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# Level 6 Achievement objectives

## Achievement objective NA6-1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• apply direct and inverse relationships with linear proportions.

### Indicators

• Uses a variety of methods, for example, number strategies, equations, tables and graphs, in solving rates, ratios, and percentages problems.
• Uses rates in solving problems, for example, speed, blood/alcohol levels, heart rate, pay rates, comparing rates, density.
• Uses ratios in solving problems, for example, scale factor, recipes, unit costs, comparing quantities.
• Uses percentages in solving problems, for example, percentage of a quantity, expressing a ratio as a percentage.
• Uses rates, ratios, and percentages in both directions, for example, inverse percentages (finding the original amount).
• Investigates situations involving relationships of the form y = kx and y=k/x.

## Achievement objective NA6-2

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• extend powers to include integers and fractions.

### Indicators

• 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.
• Works with numbers in standard form and moves flexibly between standard form and ordinary form.
• Uses number knowledge and technology when solving problems.

## Achievement objective NA6-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• apply everyday compounding rates.

### Indicators

• Identifies situations that can be modelled with compounding rates.
• Uses tables, formula and / or graphs to solve compounding rates problems.

## Achievement objective NA6-4

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• find optimal solutions, using numerical approaches.

### Indicators

• 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).
• Finds optimal solutions, which are solutions that maximise or minimise a quantity while meeting the constraints of the situation.

## Achievement objective NA6-5

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.

### Indicators

• Solves problems that can be modelled by linear equations and inequations, quadratic and simple exponential equations and interprets solutions in context.
• Uses algebraic manipulation skills to simplify expressions, including rational expressions involving terms with positive integer exponents, for example: 25.5^(x+3).
• Uses algebra and graphing for solving linear equations and inequations.
• Uses factorising, graphical re and knowledge of parabolas for solving quadratic equations and inequations.
• Uses number knowledge (not logarithms) for solving exponential equations.
• 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.
• Uses graphing and algebra for solving simultaneous equations.

## Achievement objective NA6-6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• generalise the properties of operations with rational numbers, including the properties of exponents.

### Indicators

• Uses algebra to describe the properties of operations (addition, subtraction, multiplication and division) as they apply to rational numbers, and exponents. For example, expanding, factorising, simplifying.
• Uses the properties of addition, subtraction, multiplication, division, and exponents in solving problems.
• Uses the operations on rational numbers without technology.

## Achievement objective NA6-7

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.

### Indicators

• Demonstrates understanding of relationships, including linear, quadratic (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 an integer.
• Makes connections between representations such as number patterns, spatial patterns, tables, equations, and graphs.
• Identifies and uses key features including gradient, intercepts, vertex, and symmetry.

## Achievement objective NA6-8

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• relate rate of change to the gradient of a graph.

### Indicators

• Interprets rates of change from contextual graphs and creates contextual graphs from descriptions:
• For example: distance-time graphs, filling a bath, roller coaster ride, growth of organisms, compound interest.

## Achievement objective GM6-1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• measure at a level of precision appropriate to the task.

### Indicators

• Selects and uses appropriate units for measuring tasks.
• Identifies limits of accuracy for a measurement.
• Uses estimates sensibly.
• Understands the effect of the accuracy of a measurement on subsequent calculations, for example, measuring lengths and using these to find areas and volumes.

## Achievement objective GM6-2

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• apply the relationships between units in the metric system, including the units for measuring different attributes and derived measures.

### Indicators

• Converts between units for the attributes given in the table below. (This includes converting between units for volume (capacity) and mass, and between simple derived units.)
• 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.
• Uses derived measures to describe rates, for example:
• speed (kilometres per hour km/h, metres per second m/s)
• fuel and energy consumption (litres per 100 kilometres L/100km, joules or calories per minute)
• unit price (cents or dollars per gram)
• density (kilograms per cubic metre, kg/m3, grams per cubic centimetre g/cm3).

## Achievement objective GM6-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• calculate volumes, including prisms, pyramids, cones, and spheres, using formulae.

### Indicators

• Models objects using 3D shapes.
• Solves problems involving finding volume(s).
• Uses volume formulae appropriately.

## Achievement objective GM6-4

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• deduce and apply the angle properties related to circles.

### Indicators

• Finds unknown angles in circles using angle properties, including:
• angle at centre is twice the angle at circumference on the same arc
• angles subtended by the same arc are equal
• radius perpendicular to the tangent
• angle in a semi-circle equals 90°
• each exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.
• Communicates reasoning, citing the angle properties used to solve problems.

## Achievement objective GM6-5

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• recognise when shapes are similar and use proportional reasoning to find an unknown length.

### Indicators

• Recognises similar shapes using their properties.
• Uses properties of similar shapes in solving problems:
• Matching angles are equal.
• Matching lengths are proportional.

## Achievement objective GM6-6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• use trigonometric ratios and Pythagoras’ theorem in two and three dimensions.

### Indicators

• Solves problems that can be modelled with right angle triangles.
• Uses trigonometric ratios to find lengths and angles in 2- and 3- dimensions.
• Uses Pythagoras’ theorem to find lengths in 2- and 3- dimensions.

## Achievement objective GM6-7

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• use a co-ordinate plane or map to show points in common and areas contained by two or more loci.

### Indicators

• Uses geometric constructions and/or technology to construct loci.
• Finds areas that meet set constraints on co-ordinate planes or maps.

## Achievement objective GM6-8

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• compare and apply single and multiple transformations.

### Indicators

• Reflects, rotates, enlarges and translates figures.
• Identifies and uses key features of transformations, such as centres and angles of rotation, centres of enlargement, scale factors, lines of symmetry, vectors.
• Links combinations of transformations to a single transformation with the same result.

## Achievement objective GM6-9

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• analyse symmetrical patterns by the transformations used to create them.

### Indicators

• Describes transformations used to create patterns using key features such as centres and angles of rotation, centres of enlargement, scale factors, lines of symmetry, and vectors.
• Knows and applies variant and invariant properties of transformations.

## Achievement objective S6-1

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• Plan and conduct investigations using the statistical enquiry cycle:

• A – justifying the variables and measures used
• B – managing sources of variation, including through the use of random sampling
• C – identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays
• D – making informal inferences about populations from sample data
• E – justifying findings, using displays and measures.

### Indicators

• Uses the statistical enquiry cycle to conduct investigations:
• Poses investigative questions to solve a problem.
• 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.
• Selects and uses appropriate sampling methods, for example, simple random techniques (names drawn from a hat, dice, or random number generators).
• 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.
• Preparing data for analysis (sorting, cleaning, recategorizing).
• Uses appropriate statistical graphs and tables to explore the data and communicates relevant detail and overall distributions.
• Explores summary, comparative, bivariate, and time series data:
• Links multiple representations and sees the connections between them.
• 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.
• Understanding sampling variation.
• Providing alternative explanation for observed patterns in the data.
• Contextual knowledge plays an important role in the entire statistical enquiry cycle.

## Achievement objective S6-2

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• evaluate statistical reports in the media by relating the displays, statistics, processes, and probabilities used to the claims made.

### Indicators

• Evaluates statistical reports using critical questions.
• Relates statistical process to claims made.
• Evaluation of statistical reports in the media.

## Achievement objective S6-3

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

• Investigate situations that involve elements of chance:
• A – comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size
• B – calculating probabilities in discrete situations.

### Indicators

A. Comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size:

B. Calculating probabilities in discrete situations:

• Uses systematic lists, tables (including two-way tables), and tree diagrams with counts to solve probability problems in discrete situations.
• Calculates expected number and informal simple conditional probabilities from a two-way table.

Last updated September 17, 2018