GED® Math Foundations: Number Sense & Measurement Mastery

GED® Math Foundations: Number Sense & Measurement Mastery

Course purpose

This 24-session course builds the quantitative control needed for GED® Mathematical Reasoning. It connects place value, rational numbers, estimation, factors, powers, formulas, units, and measurement so learners can choose a method, calculate accurately, and judge whether an answer makes sense.

Entry knowledge

No formal prerequisite course is required. Learners should be willing to review basic addition, subtraction, multiplication, and division. A calculator is helpful in later sessions, but every session also develops estimation and non-calculator reasoning.

Suggested pace

Complete two sessions per week for 12 weeks, or divide each session across two study days. A full session is designed for 90-120 minutes: brief retrieval, foundation reading, study of the SVG model, ten step-by-step worked examples, guided practice, a session check with feedback, and an exit reflection. Learners may study Examples 1-5 on the first day and Examples 6-10 on the second. Revisit missed skills after one day and again after one week.

Learning sequence

• Sessions 1-6: Magnitude and signed number sense - place value, comparison, estimation, integers, change, distance, and tolerance.
• Sessions 7-13: Rational-number structure and fluency - factors, GCF/LCM, fractions, decimals, precision, and percent equivalence.
• Sessions 14-16: Expression and scale control - operation order, exponents, roots, powers of ten, and scientific notation.
• Sessions 17-23: Measurement mastery - metric and customary systems, time, temperature, money, dimensional analysis, rates, area, volume, and capacity.
• Session 24: Cumulative GED® problem control - method selection, multi-step reasoning, error analysis, and verification.

Assessment and mastery

• Use each embedded session check as low-stakes feedback, not as a one-attempt grade.
• Complete the 15 lesson-linked MCQs after each session: five foundational, five applied, and five multi-step or error-analysis questions.
• Treat 12 of 15 correct as the initial mastery threshold, then correct every missed question from a blank page before retrying.
• Explain at least two worked examples aloud or in writing before independent practice, including why each verification step is valid.
• Maintain an error log labeled concept, method selection, calculation, unit, or checking.
• Aim for at least 80% on mixed practice, then correct every missed solution and retry after a delay.
• Complete the separate 46-question cumulative final exam only after mixing topics from all four course blocks. The exam includes 15 foundational, 15 applied, and 16 challenging questions and samples every session.

Course outline

Evidence-informed learning design

The learning sequence uses four recurring design choices:

1. Adult-life contexts are treated as part of numeracy, not decoration. Adult numeracy includes managing mathematical, quantitative, and statistical demands in real situations, so lessons connect representations and procedures to money, work, measurement, data, and daily decisions (Goos et al., 2023).
2. New procedures begin with explicit worked examples. The course shows a plan, a complete solution, and a verification prompt before expecting independent selection of a method. Worked examples can reduce unproductive search, while prior knowledge remains an important moderator of learning (Lee & Ayres, 2024).
3. Practice becomes cumulative and mixed after an initial focused introduction. A randomized classroom trial found that a higher dose of interleaved mathematics practice improved performance on a delayed, unannounced test. The authors also note that interleaving may feel harder and may work best after some initial focused practice (Rohrer et al., 2020).
4. Retrieval is paired with corrective feedback and restudy of reasoning. Retrieval practice does not automatically improve mathematical word-problem procedures, so every session check is followed by a worked explanation and an invitation to repair the method, not merely mark an answer right or wrong (Huang et al., 2023).

References

Goos, M., Prendergast, M., & O'Meara, N. (2023). Supporting adults to become numerate citizens: A study of adult numeracy provision in Ireland. ZDM - Mathematics Education, 55(5), 995-1008. https://doi.org/10.1007/s11858-023-01480-9

Huang, X., Zheng, S., & Yu, Z. (2023). Retrieval practice may not benefit mathematical word-problem solving. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1093653

Lee, H. M., & Ayres, P. (2024). The worked-example effect and a mastery approach goal orientation. Education Sciences, 14(6), 597. https://doi.org/10.3390/educsci14060597

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

By the end of the 24 sessions, a learner will be able to:

Number sense and representation

1. Read, write, expand, compare, and order whole numbers and decimals by place value.
2. Explain changes in magnitude caused by multiplication or division by powers of ten.
3. Place integers, fractions, and decimals on a number line and compare their values.
4. Round to a stated place and choose an estimation method appropriate to the calculation.
5. Use benchmarks to reject answers with unreasonable signs or magnitudes.
6. Interpret positive and negative quantities relative to a defined zero point.
7. Use opposites and absolute value to describe direction, distance, error, and tolerance.
8. Distinguish final position, signed change, total distance, and absolute difference.

Rational-number structure and operations

1. Apply divisibility tests and classify whole numbers as prime or composite.
2. Produce and verify prime factorizations.
3. Find and apply greatest common factors and least common multiples.
4. Interpret fractions as quotients, equal parts, and number-line positions.
5. Generate, simplify, compare, and order equivalent fractions and mixed numbers.
6. Add, subtract, multiply, and divide fractions in measurement contexts.
7. Perform decimal operations with correct place alignment and scale.
8. Convert among fraction, decimal, and percent forms and use benchmark equivalents.

Expressions, powers, and scale

1. Evaluate expressions using grouping, exponent, and equal-priority left-to-right rules.
2. Substitute signed and decimal values into numerical formulas with correct grouping.
3. Evaluate powers, squares, cubes, and exact roots and estimate nonperfect square roots.
4. Distinguish a negative base in parentheses from an external negative sign.
5. Convert, compare, multiply, and divide values written in scientific notation.

Measurement and dimensional reasoning

1. Select appropriate metric and U.S. customary units for length, mass, capacity, time, temperature, and money.
2. Convert metric quantities using powers of ten and customary quantities using stated unit equalities.
3. Build one-step and multi-step dimensional-analysis chains whose units cancel correctly.
4. Calculate and interpret unit rates and compound measures such as speed, unit price, and flow rate.
5. Solve elapsed-time, signed-temperature-change, and multi-step money problems.
6. Distinguish linear, square, and cubic measures by meaning and unit type.
7. Apply perimeter, circumference, area, rectangular-prism volume, and cylinder volume formulas.
8. Convert square and cubic units by squaring or cubing the underlying linear factor.
9. Relate volume and capacity when a valid conversion relationship is provided.

GED® problem control

1. Translate a multi-step quantitative situation into labeled operations, formulas, and conversions.
2. Decide when a calculator, mental strategy, exact value, or estimate is appropriate.
3. Verify solutions with inverse operations, estimation, dimensional analysis, precision, and context.
4. Diagnose whether an incorrect solution reflects a concept, method-selection, calculation, unit, or checking error.
5. Explain a complete solution in words, symbols, and units so another learner can follow and verify it.