R. F., & Hartwig, M. K. (2020). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology, 112(1), 40-52. https://doi.org/10.1037/edu0000367
Course Outcomes
Course outcomes
By the end of the 24 sessions, learners will be able to:
- reason fluently with whole numbers, integers, fractions, decimals, ratios, rates, and percentages;
- evaluate expressions and solve equations, inequalities, functions, systems, and linear models;
- convert units and distinguish linear, square, and cubic measurement;
- solve perimeter, area, Pythagorean, coordinate, volume, and surface-area problems;
- summarize and interpret data and calculate probabilities from organized sample spaces;
- translate adult-life situations among words, diagrams, tables, graphs, and equations;
- choose a method in mixed problems rather than relying on a topic label;
- estimate before calculating and verify answers using units, sign, magnitude, substitution, or inverse operations;
- explain common errors and maintain a correction process that supports durable learning;
- complete mixed GED®-style mathematical reasoning with clear setup, accurate calculation, and a defensible answer sentence.
📝 Practice Questions
415 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.