YEAR 6 MATHS FOCUS
NUMBERS AND ALGEBRA
Addition & Subtraction
Learning Experience
Addition & Subtraction
ADDITION & SUBTRACTION
OUTCOME
A student:
MA3-5NA:
selects and applies appropriate strategies for addition and subtraction with counting numbers of any size
STRATEGIES | Written strategies using informal mental strategies (empty number line):
The difference can be shifted one unit to the left on an empty number line, so that 8000 − 673 becomes 7999 − 672, which is an easier subtraction to calculate.
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Written strategies using a formal algorithm (decomposition method):
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TEACHING POINTS | In Stage 3, mental strategies need to be continually reinforced. |
| Students may find recording (writing out) informal mental strategies to be more efficient than using formal written algorithms, particularly in the case of subtraction. |
| LANGUAGE | Students should be able to communicate using the following language: plus, sum, add, addition, increase, minus, the difference between, subtract, subtraction, decrease, equals, is equal to, operation, digit. When solving word problems, students should be encouraged to write a few key words on the left-hand side of the equals sign to identify what is being found in each step of their working, eg ‘amount to pay = …’, ‘change = …’. Refer also to language in Addition and Subtraction 1. |
Expectations of Attainment
Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123) | solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg ‘I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?’ {Critical and creative thinking} |
| – select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems {Problem Solving, Literacy, Information and communication technology capability, Critical and creative thinking} | |
| – explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method {Communicating, Problem Solving, Reasoning, Critical and creative thinking} | |
| – reflect on their chosen method of solution for a problem, considering whether it can be improved {Communicating, Reasoning, Critical and creative thinking} | |
| – give reasons why a calculator was useful when solving a problem {Communicating, Reasoning} | |
| record the strategy used to solve addition and subtraction word problems {Literacy} | |
| – use selected words to describe each step of the solution process {Communicating, Problem Solving, Literacy} |
Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) | round numbers appropriately when obtaining estimates to numerical calculations |
| use estimation to check the reasonableness of answers to addition and subtraction calculations, e.g. 1438 + 129 is about 1440 + 130 {Critical and creative thinking} |
Create simple financial plans (ACMNA106) | use knowledge of addition and subtraction facts to create a financial plan, such as a budget, eg organise a class celebration on a budget of $60 for all expenses {Personal and social capability, Work and enterprise} |
| – record numerical data in a simple spreadsheet {Communicating, Information and communication technology capability} | |
| – give reasons for selecting, prioritising and deleting items when creating a budget {Communicating, Reasoning, Critical and creative thinking, Personal and social capability, Work and enterprise} |
Learning Experience
To be added
STATISTICS AND PROBABILITY
Data
Chance
Data
DATA
OUTCOME
A student:
MA3-18SP:
uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables
| TEACHING POINTS | Data selected for interpretation can include census data, environmental audits of resources such as water and energy, and sports statistics. Also see Year 5 |
| LANGUAGE | Students should be able to communicate using the following language: data, collect, category, display, table, column graph, scale, axes, two-way table, side-by-side column graph, misleading, bias. |
Expectations of Attainment
Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147) | interpret data presented in two-way tables {Literacy, Civics and citizenship} |
| create a two-way table to organise data involving two categorical variables | |
| interpret side-by-side column graphs for two categorical variables, eg favourite television show of students in Year 1 compared to that of students in Year 6 {Literacy} | |
| interpret and compare different displays of the same data set to determine the most appropriate display for the data set | |
| – compare the effectiveness of different student-created data displays {Communicating} | |
| – discuss the advantages and disadvantages of different representations of the same data {Communicating, Critical and creative thinking, Ethical understanding} | |
| – explain which display is the most appropriate for interpretation of a particular data set {Communicating, Reasoning, Literacy, Critical and creative thinking} | |
| – compare representations of the same data set in a side-by-side column graph and in a two-way table {Reasoning, Critical and creative thinking} |
Interpret secondary data presented in digital media and elsewhere (ACMSP148) | interpret data representations found in digital media and in factual texts {Literacy, Information and communication technology capability} |
| – interpret tables and graphs from the media and online sources, eg data about different sports teams {Reasoning, Information and communication technology capability, Critical and creative thinking} | |
| – identify and describe conclusions that can be drawn from a particular representation of data {Communicating, Reasoning, Literacy} | |
| critically evaluate data representations found in digital media and related claims {Literacy, Information and communication technology capability. Critical and creative thinking, Personal and social capability, Ethical understanding} | |
| – discuss the messages that those who created a particular data representation might have wanted to convey {Communicating, Literacy, Critical and creative thinking, Personal and social capability, Ethical understanding, Civics and citizenship} | |
| – identify sources of possible bias in representations of data in the media by discussing various influences on data collection and representation, eg who created or paid for the data collection, whether the representation is part of an advertisement {Communicating, Reasoning, Literacy, Critical and creative thinking, Personal and social capability, Ethical understanding} | |
| – identify misleading representations of data in the media, eg broken axes, graphics that are not drawn to scale {Reasoning, Literacy, Information and communication technology capability, Critical and creative thinking, Personal and social capability, Ethical understanding} |
Describe and interpret different data sets in context (ACMSP120) | interpret line graphs using the scales on the axes {Literacy} |
| describe and interpret data presented in tables, dot plots, column graphs and line graphs, eg ‘The graph shows that the heights of all children in the class are between 125 cm and 154 cm’ {Literacy} | |
| – determine the total number of data values represented in dot plots and column graphs, eg find the number of students in the class from a display representing the heights of all children in the class {Problem Solving, Reasoning} | |
| – identify and describe relationships that can be observed in data displays, eg ‘There are four times as many children in Year 5 whose favourite food is noodles compared to children whose favourite food is chicken’ {Communicating, Reasoning, Literacy} | |
| – use information presented in data displays to aid decision making, eg decide how many of each soft drink to buy for a school fundraising activity by collecting and graphing data about favourite soft drinks for the year group or school {Reasoning, Critical and creative thinking} |
Chance
CHANCE
OUTCOME
A student:
MA3-19SP:
conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes
TEACHING POINTS | Random generators include coins, dice, spinners and digital simulators. |
| As the number of trials in a chance experiment increases, the observed probabilities should become closer in value to the expected probabilities. | |
| Refer also to background information in Chance 1. |
LANGUAGE | Students should be able to communicate using the following language: chance, event, likelihood, equally likely, experiment, outcome, expected outcomes, random, fair, trials, probability, expected probability, observed probability, frequency, expected frequency, observed frequency. |
| The term ‘frequency’ is used in this substrand to describe the number of times a particular outcome occurs in a chance experiment. In Stage 4, students will also use ‘frequency’ to describe the number of times a particular data value occurs in a data set. |
EXPECTATIONS OF ATTAINMENT
Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145) | assign expected probabilities to outcomes in chance experiments with random generators, including digital simulators, and compare the expected probabilities with the observed probabilities after both small and large numbers of trials {Information and communication technology capability} |
| – determine and discuss the differences between the expected probabilities and the observed probabilities after both small and large numbers of trials {Communicating, Reasoning, Literacy} | |
| – explain what happens to the observed probabilities as the number of trials increases {Communicating, Reasoning, Literacy} | |
| use samples to make predictions about a larger ‘population’ from which the sample comes, eg take a random sample of coloured lollies from a bag, calculate the probability of obtaining each colour of lolly when drawing a lolly from the bag, and use these probabilities and the total number of lollies in the bag to predict the number of each colour of lolly in the bag {Critical and creative thinking} | |
| – discuss whether a prediction about a larger population, from which a sample comes, would be the same if a different sample were used {Communicating, Reasoning, Literacy, Critical and creative thinking} |