NSW Syllabuses

# Mathematics K–10 - Stage 2 - Statistics and Probability Data

## Data 1

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM

selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-18SP

selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

### Content

• Students:
• Identify questions or issues for categorical variables; identify data sources and plan methods of data collection and recording (ACMSP068)
• recognise that data can be collected either by the user or by others
• identify possible sources of data collected by others, eg newspapers, government data-collection agencies, sporting agencies, environmental groups
• pose questions about a matter of interest to obtain information that can be recorded in categories
• predict and create a list of categories for efficient data collection in relation to a matter of interest, eg 'Which breakfast cereal is the most popular with members of our class?'
• identify issues for data collection and refine investigations, eg 'What if some members of our class don't eat cereal?' (Problem Solving)
• Collect data, organise it into categories, and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069)
• collect data and create a list or table to organise the data, eg collect data on the number of each colour of lollies in a packet
• use computer software to create a table to organise collected data, eg a spreadsheet (Communicating)
• use grid paper to assist in constructing graphs that represent data using one-to-one correspondence (Communicating)
• use the terms 'horizontal axis', 'vertical axis' and 'axes' appropriately when referring to column graphs (Communicating)
• use graphing software to enter data and create column graphs that represent data (Communicating)
• mark equal spaces on axes, name and label axes, and choose appropriate titles for column graphs (Communicating)
• choose an appropriate picture or symbol for a picture graph and state the key used (Communicating)
• describe and interpret information presented in simple tables, column graphs and picture graphs
• make conclusions about data presented in different data displays, eg 'Football is the most popular sport for students in Year 3 at our school' (Communicating, Reasoning)
• represent the same data set using more than one type of display and compare the displays
• discuss the advantages and/or disadvantages of different representations of the same data (Communicating, Reasoning)

### Background Information

Data could be collected from the internet, newspapers or magazines, as well as through students' surveys, votes and questionnaires.

In Stage 2, students should consider the use of graphs in real-world contexts. Graphs are frequently used to persuade and/or influence the reader, and are often biased.

One-to-one correspondence in a column graph means that one unit (eg 1 cm) on the vertical axis is used to represent one response/item.

Categorical data can be separated into distinct groups, eg colour, gender, blood type. Numerical data has variations that are expressed as numbers, eg the heights of students in a class, the number of children in families.

### Language

Students should be able to communicate using the following language: information, data, collect, category, display, symbol, list, table, column graph, picture graph, vertical columns, horizontal bars, equal spacing, title, key, vertical axis, horizontal axisaxes, spreadsheet.

Column graphs consist of vertical columns or horizontal bars. However, the term 'bar graph' is reserved for divided bar graphs and should not be used for a column graph with horizontal bars.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑18SP the sub-elements (and levels) of Interpreting and representing data (IRD1-IRD2, IRD4) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.

## Data 2

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-2WM

selects and uses appropriate mental or written strategies, or technology, to solve problems

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-18SP

selects appropriate methods to collect data, and constructs, compares, interprets and evaluates data displays, including tables, picture graphs and column graphs

### Content

• Students:
• Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)
• create a survey and related recording sheet, considering the appropriate organisation of categories for data collection
• choose effective ways to collect and record data for an investigation, eg creating a survey with a scale of 1 to 5 to indicate preferences (1 = don't like, 2 = like a little, 3 = don't know, 4 = like, 5 = like a lot) (Communicating, Problem Solving)
• refine survey questions as necessary after a small trial
• discuss and decide the most suitable question to investigate a particular matter of interest, eg by narrowing the focus of a question from 'What is the most popular playground game?' to 'What is the most popular playground game among Year 3 students at our school?' (Communicating, Reasoning)
• after conducting a survey, discuss and determine possible improvements to the questions or recording sheet (Communicating, Reasoning)
• compare the effectiveness of different methods of collecting and recording data, eg creating categories of playground games and using tally marks, compared to asking open-ended questions such as 'What playground game do you like to play?'
• discuss the advantages and/or disadvantages of open-ended questions in a survey, compared to questions with predetermined categories (Communicating, Reasoning)
• Construct suitable data displays, with and without the use of digital technologies, from given or collected data; include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)
• represent given or collected categorical data in tables, column graphs and picture graphs, using a scale of many-to-one correspondence, with and without the use of digital technologies
• discuss and determine a suitable scale of many-to-one correspondence to draw graphs for large data sets and state the key used, eg  = 10 people, if there are 200 data values (Communicating, Reasoning)
• use grid paper to assist in drawing graphs that represent data using a scale of many-to-one correspondence (Communicating)
• use data in a spreadsheet to create column graphs with appropriately labelled axes (Communicating, Problem Solving)
• mark equal spaces on axes, name and label axes, and choose appropriate titles for graphs (Communicating)
• Evaluate the effectiveness of different displays in illustrating data features, including variability (ACMSP097)
• interpret and evaluate the effectiveness of various data displays found in media and in factual texts, where displays represent data using a scale of many-to-one correspondence
• identify and discuss misleading representations of data (Communicating, Reasoning)
• discuss and compare features of data displays, including considering the number and appropriateness of the categories used, eg a display with only three categories (blue, red, other) for car colour is not likely to be useful (Communicating)
• discuss the advantages and disadvantages of different representations of the same categorical data, eg column graphs compared to picture graphs that represent data using scales of many-to-one correspondence (Communicating)

### Background Information

A scale of many-to-one correspondence in a picture graph or column graph uses one symbol or one unit to represent more than one item or response, eg  = 10 people, or 1 centimetre represents 5 items/responses.

### Language

Students should be able to communicate using the following language: data, collect, survey, recording sheet, rating scale, category, display, symbol, tally mark, table, column graph, picture graph, vertical columns, horizontal bars, scale, equal spacing, title, key, vertical axis, horizontal axis, axes, spreadsheet, misleading.

Refer also to language in Data 1.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA2‑18SP the sub-elements (and levels) of Interpreting and representing data (IRD2-IRD5) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.