After One Year at School

Statistics

Stages 1-4 CA - AC Stage 5 EA Stage 6 AA Stage 7 AM Level One Level Two Level Three Level Four Statistical investigation Statistical investigation Statistical investigation Statistical investigation • Conduct investigations using the statistical enquiry cycle: • Conduct investigations using the statistical enquiry cycle: • Conduct investigations using the statistical enquiry cycle: • Plan and conduct investigations using the statistical enquiry – posing and answering questions; – posing and answering questions; – gathering, sorting, and displaying multivariate category and cycle: – gathering, sorting and counting, and displaying category data; – gathering, sorting, and displaying category and whole-number whole number data and simple time-series data to answer – determining appropriate variables and data collection – discussing the results. data; questions; methods; – communicating findings based on the data. – identifying patterns and trends in context, within and between – gathering, sorting, and displaying multivariate category, Statistical literacy data sets; measurement, and time-series data to detect patterns, variations, • Compare statements with the features of simple data displays – communicating findings, using data displays. relationships, and trends; from statistical investigations or probability activities Statistical literacy – comparing distributions visually; undertaken by others. • Evaluate the effectiveness of different displays in representing – communicating findings, using appropriate displays. Probability the findings of a statistical investigation or probability activity Statistical literacy • Investigate simple situations that involve elements of chance, undertaken by others. • Evaluate statements made by others about the findings of recognizing equal and different likelihoods and acknowledging Probability statistical investigations and probability activities. uncertainty • Investigate simple situations that involve elements of chance Probability Statistical literacy . by comparing experimental results with expectations from • Investigate situations that involve elements of chance by models of all the outcomes, acknowledging that samples vary comparing experimental distributions with expectations from • Interpret statements made by others from statistical models of the possible outcomes, acknowledging variation and investigations and probability activities. . independence. Probability • Investigate situations that involve elements of chance, • Use simple fractions and percentages to describe probabilities. acknowledging and anticipating possible outcomes.

After one year After two years After three years By end of year 4 By end of year 5 By end of year 6 By end of year 7 By end of year 8 • investigate questions by • investigate questions by • investigate questions by • investigate questions by • investigate summary and • investigate summary and • investigate summary, • investigate summary, using the statistical using the statistical using the statistical using the statistical comparison comparison comparison, and comparison, and enquiry cycle (with support), enquiry cycle (with support), enquiry cycle (with support): enquiry cycle independently: questions by using the questions by using the relationship questions by relationship questions by statistical enquiry cycle: statistical enquiry cycle: using the statistical using the statistical enquiry cycle: enquiry cycle:

- gathering, displaying, - gathering, displaying and/or - gather and display category - gather and display category - gather, display, and - gather or access - gather or access - gather or access multivariate and/or counting category identifying similarities and and simple whole-number and simple whole-number identify patterns in category multivariate category and multivariate category and category, measurement, and data. differences in category data data and whole-number data whole-number data measurement data time-series data data;

- sort data into categories or - sort data and display it in - sort data and display it in intervals, display it in multiple ways, identifying multiple ways, identifying different ways, and identify patterns and variations patterns, variations, patterns relationships, and trends and using ideas about middle and spread where appropriate

- interpret displays in context; - interpret displays in context; - interpret results in context; - interpret results in context, - interpret results in context, - interpret results in context, accepting that samples accepting that samples vary identifying factors that vary; and have no effect on one produce uncertainty; another;

• describe the likelihoods of • compare and explain the • compare and explain the • order the likelihoods of • order the likelihoods of • order the likelihoods of • express as fractions the outcomes for a simple likelihoods of outcomes for a likelihoods of outcomes for a outcomes for simple outcomes for situations outcomes for situations likelihoods of outcomes for situation involving chance, simple situation involving simple situation involving situations involving chance, involving chance, involving chance, checking situations involving chance, using everyday language. chance. chance, acknowledging experimenting or listing all considering experimental for consistency between checking for consistency uncertainty. possible outcomes. results and models of all experimental results and between experimental results possible outcomes. models of all possible and models of all outcomes. possible outcomes. Level 1 The Statistical Enquiry Cycle: Statistical Investigations. AO1: Conduct investigations using the statistical enquiry cycle: – posing and answering questions;, gathering, sorting and counting, and displaying category data;, discussing the results. This means students will collect, sort and count data. Students will mostly encounter category data. This data arises from classifying, for example sorting data into colour categories. Simple number data generated through measurement with whole units is also manageable. Students should become familiar with displaying category data using pictographs, set diagrams and bar charts. Discussion should centre on similarities and differences between categories, for example “Six more people like hokey-pokey ice cream than vanilla”.

Statistical literacy. AO1: Interpret statements made by others from statistical investigations and probability activities. This means students will match comments made by others, usually their classmates, with the features of displays. These displays will be showing category data as pictographs, set diagrams, and bar charts.

Probability AO1: Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes. This means students will consider the possible outcomes of events. Possible outcomes can be listed, for example when tossing a coin the outcomes are heads and tails. The possible outcomes should be the basis for predictions rather than perceptions of luck.

Level 2 Statistical investigation AO1: Conduct investigations using the statistical enquiry cycle: – posing and answering questions, gathering, sorting, and displaying category and whole-number data;, communicating findings based on the data. At Level Two students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. The data involved may be either category data or whole number data. Category data arises from classifying and the interest is in how many of the data items fall in each category (called frequency). Colour and number of doors are two ways to classify cars that will produce category data. Whole number data comes from situations where only whole number values are possible, e.g. how many people live in your house? or from rounding of measures, e.g. how long is your pencil to the nearest centimetre? The most common graphs for displaying category data are pictographs, bar, strip and pie graphs. Whole number data can be displayed using dot plots or stem and leaf graphs. Students should communicate their result through reference to their data displays with an emphasis on similarity and difference, e.g. boys like outdoor games more than girls..

Statistical literacy AO1: Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others. This means students will critically consider comments made by others, usually their classmates, by referring to the features of displays on which the person is making claims. These displays will be showing either category data (pictographs, bar, strip, and pie graphs) or whole number data (dot plots or stem and leaf graphs). Students should also consider whether the chosen display/s best shows patterns in the data, e.g. strip and pie graphs show proportions well, pictographs and bar graphs show differences well.

Probability AO1: Investigate simple situations that involve elements of chance, recognizing equal and different likelihoods and acknowledging uncertainty This means students will recognise that probability is about the chance of outcomes occurring. Through activities that involve them personally, students at Level Two are expected to consider the possible outcomes of events in predicting what might occur. Through carrying out experiments, e.g. playing a game of chance, and making simple models of all the outcomes, e.g. lists or tables, students should recognise when outcomes appear to be equally likely, e.g. getting an even number when tossing a dice. Students should also recognise that where an event has more than one possible outcome they cannot predict the outcome with certainty, e.g. "it probably won’t be a six but it might be" when rolling a dice. Students should relate probability to events in their daily life, e.g. "it is very likely to rain today".

Level 3 Statistical investigation AO1: Conduct investigations using the statistical enquiry cycle: – gathering, sorting, and displaying multivariate category and whole number data and simple time-series data to answer questions; - identifying patterns and trends in context, within and between data sets; - communicating findings, using data displays. At Level Three students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. he data involved should be multivariate so it should include many variables, e.g. gender, age, height, eye colour, bedtime, etc., so that relationships between the variables can be explored. Students should be able to ask summary questions (of a variable), e.g. what is the usual range in heights for 10 year old students?, comparison questions, e.g. are girls taller than boys?, and relationship questions, e.g. do older students go to bed later than younger students. Data displays, including tables and graphs, expected at Level Three are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots and stem and leaf graphs for whole-number data, and simple line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns, including trends over time, in data as well as to communicate their findings to others. They should be able to justify their choice of display/s with reference to the patterns they wish to highlight.

Statistical Literacy AO1: Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others. This means students will learn to become critical consumers of statistically based information. This involves critically analysing the choice of display people have made to convey statistical information. At Level Three students should be able to gain information from all of the displays mentioned in Statistical Investigation, and be aware of the type of data each display is appropriate for and the kind of pattern or relationship that the display is best at communicating. For example, pictographs, and bar graphs highlight difference between frequencies of categories, e.g. four more students have blue eyes than green, while pie charts and strip graphs highlight proportions, e.g. spinner landed on red about one third of the time. Students should link the claims made by others with the appropriateness of display used.

Probability AO1: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, e.g. The chance is of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, e.g. March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, e.g. tossing a coin ten times, vary from one another, and from the proportions expected from a model, i.e. most times five heads do not come