다단계 실습 모델에서의 필수 기술
도입됨| English | 의미 |
|---|---|
| model parameter/ˈmɒdl pəˈræmɪtə/ | 모델 매개변수 |
| model assumption/ˈmɒdl əˈsʌmpʃn/ | 모델 가정 |
A decision before an answer
- A delivery model C=8+3d charges a fixed amount even at zero distance. Treating it as direct proportion changes the problem.
- Your goal: Build a model connecting quantities, rates and geometric measures.
Read the relationship
- Define variables with units and translate each part of the situation. A fixed fee plus a rate gives C=b+md; direct proportion C=md applies only when the intercept is zero. Ratios compare quantities in a chosen order, and successive percentage changes multiply their changing bases. A model should preserve those relationships before any arithmetic begins.
- Interpret parameters and test the model’s assumptions.
C=5+2d. For d=7, C is:
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Fixed fee 5 plus 2·7=19.
Use the defining rule
- Convert units by multiplying factors that cancel. For scale models, length factors square for area and cube for volume when every dimension is scaled. Combining a geometric formula with a unit price can model material cost; for example, paint area times cost per square metre gives currency, while using wall volume would have the wrong physical meaning.
- Evaluate predictions and adjust a parameter using new evidence.
Every prediction is 3 units too low across several distances. First adjustment to inspect:
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A constant offset suggests the fixed contribution is low.
Check the conditions
- Interpret and test the model. Ask whether a constant rate is plausible across the domain, whether a fixed charge is already included and whether an estimated area excludes doors or overlap. Compare a prediction with observed data and identify which assumption or parameter may need revision. A model’s neat algebra does not establish that it fits reality.
- Evaluate predictions and adjust a parameter using new evidence.
Original delivery model C=8+3d, d in kilometres, predicts 23 units for 5 km. Bills are consistently 2 units higher at several distances, supporting a revised intercept 10 while keeping slope 3. A wall 4 m by 2.5 m has area 10 m²; subtracting a 2 m² doorway gives 8 m² to paint. At 6 units/m², cost is 48. A 1:50 plan of a 4 m wall shows 8 cm.
A 3 m length on a 1:100 plan is ____ cm.
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3 m=300 cm, divided by 100.
Apply the task format
- Improve a model by adjusting the parameter supported by evidence. If every predicted bill is exactly two units low, revising the fixed fee may fit better than changing the per-distance slope. A trend in errors with distance points toward the rate instead. Keep modelling as an overlapping activity across content areas, not a separate extra block of official questions.
- Evaluate predictions and adjust a parameter using new evidence.
Do not treat an intercept model as direct proportion or adjust every parameter when evidence identifies one systematic error.
다음 중 이 사례에 부합하는 답안은 무엇입니까?
양, 비율 및 기하학적 측정치를 연결하는 모델을 구성합니다
Modelling is counted only in a separate block of enhanced ACT math items.
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It overlaps other reporting categories.
Keep the distinctions
- model parameter 模型参数 — A quantity setting a rule’s rate, scale or fixed contribution.
- model assumption 模型假设 — A condition under which the representation is intended to work.
- Build a model connecting quantities, rates and geometric measures.
- Interpret parameters and test the model’s assumptions.
- Evaluate predictions and adjust a parameter using new evidence.
Match each term with its precise meaning in this lesson.
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Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
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The order follows the stated process; check each stage before the next.