Planning a mathematical exploration · 规划数学探究
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| assumption/əˈsʌmpʃn/ | 假设 | jiǎ shè |
What makes an investigation mathematical?
- A student wants to predict queue waiting time at the school canteen. A useful exploration needs a question, data and mathematics the student can explain.
- This lesson studies assumption 假设: A condition adopted to make a mathematical model possible and whose effect should be evaluated.
Choose the mathematical structure
- Frame a focused question with measurable variables and a feasible method. Keep a dated record of decisions, sources and mathematical reasoning. Use technology to support analysis, and explain every important output in your own words.
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines assumption? · 下列哪项描述正确定义了假设？
A condition adopted to make a mathematical model possible and whose effect should be evaluated. · 为使数学模型可行而设定的条件，且其影响应被评估。
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
A pilot records mean waiting times of 3,5,7 minutes when 10,20,30 people are ahead. A first model is t=1+0.2n. At n=25 it predicts 6 minutes. An actual wait of 8 gives residual 2; investigate varying service rates rather than hiding the mismatch.
Planning a mathematical exploration · 规划数学探究
Frame a focused question with measurable variables and a feasible method · 提出一个具有可测量变量且方法可行的聚焦问题
Explain the residual using the student’s own measurements and model assumptions. · 利用学生自己的测量数据和模型假设解释残差。
For t=1+0.2n, find predicted wait at n=25. · 当 t=1+0.2n 时，求 n=25 时的预测等待时间。
Use n=25 in the model: 1+0.2×25=6 minutes. · 使用模型中的 n=25：1+0.2×25=6 分钟。
Test a tempting shortcut
- Do not copy a sample exploration, invent data or manufacture personal engagement. A prediction is not evidence until it is compared with observations. Consent and privacy matter when collecting school data.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
The school-supervised mathematical exploration can be replaced by a timed written mock exam. This claim is false. Explain which definition or assumption it violates.
Find the residual for observed 8 and predicted 6. · 求观测值 8 与预测值 6 的残差。
Residual=8-6=2 minutes. · 残差 = 8 - 6 = 2 分钟。
The school-supervised mathematical exploration can be replaced by a timed written mock exam. · 学校监督下的数学探究可由限时模拟笔试替代。
Do not copy a sample exploration, invent data or manufacture personal engagement. A prediction is not evidence until it is compared with observations. Consent and privacy matter when collecting school data. · 切勿抄袭范例探究、编造数据或伪造个人参与情况。在将其与观测结果进行比较之前，预测不能作为证据。收集学校数据时需重视知情同意和隐私保护。
Interpret a new situation
- The school supervises topic approval, checkpoints, authenticity and assessment. For the current 2021 course use the current school's guide and criteria; the 2029 inquiry criteria belong to a different assessment version.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Three independent measurements are 4,6,8. Find their mean. · 三次独立测量值为 4,6,8。求其平均值。
Mean=(4+6+8)/3=6. · 平均值 = (4 + 6 + 8) / 3 = 6。
Match each part of a complete solution to its purpose. · 将完整解答的每个部分与其目的相匹配。
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · 假设用于论证模型的合理性；检查用于验证结果；解释用于将其与问题建立联系。
Use this in your course
- Current first-assessment-2021 Analysis and Approaches HL. This is authored concept support; the full guide is needed to certify every objective.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
A condition adopted to make a mathematical model possible and whose effect should be evaluated. Choose the relationship, show the method, check its assumptions and interpret the result.