NCEA+Level+1+Prob+Stats+Content

The standard [] NCEA []

NZMATHS: [] Probability Level 4 []

Quotes from []

=Level 4: Statistical literacy= AO1: Evaluate statements made by others about the findings of statistical investigations and probability activities. This means students will critically evaluate the strength of arguments proposed by others that is supported by statistical information. At Level Four students should consider features of the statistical investigation of others in weighing the strength of the findings. These features include the appropriateness of sampling methods (e.g. number, representativeness), quality of the data collection (e.g. questions asked, accuracy of measurement, fairness of the experiment), data analysis (technology use, choice of displays) and the extent to which claims made are supported by the evidence.

=Level 5 Statistical literacy= AO1: Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings.

=Level 6 Statistical literacy= AO1: Evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.

=Level 4: Probability= AO1: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), e.g. Take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample. AO2: Use simple fractions and percentages to describe probabilities. Simple fractions and percentages in this objective are common benchmarks like one half (50%), thirds (33.3% and 66.6%), quarters (25% and 75%), fifths (20%, 40%, 60%, 80%), tenths (10%, 30%, etc). Students should know that outcomes that are certain are described by fractions equalling one, including 100%, and outcomes that are impossible are described by fractions equalling zero, including 0%. In contrived situations involving elements of chance, e.g. totalling two dice, students should know that the count of all possible outcomes gives the denominator of a probability fraction, e.g. 36 possible outcomes, and the number of desired outcomes gives the numerator, e.g. there are 9 ways to get a total of either 2,4 or 6 so the probability is 9/36 or 1/4. In realistic situations where probabilities are estimated, e.g. the chance of a drawing pin landing safe, students are expected to accept variation from an exact fraction, e.g. 37 out of 100 were safe which is about or 33.3%..

=Level 5 Probability Year 11 12th August= A01: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. AO2: Calculate probabilities, using fractions, percentages, and ratios.

=Level 6 Probability= AO1: Investigate situations that involve elements of chance: comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size; calculating probabilities in discrete situations.

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