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1 | Index page | Index page URL | Original text/links | Concern rationale for change | Updated text/content | |||||||||||||

2 | Achievement Objective | whats new/changed plus associated bullet points | this document has been in place for several years and this is no longer needed | delete all what's new / changed; where necessary key elelements of this text has been added to indicators. | ||||||||||||||

3 | Achievement objective NA6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-1 | Uses a variety of methods, for example, equations, tables and graphs, in solving rates, ratios, and percentages problems. | addition of "numeracy strategies" requires the inclusion of numeracy as well as algebra strategies | Uses a variety of methods, for example, number strategies, equations, tables and graphs, in solving rates, ratios, and percentages problems. | |||||||||||||

4 | Achievement objective NA6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-1 | Investigates situations involving relationships of the form y = kx. | Both direct and inverse relationships are mentioned in the AO | Investigates situations involving relationships of the form y = kx and y=k/x. | |||||||||||||

5 | Achievement objective NA6-2 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-2 | Uses integer and fractional powers in solving problems. Uses number knowledge to find roots of numbers. | Clarifies level of fractional indices that are required | Uses integer powers in solving problems. Uses number knowledge, with fractional powers, to find square and cube roots that generate rational solutions, for example: (4/9)^0.5=√(4/9)=2/3 | |||||||||||||

6 | Achievement objective NA6-4 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-4 | Solves problems that can be modelled by a systematic approach, such as: trial and improvement making lists of possibilities and comparing table of values. | At this level trial and improvement needs to be clarified with respect to what is required. This is not random guess and checking of solutions | Solves problems that can be modelled by a systematic approach, such as: * making lists of possibilities and comparing * constructing a table of values (trial and improvement) | |||||||||||||

7 | Achievement objective NA6-5 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-5 | Uses algebraic manipulation skills to simplify expressions, including rational expressions involving exponents | Clarifies level of fractional indices that are required | Uses algebraic manipulation skills to simplify expressions, including rational expressions involving terms with positive integer exponents, for example: 25.5^(x+3) | |||||||||||||

8 | Achievement objective NA6-5 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-5 | Uses factorising and graphing for solving quadratic equations. | Offers a wider scope for solving problems | Uses factorising, graphical relationships and knowledge of parabolas for solving quadratic equations and inequations. | |||||||||||||

9 | Achievement objective NA6-5 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-5 | Solves problems that can be modelled by linear equations and inequations, quadratic and simple exponential equations and interprets solutions in context. | Clarifies level of quadratics and exponentials that are required | Solves problems that can be modelled by: -linear equations and inequations and interprets solutions in context. -quadratic equations (where neither a nor c are equal to 1) and interprets solutions in context. -simple exponential equations (of the form a^f(x)=b where f(x) is a linear function and a is a positive integer) and interprets solutions in context. | |||||||||||||

10 | Achievement objective NA6-7 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-NA6-7 | Demonstrates understanding of relationships, including linear, quadratic (y = ax2 + bx + c, where a is not zero), and simple exponential relationships (y=ax , where a is a positive integer). | Demonstrates understanding of relationships, including linear, quadratic (y = ax2 + bx + c, where neither a nor c are equal to 1), and simple exponential relationships (y=a^f(x) , where f(x) is a linear function) and a is a positive integer. | ||||||||||||||

11 | Achievement objective GM6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-1 | Selects appropriate units for measuring tasks. | Needs to use the measurements because the AO is about solving problems | Selects and uses appropriate units for measuring tasks. | |||||||||||||

12 | Achievement objective GM6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-1 | Estimates sensibly. | AO requires to students to use sensible estimates to solve problems | Uses estimates sensibly. | |||||||||||||

13 | Achievement objective GM6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-1 | Makes links to appropriate units GM6-2 and measurement of triangles GM6-6. | The link to GM6-6 is incorrect | Makes links to appropriate units GM6-2 | |||||||||||||

14 | Achievement objective GM6-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-2 | Understands the role of prefixes as conversion factors of base units, for example, kilo means one thousand, milli means one thousandth. | Understands the role of prefixes as conversion factors of base units, for example, kilo means one thousand, milli means one thousandth, GB means 10^9 bytes. | ||||||||||||||

15 | Achievement objective GM6-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-2 | Table of attributes, units and abbreviations | Not required and the existing table goes beyond the metric system of the AO | delete heading and table | |||||||||||||

16 | Achievement objective GM6-6 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-GM6-6 | Possible context elaborations | Bearings is a common context | add:Use trigonometric ratios and Pythagoras to find bearings | |||||||||||||

17 | Achievement objective M7-2 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-2 | exponential y = e^x or y = b^x | exponential including the use of base e | ||||||||||||||

18 | Achievement objective M7-2 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-2 | Demonstrates understanding of properties of functions, that is, one-to-one and many-to-one, and examples of relations that are not functions. | Greater clarity | Demonstrates understanding of properties of functions, that is, one-to-one and many-to-one, and examples of relations that are not functions (e.g. a circle). | |||||||||||||

19 | Achievement objective M7-2 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-2 | Demonstrates understanding of trigonometric functions and the relationships between the graph of functions, y= trig(x), and the graphs of their transformations of the form y= A trig (Bx) +C. Trig functions include sine, cosine and tangent with x in degrees. | To be consistent with another AO | Trig functions include sine, cosine and tangent with x in degrees or radians. | |||||||||||||

20 | Achievement objective M7-4 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-4 | Possible context elaborations (sample identities and sample exact values) | delete | ||||||||||||||

21 | Achievement objective M7-6 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-6 | Makes links between the concepts, properties, and manipulation of exponents and logarithms. | Clarity | Makes links between the concepts, properties, and manipulation of exponents and logarithms, and the inverse relationship between them. | |||||||||||||

22 | Achievement objective M7-6 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-6 | Solves problems that involve rational, exponential, and logarithmic algebraic expressions. Methods that could be used in solving problems include...: | Products and quotients are covered in Level 7, and product rule is needed to prove power rule. However for some reason they were removed in the old version without any reason given.They are not tested in Level 8 but assumed knowledge. | Add a further bullet point: simplifying expressions including logarithms involving the power rule and also products and quotients | |||||||||||||

23 | Achievement objective M7-7 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-7 | this AO 7-7 causes all sorts of problems as it contradicts the changes at Level 6. Forming exponential equations should be here and linear equations in isolation are not Level 7 | Linear and quadratic only are at level 6 so in isolation is not at the level 7 | Solves problems that can be modelled by a combination of linear or quadratics, simple trigonometric equations and interprets solutions in context | |||||||||||||

24 | Achievement objective M7-7 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-7 | Also in the context elaborations there are instances where x^2 is written as x2, which needs changing | typos | replace x2 by x^2 in four instances | |||||||||||||

25 | Achievement objective M7-8 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M7-8 | Solves problems that can be modelled by a system of linear inequations in two variables. | Contradicts AO | delete | |||||||||||||

26 | Achievement objective M8-7 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-7 | Solves quadratic and cubic equations with complex roots. | Clarification | Add in: These equations are likely to involve real coefficients so that solutions are complex conjugate pairs. | |||||||||||||

27 | Achievement objective M8-10 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-10 | Finds limits algebraically, graphically, and numerically by considering behaviour as: | Typo. Add the word 'such' in | Finds limits algebraically, graphically, and numerically by considering behaviour such as: | |||||||||||||

28 | Achievement objective M8-10 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-10 | Add in for clarification | Determines the continuity and differentiability of a function | ||||||||||||||

29 | Achievement objective M8-11 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-11 | Using numerical methods for finding areas under curves (rectangle rule, trapezium rule) | Add in Simpson's rule | Using numerical methods for finding areas under curves (rectangle rule, trapezium rule and Simpson’s rule)) | |||||||||||||

30 | Achievement objective M8-11 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-11 | Applications include: Finding areas under and between curves Rates of change Kinematics | Add in further applications | Applications include: Finding areas under and between curves (Related) Rates of change Kinematics Optimisation Points of Inflection Concavity | |||||||||||||

31 | Achievement objective M8-11 | https://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-M8-11 | Uses a variety of integration techniques for functions including: integral symbol ' / integral | Typo. This should not have integral symbols, but rather should have f | Uses a variety of integration techniques for functions including: f '(x)/f(x) | |||||||||||||

32 | Achievement objective S6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-1 | Poses investigative questions. | investigative questions should be posed for a purpose. | Poses investigative questions to solve a problem | |||||||||||||

33 | Achievement objective S6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-1 | Selects, uses and justifies variables and their measures to use in order to solve a problem. For example, if investigating how to improve the school canteen, students need to decide what ‘improve’ means and select data measures to capture improvement. | investigative questions should be posed for a purpose. | Selects, and, uses and justifies variables and their measures to answer the investigative question. For example, if investigating how to improve the food in the school canteen, students need to decide what ‘improve’ means and select data measures to capture improvement. | |||||||||||||

34 | Achievement objective S6-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-1 | Selects and uses appropriate sampling methods, for example, systematic and or simple random techniques (names drawn from a hat, dice, or random number generators). | Keep only simple random sampling at L6 as other methods come in at L7. | Selects and uses appropriate sampling methods, for example, simple random techniques (names drawn from a hat, dice, or random number generators). | |||||||||||||

35 | Achievement objective S6-1 | Uses a variety of data collection methods, such as web survey, face-to-face questionnaire, and automated computer logs. | More general examples of data collection methods rather than specifying types of questionnaire. Emphasise the importance of managing sources of variation. | Manages the data collection process using a variety of different of data collection methods, such as questionnaires and counts and measures. This includes identifying and managing possible sources of variation. | ||||||||||||||

36 | Achievement objective S6-1 | Data collection now in row 36 above. Emphasise the importance of data cleaning sorting and recategorising. | Preparing data for analysis (sorting, cleaning, recategorising) | |||||||||||||||

37 | Achievement objective S6-1 | Writes and presents a concise and informative report that includes communicating features in context; relevant summary statistics, graphs and tables to support the findings of the investigation; quantitative and qualitative statements; informal inferences about a population from a sample; justified conclusions. | Emphasise the importance of visual evidence. Summary statistics must used to support observations, not just given. Statements must be in context. | Writes and presents a concise and informative report that includes: using visual evidence to communicate features in context; using relevant summary statistics, graphs and tables to support the contextual findings of the investigation; quantitative and qualitative statements; informal inferences about a population from a sample; justified conclusions. | ||||||||||||||

38 | Achievement objective S6-1 | No original text | These need to be added because the "what's new/changed" will be deleted. | Understanding sampling variation. | ||||||||||||||

39 | Achievement objective S6-1 | No original text | These need to be added because the "what's new/changed" will be deleted. | Providing alternative explanation for observed patterns in the data. | ||||||||||||||

40 | Achievement objective S6-1 | No original text | These need to be added because the "what's new/changed" will be deleted. | Contextual knowledge plays an important role in the entire statistical enquiry cycle. | ||||||||||||||

41 | Achievement objective S6-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-2 | No original text | Emphasises that probability as well as statistics is a focus here. | Evaluates claims made about probability situations. | |||||||||||||

42 | Achievement objective S6-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-2 | No original text | These need to be added because the "what's new/changed" will be deleted. | Evaluation of statistical reports in the media. | |||||||||||||

43 | Achievement objective S6-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-3 | Uses systematic lists, tables of outcomes, and tree diagrams with counts to solve probability problems in discrete situations. | two tables are used regularly at CL6 | Uses systematic lists, tables (including two-way tables), and tree diagrams with counts to solve probability problems in discrete situations. | |||||||||||||

44 | Achievement objective S6-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-3 | No original text | Intuitive simple conditional probability and expected number is easily understood at this level. | Calculates expected number and informal simple conditional probabilities from a two-way table. | |||||||||||||

45 | Achievement objective S6-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S6-3 | No original text | These need to be added because the "what's new/changed" will be deleted. | Appreciating the role of sample size, the connection between sample size and variation. | |||||||||||||

46 | Achievement objective S6-3 | No original text | These need to be added because the "what's new/changed" will be deleted. | Laying down foundations for the binomial distribution (discrete situations). | ||||||||||||||

47 | Achievement objective S7-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-1 | Makes statistical inferences.(1st occurrence) | correct terminology for sample to population inference at CL7 | Makes informal statistical inferences | |||||||||||||

48 | Achievement objective S7-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-1 | Makes statistical inferences.(2nd occurence) | correct terminology for experiments | suggestive statistical inferences | |||||||||||||

49 | Achievement objective S7-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-1 | statistical inferences (1st occurence) | correct terminology for sample to population inference at CL7 | informal statistical inferences | |||||||||||||

50 | Achievement objective S7-1 | statistical inferences (2nd occurence) | correct terminology for experiments | suggestive statistical inferences | ||||||||||||||

51 | Achievement objective S7-1 | Communicates findings in a report which includes: relevant summary statistics, graphs and tables to support the findings of the survey | The word "survey" in this bullet point is an error. The statistical inferences at L7 are informal. | Communicates findings in a report which includes: relevant summary statistics, graphs and tables to support the findings of the experiment. | ||||||||||||||

52 | Achievement objective S7-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-2 | Uses a scatterplot from a sample to make sensible predictions within the given data by plotting the trend informally by eye and showing likely variation band for a particular value of x, the explanatory variable. | This clarifies the meaning of "variation band". | Uses a scatterplot from a sample to make sensible predictions within the given data by plotting the trend informally by eye and showing likely variation band of response (y) values for a particular value of x, the explanatory variable. | |||||||||||||

53 | Achievement objective S7-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-2 | Uses an informal confidence interval to make an inference about the population median from sample data plot. | Informal confidence intervals at L7. | Uses an informal confidence interval to make an informal statistical inference about the population median from sample data plot. | |||||||||||||

54 | Achievement objective S7- 3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-3 | Calculates and interprets risk, selects baseline group, and calculates and interprets relative risk and writes a news clip reporting on findings. | this should be an example rather than a specification. | Calculates and interprets risk, selects baseline group, and calculates and interprets relative risk (eg writes a news clip reporting on findings) | |||||||||||||

55 | Achievement objective S7-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-3 | identifies whether risk applies personally and why. | We don't understand this bit. | delete | |||||||||||||

56 | Achievement objective S7-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-3 | In a media report on a survey or a poll, identifies sampling error and explains the connection among sample, population, sampling variability, and sampling error. | "between" is clearer than "among" | In a media report on a survey or a poll, identifies sampling error and explains the connection between sample, population, sampling variability, and sampling error. | |||||||||||||

57 | Achievement objective S7-3 | In a media report on a survey or a poll, identifies and evaluates, using critical questions (look under the heading critical questions in the work doc below), sampling methods and possible non-sampling errors such as self-selection, non response bias, behavioural considerations. | The reference to the doc below is unnecessary | In a media report on a survey or a poll, identifies and evaluates, using critical questions, sampling methods and possible non-sampling errors such as self-selection, non response bias, behavioural considerations. | ||||||||||||||

58 | Achievement objective S7-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-4 | Uses two-way frequency tables to solve simple probability problems, including starting to work with simple conditional probabilities. | This reflects the fact that students are working intuitively with simple conditional probabilities at L6. | Uses two-way frequency tables to solve simple probability problems, including working informally with conditional probabilities. | |||||||||||||

59 | Achievement objective S7-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-4 | Students learn that situations involving real data from statistical investigations can be investigated from a probabilistic perspective. | Students have learned this previously and have been working with probabilities from data at L6. | Students investigate probabilities from situations involving real data. | |||||||||||||

60 | Achievement objective S7-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S7-4 | No original text | These need to be added because the "what's new/changed" will be deleted. | Uses theoretical distributions such as the normal distribution to solve probability problems. | |||||||||||||

61 | Achievement objective S8-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-1 | Conducts surveys to find solutions to problems: | The purpose is to investigate. A solution may or may not be found. | Conducts surveys to investigate problems: | |||||||||||||

62 | Achievement objective S8-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-1 | Collects own survey data using a questionnaire. | Data may be collected in other ways than a questionnaire. | Collects own survey data. | |||||||||||||

63 | Achievement objective S8-1 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-1 | Uses existing data sets to find solutions to problems: | Gives additional option to reflect current statistical analysis. | add - (may use non-linear regression) | |||||||||||||

64 | Achievement objective S8-1 | linear regression for bivariate data additive models for time-series data | Gives additional option to reflect current statistical analysis. | add - (may use multiplicative models) | ||||||||||||||

65 | Achievement objective S8-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-2 | The approach to teaching confidence intervals may be entirely based on a simulation using technology, as will be the methods for resampling. | Reworded for clarity. | The approach to teaching confidence intervals may be entirely based on a resampling simulation using technology. | |||||||||||||

66 | Achievement objective S8-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-2 | See Census at School for further information and resources. | Remove text - redundant | ||||||||||||||

67 | Achievement objective S8-2 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-2 | determines and interprets confidence intervals in a range of situations and draws relevant conclusions with justification | Use of medians reflects current statistical practice. Central limit theorem is not used for confidence intervals. | determines and interprets confidence intervals in a range of situations (eg: the difference of means or medians) and draws relevant conclusions with justification | |||||||||||||

68 | Achievement objective S8-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-3 | The approach here is new to the statistics curriculum. It is based on making informed approximations or rules of thumb to interpret reported margins of error and is linked to confidence intervals. | No longer new to statistics. | Using informed approximations or rules of thumb to interpret reported margins of error linked to confidence intervals. | |||||||||||||

69 | Achievement objective S8-3 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-3 | No original text | new | Evaluate a wide range of statistically based reports. | |||||||||||||

70 | Achievement objective S8-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-4 | Students learn that some situations involving chance produce discrete numerical variables, that situations involving real data from statistical investigations can be investigated from a probabilistic perspective | students have learned earlier that data can be investigated from a probabilistic perspective and are now doing investigations into probabililty. | Students investigate probability situations involving real data using discrete and continuous numerical variables. | |||||||||||||

71 | Achievement objective S8-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-4 | Students learn that some situations involving chance produce discrete numerical variables, that situations involving real data from statistical investigations can be investigated from a probabilistic perspective. These have probability distributions. They can be investigated by making assumptions about the situation and applying probability rules and/or by doing repeated trials of the situation and collecting frequencies. | We think this is a clearer way of stating this | Students investigate probability situations involving real data using discrete and continuous numerical variables. They can be investigated by making assumptions about the situation and applying probability rules and/or by doing repeated trials of the situation and collecting frequencies. Students use random variables and their probability distributions. | |||||||||||||

72 | Achievement objective S8-4 | http://seniorsecondary.tki.org.nz/Mathematics-and-statistics/Achievement-objectives/AOs-by-level/AO-S8-4 | Interprets results of probability investigations, demonstrating understanding of the relationship between true probability (unknown and unique to the situation), model estimates (theoretical probability), and experimental estimates. | This is a better explanation of current understanding of model estimates of probability. | Interprets results of probability investigations, demonstrating understanding of the relationship between true probability (unknown and unique to the situation), model estimates (incorporating theoretical probability and assumptions about the situation), and experimental estimates. | |||||||||||||

73 | Achievement objective S8-4 | Selects and uses appropriate tools to solve problems in probability, including two-way tables, Venn diagrams, and tree diagrams, including combined events. | There are many types of tree diagram. This specifies that we are using probability trees. | Selects and uses appropriate tools to solve problems in probability, including two-way tables, Venn diagrams, and probability tree diagrams, including combined events. | ||||||||||||||

74 | Achievement objective S8-4 | Solves probability problems involving conditional probabilities, randomness, independence, and mutually exclusive events. | complementary events is a key probabililty concept that should be understood with mutually exclusive events. | Solves probability problems involving conditional probabilities, randomness, independence, complementary and mutually exclusive events. | ||||||||||||||

75 | Achievement objective S8-4 | Selects and uses an appropriate distribution to solve a problem, demonstrating understanding of the relationship between true probability (unknown and unique to the situation), model estimates (theoretical probability) and experimental estimates. | This is a better explanation of current understanding of model estimates of probability. | Selects and uses an appropriate distribution to solve a problem, demonstrating understanding of the relationship between true probability (unknown and unique to the situation), model estimates (combining theoretical probability and assumptions about the situation) and experimental estimates. | ||||||||||||||

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