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Science and society, grade 10 (3 units)

The mathematics of the news, of health and of elections: how to read information, process it and draw conclusions from it.Subjects

The topics, in order:

  • drawing conclusions from information: what the data say and what they do not, misleading graphs, surveys and samples;
  • different representations – words, a table, a graph and a formula – and moving between them; reading the graph of a process;
  • statistical processing: the measures of centre and choosing the right one, the weighted mean, grouped data;
  • probability in social and scientific contexts, the two-way table and the tree diagram;
  • statistics and probability: relative frequency as an estimate of probability.

There are two kinds of lessons:

  • Learning lessons – an explanation, solved examples and a few questions to try;
  • Practice lessons – questions only.

How the page works: Using a page.

  1. Drawing conclusions from informationLearningWhat to check in a chart before drawing a conclusion, a conclusion the data support and one they do not, absolute numbers against a rate per 1,000 people, and two things rising together – a third factor.
  2. Misleading graphsLearningAn axis that does not start at 0, an axis stretched upwards, a period chosen on purpose, a picture that grows in both directions and a pie chart adding up to more than 100% – and how to work out the real change.
  3. Surveys and samplesLearningPopulation and sample, an estimate for the whole population from a percent in the sample, a representative sample and a biased one, wording a question, and the margin of error of an election poll.
  4. Representations and moving between themLearningOne relation in words, a table, a graph and a formula; which representation answers which question; a scientific phenomenon as a formula – the temperature falls with height; and from a table to a formula.
  5. Reading the graph of a processLearningWhere a graph rises and falls, its maximum and minimum points, on the graph of a real process – a patient's temperature, the water in a reservoir, the temperature during a day; the average rate of change between two points; and a steep part – a fast change.
  6. Practice: information and representationsPracticeA rate per 1,000 residents, a chart whose axis does not start at 0, an estimate from a sample, the margin of error, the formula of a linear relation, reading the graph of a process, and a third factor.
  7. Measures of centre and choosing oneLearningThe mean, the median and the mode in real data: pay in a small company, what an outlier does to each measure, choosing the measure that fits the question, and the same data in two quotes.
  8. The weighted meanLearningThe weighted mean: a final mark by weights in percent, the mean of two groups of different sizes, the mean of a frequency table as a weighted mean, and the mark needed to reach a mean – by an equation.
  9. Grouped dataLearningData grouped in classes, the histogram and the modal class, the class middle and an estimate of the mean, the median's class, and from raw data to a table of classes.
  10. Practice: statistical processingPracticeThe mean, the median and the mode in data with an outlier, choosing the measure, the weighted mean, the mean of two groups, grouped data – an estimate of the mean and the median's class – and what a change in the data does to the measures.
  11. Probability in society and scienceLearningChoosing at random from a population: the probability is the population's share; blood groups, probability as a fraction, a decimal and a percent, the complement and "at least", and a raffle.
  12. Two stages: the two-way table and the treeLearningProbability from a two-way table of real data – out of the whole population and within one row; a medical test and a false positive; the tree diagram for two stages, and "at least once".
  13. Relative frequency as an estimate of probabilityLearningEstimating a probability from a lot of data: births, an experiment repeated many times, insurance and the expected count, what "70% rain" means, and when the estimate is poor.
  14. Practice: probability and statisticsPracticeChoosing at random from a population, the complement and "at least", probability from a two-way table and within a row, the tree diagram, drawing without putting back, a medical test, and estimating a probability from relative frequency.
  15. ReviewPracticeQuestions from the whole course: a rate per 1,000 residents, a misleading graph, a survey and its sampling error, representations and a formula, the rate of change, an outlier and choosing a measure, the weighted mean, grouped data, probability from a two-way table, and an estimate from relative frequency.
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