## Educators' Guide for Pedagogy and Assessment

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### Learning Area: Mathematics

# Core Mathematics > LEVEL 8

### Learning Area Outcome: I can identify, interpret and analyse mathematical information, simplify and solve problems, assess risk and make informed decisions.

## Subject Focus: Mathematical Application

1] I can represent practical problems in familiar and unfamiliar contexts mathematically, for example, practical problems involving basic operations for fractions, percentages and decimals with converting between all three.

COGNITIVE LEARNING

2] I can identify and obtain necessary mathematical information to tackle a task, project or a mathematical problem.

3] I can select mathematical operations and strategies in an organised way to find solutions.

4] I can apply my knowledge of mathematical operations in a logical and organised way.

5] I can make decisions about ways to undertake a given mathematical project.

6] I can work as an individual or as part of a group on a given mathematical project.

INTERPERSONAL

7] I can produce a product or presentation to show the outcomes of project-based mathematical challenges.

8] I can discuss the development and outcome of a project.

INTERPERSONAL

9] I can apply the checking procedures at each stage of a mathematical process.

10] I can explain the contribution made by a mathematician to human advancement

11] I can use a calculator and a spreadsheet for tedious calculations involving whole numbers, fractions, decimals and percentages.

COGNITIVE LEARNING

2] I can identify and obtain necessary mathematical information to tackle a task, project or a mathematical problem.

3] I can select mathematical operations and strategies in an organised way to find solutions.

4] I can apply my knowledge of mathematical operations in a logical and organised way.

5] I can make decisions about ways to undertake a given mathematical project.

6] I can work as an individual or as part of a group on a given mathematical project.

INTERPERSONAL

7] I can produce a product or presentation to show the outcomes of project-based mathematical challenges.

8] I can discuss the development and outcome of a project.

INTERPERSONAL

9] I can apply the checking procedures at each stage of a mathematical process.

10] I can explain the contribution made by a mathematician to human advancement

*e.g. the work of Pythagoras.*11] I can use a calculator and a spreadsheet for tedious calculations involving whole numbers, fractions, decimals and percentages.

### Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

## Subject Focus: Number - The Number System

1] I can demonstrate the order or operations when calculating.

2] I can design and explain mathematical patterns.

3] I can present large numbers in expanded notation,

4] I can write large numbers in standard form and can use numbers in standard form in calculations.

WRITING

2] I can design and explain mathematical patterns.

3] I can present large numbers in expanded notation,

*e.g. 293 as 2x100*+*9x10+3*4] I can write large numbers in standard form and can use numbers in standard form in calculations.

WRITING

### Learning Area Outcome: I can calculate mentally, using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

## Subject Focus: Number - Numerical Calculations

1] I can work through simple situations involving percentage increases and decreases using a multiplying factor.

2] I can work out reverse percentage calculations.

COGNITIVE LEARNING

3] I can work out the number of repayments needed to repay a loan.

4] I can work out compound interest, appreciation and depreciation.

5] I can make estimations and approximations.

6] I can round numbers to a specified degree of approximation.

7] I can check the reasonableness of results.

8] I can make reasonable approximations and can use these approximations to check the calculations.

9] I can use rounded numbers to carry out rough approximations.

COGNITIVE LEARNING

10] I can calculate and convert between currencies.

11] I can calculate with units of measure between systems, using conversion tables and scales, and approximate conversion factors.

2] I can work out reverse percentage calculations.

COGNITIVE LEARNING

3] I can work out the number of repayments needed to repay a loan.

4] I can work out compound interest, appreciation and depreciation.

5] I can make estimations and approximations.

6] I can round numbers to a specified degree of approximation.

7] I can check the reasonableness of results.

8] I can make reasonable approximations and can use these approximations to check the calculations.

9] I can use rounded numbers to carry out rough approximations.

COGNITIVE LEARNING

10] I can calculate and convert between currencies.

11] I can calculate with units of measure between systems, using conversion tables and scales, and approximate conversion factors.

### Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

## Subject Focus: Algebra - Fundamentals of Algebra

1] I can construct formulae to solve word problems involving one or two operations.

2] I can evaluate expressions by substituting values.

3] I can construct formulae to solve word problems involving one or two operations.

4] I can extend patterns, sequences and relationships in mathematics.

5] I can use symbols, notation, graphs and diagrams to represent and communicate mathematical relationships and concepts.

6] I can understand, interpret and calculate the gradient of a line.

7] I can solve two simultaneous linear equations graphically.

8] I can interpret linear and non-linear graphs arising from real-life situations.

9] I can produce graphical representations of direct and inverse proportion to determine unknown quantities, including speed vs time.

LEARNING TO DO

10] I can work through situations leading to solutions of linear equations in one unknown.

2] I can evaluate expressions by substituting values.

3] I can construct formulae to solve word problems involving one or two operations.

4] I can extend patterns, sequences and relationships in mathematics.

5] I can use symbols, notation, graphs and diagrams to represent and communicate mathematical relationships and concepts.

6] I can understand, interpret and calculate the gradient of a line.

7] I can solve two simultaneous linear equations graphically.

8] I can interpret linear and non-linear graphs arising from real-life situations.

9] I can produce graphical representations of direct and inverse proportion to determine unknown quantities, including speed vs time.

LEARNING TO DO

10] I can work through situations leading to solutions of linear equations in one unknown.

### Learning Area Outcome: I understand and use various forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, Space and Measures - Measures

1] I can express any angle as a fraction of 360°.

2] I can use systems of measurement and interpret numbers on a range of measuring instruments, and choose and use appropriate units.

3] I can find the area and circumference of circles.

4] I can calculate the length of an arc and the area of sector as fractions of a circle.

5] I can calculate the area of compound shapes.

6] I can calculate the surface area and volume of a prism or cylinder.

7] I can demonstrate the difference between length, area and volume using appropriate formula and units of measurement.

8] I can calculate the surface area and volume of a prism or cylinder.

9] I can draw and use scale drawings to find the actual distances and areas.

10] I can estimate distance and then find the actual distances using Google Earth.

MANAGING LEARNING

11] I can use and apply Pythagoras' Theorem when solving 2D problems.

12] I can apply trigonometric ratios in right-angled triangles when solving problems.

2] I can use systems of measurement and interpret numbers on a range of measuring instruments, and choose and use appropriate units.

3] I can find the area and circumference of circles.

4] I can calculate the length of an arc and the area of sector as fractions of a circle.

5] I can calculate the area of compound shapes.

6] I can calculate the surface area and volume of a prism or cylinder.

7] I can demonstrate the difference between length, area and volume using appropriate formula and units of measurement.

8] I can calculate the surface area and volume of a prism or cylinder.

9] I can draw and use scale drawings to find the actual distances and areas.

10] I can estimate distance and then find the actual distances using Google Earth.

MANAGING LEARNING

11] I can use and apply Pythagoras' Theorem when solving 2D problems.

12] I can apply trigonometric ratios in right-angled triangles when solving problems.

### Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

## Subject Focus: Shape, Space and Measures - Euclidean Geometry

1] I can work out the size of the interior and exterior angles of convex polygons including regular polygons.

2] I can construct the locus of points which are at a fixed distance from a given point using a variety of methods including ruler and compasses and assistive technology.

COGNITIVE LEARNING

3] I can construct the locus of points which are equidistant from two given points using a variety of methods including ruler and compasses and assistive technology.

COGNITIVE LEARNING

2] I can construct the locus of points which are at a fixed distance from a given point using a variety of methods including ruler and compasses and assistive technology.

COGNITIVE LEARNING

3] I can construct the locus of points which are equidistant from two given points using a variety of methods including ruler and compasses and assistive technology.

COGNITIVE LEARNING

### Learning Area Outcome: I can describe the position and movement of shapes in 2D.

## Subject Focus: Shape, Space and Measures - Transformation Geometry

1] I can use the notions of similarity and congruence.

2] I can draw and describe reflections.

MANAGING LEARNING

3] I can draw and describe rotations.

MANAGING LEARNING

4] I can draw and describe translations using polygons.

MANAGING LEARNING

5] I can draw and describe enlargements.

MANAGING LEARNING

6] I understand that reflections, rotations and translations preserve length and angle.

7] I can understand that enlargements preserve anglebut not length.

COGNITIVE LEARNING

8] I can work out and use positive scale factors of enlargement.

2] I can draw and describe reflections.

MANAGING LEARNING

3] I can draw and describe rotations.

MANAGING LEARNING

4] I can draw and describe translations using polygons.

MANAGING LEARNING

5] I can draw and describe enlargements.

MANAGING LEARNING

6] I understand that reflections, rotations and translations preserve length and angle.

7] I can understand that enlargements preserve anglebut not length.

COGNITIVE LEARNING

8] I can work out and use positive scale factors of enlargement.

### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data Handling and Chance - Statistics

1] I can design a survey to generate quantitative data. PRACTICAL

2] I can construct and interpret a histogram with equal intervals from a grouped frequency table.

3] I can calculate the mean, mode, median and range from a frequency table.

4] I can calculate and estimate the mean, identify the modal class, the range and find the class interval in which the median lies for a grouped frequency table. PRACTICAL

2] I can construct and interpret a histogram with equal intervals from a grouped frequency table.

3] I can calculate the mean, mode, median and range from a frequency table.

4] I can calculate and estimate the mean, identify the modal class, the range and find the class interval in which the median lies for a grouped frequency table. PRACTICAL