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LA 2100 · Quadrivium: The School of Arithmetic — Module 4: Common Fractions

Led by James B. Thomson Simulacrum

1 modules 11 tutorials · ~15 hours Mathematics Updated today

The largest module in the school and the one where arithmetic students historically fail. Fractions taught from five general principles, so that every rule can be rebuilt rather than remembered.

Common Fractions4
  1. Module 4

    Common Fractions

    Led by James B. Thomson Simulacrum

    The question

    Eleven sittings, Thomson's pages 88 to 128. You begin by folding

    Outcome

    The student can reduce any fraction to its lowest terms or to a

    Sub-units

    1. ○ 4.1 The Idea Before the Notation
    2. ○ 4.2 Numerator, Denominator, and the Kinds
    3. ○ 4.3 The Five General Principles
    4. ○ 4.4 Reduction
    5. ○ 4.5 Common Denominators
    6. ○ 4.6 Addition and Subtraction of Fractions
    7. ○ 4.7 Multiplication of Fractions
    8. ○ 4.8 Division of Fractions
    9. ○ 4.9 Fractional Relation of Numbers
    10. ○ 4.10 Fractions in Analysis
    11. ○ 4.11 Review and Selection

    Practice scenarios

    The Pupil Who Has the Rules

    A pupil arrives from another school able to add, subtract, multiply and divide fractions correctly and quickly. She inverts and multiplies without hesitation. She has no idea why any of it works, and when asked, says that this is how it is done, which is what she was told. Her answers are right. She sees no problem, and neither does anyone else.

    Your goals

    • Establish that there is a problem, to a pupil whose results are excellent
    • Find the question she cannot answer — it exists, and it is not a harder sum
    • Decide whether to re-teach the five principles or let her proceed
    • Predict concretely where her method will fail
    • Say what you would do if she were three weeks from an examination rather than
    • at the start of the year