MATH-05 · Foundation · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Pre-Algebra and Signed Numbers
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Sign in to save this learning pathPractical outcome: Model daily temperature changes with a number line.
Explain negative numbers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain absolute value using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain adding signed numbers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain subtracting signed numbers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Use the first concepts from this section. Model daily temperature changes with a number line. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain multiplying signed numbers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain dividing signed numbers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain powers using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Explain square roots using a visual and one worked real-world example. Context: Model daily temperature changes with a number line. End with a prediction or check-for-understanding.
Model daily temperature changes with a number line. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Negative numbers, Absolute value, Adding signed numbers and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Write a cost expression for a small stationery order.
Explain variables as placeholders using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain substitution using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain like terms using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain distributive law using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Use the first concepts from this section. Write a cost expression for a small stationery order. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain expanding brackets using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain factoring a common term using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain translating words to expressions using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Explain formula rearrangement using a visual and one worked real-world example. Context: Write a cost expression for a small stationery order. End with a prediction or check-for-understanding.
Write a cost expression for a small stationery order. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Variables as placeholders, Substitution, Like terms and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Use a balance drawing to recover an unknown quantity.
Explain equality as balance using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain one-step equations using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain two-step equations using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain equations with brackets using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Use the first concepts from this section. Use a balance drawing to recover an unknown quantity. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain variables on both sides using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain linear inequalities using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain compound inequalities using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Explain checking solutions using a visual and one worked real-world example. Context: Use a balance drawing to recover an unknown quantity. End with a prediction or check-for-understanding.
Use a balance drawing to recover an unknown quantity. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Equality as balance, One-step equations, Two-step equations and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Use a balance drawing to recover an unknown quantity. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Pre-Algebra and Signed Numbers, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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