MATH-03 · 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 | Fractions, Decimals and Percentages
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Sign in to save this learning pathPractical outcome: Partition a paper recipe into equal portions and scale it.
Explain equal parts of a whole using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain numerators and denominators using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain fractions on a number line using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain equivalent fractions using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Use the first concepts from this section. Partition a paper recipe into equal portions and scale it. 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 simplifying fractions using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain comparing fractions using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain improper fractions using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Explain mixed numbers using a visual and one worked real-world example. Context: Partition a paper recipe into equal portions and scale it. End with a prediction or check-for-understanding.
Partition a paper recipe into equal portions and scale it. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Equal parts of a whole, Numerators and denominators, Fractions on a number line and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Calculate material lengths for a model bridge.
Explain adding like denominators using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain finding a common denominator using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain adding unlike denominators using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain subtracting fractions using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Use the first concepts from this section. Calculate material lengths for a model bridge. 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 fractions using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain dividing by a fraction using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain fraction word problems using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Explain estimating fraction results using a visual and one worked real-world example. Context: Calculate material lengths for a model bridge. End with a prediction or check-for-understanding.
Calculate material lengths for a model bridge. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Adding like denominators, Finding a common denominator, Adding unlike denominators and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare shop discounts using an itemised price table.
Explain decimal place value using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain fractions as decimals using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain rounding decimals using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain decimal addition using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain decimal multiplication using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare shop discounts using an itemised price table. 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 decimal division using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain percent means per hundred using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain finding a percentage using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain percentage change using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Explain reverse percentages using a visual and one worked real-world example. Context: Compare shop discounts using an itemised price table. End with a prediction or check-for-understanding.
Compare shop discounts using an itemised price table. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Decimal place value, Fractions as decimals, Rounding decimals and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Compare shop discounts using an itemised price table. 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 Fractions, Decimals and Percentages, 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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