## Educators' Guide for Pedagogy and Assessment

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### Learning Area: Mathematics

# Mathematics > LEVEL 10

### 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 read and write Roman numerals.

2] I can represent numbers using different number bases, e.g. binary.

3] I can identify and name various number categories, e.g. natural numbers, integers, rational and real numbers.

4] I can predict particular patterns for the multiples of any number.

5] I can identify the LCM of more than three numbers.

6] I can identify the HCF of more than three numbers.

7] I can express surds in their simplest form.

8] I can develop the idea of prime numbers and semi-prime numbers in cryptography.

9] I can change recurring decimals into vulgar fractions.

10] I can describe per-mille (

11] I can deduce that there are an infinite number of fractions between any two consecutive integers.

2] I can represent numbers using different number bases, e.g. binary.

3] I can identify and name various number categories, e.g. natural numbers, integers, rational and real numbers.

4] I can predict particular patterns for the multiples of any number.

5] I can identify the LCM of more than three numbers.

6] I can identify the HCF of more than three numbers.

7] I can express surds in their simplest form.

8] I can develop the idea of prime numbers and semi-prime numbers in cryptography.

9] I can change recurring decimals into vulgar fractions.

10] I can describe per-mille (

^{0}/_{00}) and parts per million (ppm).11] I can deduce that there are an infinite number of fractions between any two consecutive integers.

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

## Subject Focus: Number - The number system (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets, computers & calculators)*and other learning resources to learn about numbers and their properties..### Learning Area Outcome: I can calculate mentally and 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 (Whole Numbers, Decimal Numbers & Fraction Numbers - The Four Operations)

1] I can compare written methods for working out multiplication and division.

### Learning Area Outcome: I can calculate mentally and 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 (Ratio & Proportion)

1] I can work out proportion problems involving three quantities.

### Learning Area Outcome: I can calculate mentally and 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 (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets, computers and calculators)*and other resources appropriate to this level to calculate and to learn about numerical calculations.### 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 can recognise and extend sequences such as Fibonacci and Triangular number sequences.

2] I can derive and use the n

3] I can work with arithmetic progressions and can find the sum of the first

4] I can work with geometric progressions and can find the sum of the first

5] I can expand brackets of the form (ax +b)

6] I can find the solution to an inequality or set of inequalities on a graph by shading the appropriate regions.

7] I can factorise expressions using the grouping method.

8] I can solve quadratic equations by completing the square.

9] I can plot the graph of higher order functions from a table of values.

10] I understand the relationship between the function

11] I can find an approximate value of the gradient of a curve at any point by drawing a tangent to that point.

12] I know that a logarithm is an index and can use simple logarithmic results such as

13] I can use the Factor Theorem to factorise cubic functions with factors of the form (x + a)(x + b)(x + c) where a, b and c are integers.

14] I can identify surds and can also rationalise the denominator.

2] I can derive and use the n

^{th}term of a quadratic sequence, e.g. 6, 11, 18, 27, ... ⇒*n*^{th}term =*n*^{2 }+ 2*n*+ 3.3] I can work with arithmetic progressions and can find the sum of the first

*n*terms of an arithmetic progression.4] I can work with geometric progressions and can find the sum of the first

*n*terms of a geometric progression.5] I can expand brackets of the form (ax +b)

^{n}where n is a positive integer using Pascal's triangle.6] I can find the solution to an inequality or set of inequalities on a graph by shading the appropriate regions.

7] I can factorise expressions using the grouping method.

8] I can solve quadratic equations by completing the square.

9] I can plot the graph of higher order functions from a table of values.

10] I understand the relationship between the function

*f*(*x*) and its graph and be able to identify what role the coefficients have in such functions.11] I can find an approximate value of the gradient of a curve at any point by drawing a tangent to that point.

12] I know that a logarithm is an index and can use simple logarithmic results such as

*log**ab = log a + log b*.13] I can use the Factor Theorem to factorise cubic functions with factors of the form (x + a)(x + b)(x + c) where a, b and c are integers.

14] I can identify surds and can also rationalise the denominator.

### 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 (Assistive Technology & Other Resources)

1] I can use assistive technology, (

*e.g. tablets and computers)*and other resources, (e.g. algebra blocks) appropriate to this level to learn about the fundamentals of algebra..### Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

## Subject Focus: Shape, space and measures – Measures (Angles)

1] I can derive the trigonometric ratios for 30°, 45° and 60°.

2] I can plot graphs of trigonometric functions and use them to solve simple trigonometric equations in conjunction with the CAST rule.

2] I can plot graphs of trigonometric functions and use them to solve simple trigonometric equations in conjunction with the CAST rule.

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

## Subject Focus: Shape, space and measures – Measures (Length, Area, Volume, Mass & Capacity)

1] I know the multiples of metric units such as deca, hecto, kilo, mega, giga and tera and subdivisions of metric units such deci, centi, milli, micro, nano and pico.

2] I can derive the formula A = ½ ab sin C.

2] I can derive the formula A = ½ ab sin C.

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

## Subject Focus: Shape, space and measures – Measures (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other resources (*e.g. 2D and 3D plastic shapes, measuring instruments)*appropriate to this level to learn about measures.### 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 (Triangles)

1] I can prove Pythagoras' theorem.

2] I can generate Pythagorean triples.

2] I can generate Pythagorean triples.

### 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 (3D Shapes)

1] I can use Euler's formula which staes that for any convex polyhedron, F + V - E = 2.

2] I can draw the net of any solid shape.

2] I can draw the net of any solid shape.

### 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 (Circles)

1] I can prove the circle theorems.

## Subject Focus: Shape, space and measures – Euclidean geometry (Constructions)

1] I can construct the circumscribed and the inscribed circle of a triangle.

## Subject Focus: Shape, space and measures – Euclidean geometry (Coordinate Geometry)

1] I can find the coordinates of vertices of the cube and cuboid in 3D space.

## Subject Focus: Shape, space and measures – Euclidean geometry (Assistive Technology & Other Resources)

1] I can write and use procedures in LOGO.

2] I can use assistive technology (

2] I can use assistive technology (

*e.g. tablets and computers)*and other resources (*e.g. 2D and 3D plastic shapes)*appropriate to this level to learn about properties of shapes.### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Reflections)

1] I can draw refections in any line.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Rotations)

1] I can draw and describe rotations of a simple shape about any point using angles of 90° and 180°.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Combining Transformations)

1] I can draw tessellations using more than one shape.

### Learning Area Outcome: I can describe position and movement of shapes in a plane.

## Subject Focus: Shape, space and measures – Transformation geometry (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other resources*(e.g. 2D and 3D plastic shapes)*appropriate to this level to learn about transformation geometry.### Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

## Subject Focus: Data handling and chance – Statistics

1] I can draw and interpret data from clustered column/bar charts and stacked column/bar charts.

2] I can explain what the standard deviation of a set of data represents.

3] I can find the standard deviation of a set of data.

4] I can draw scatter diagrams using pairs of data and recognise different types of correlation. I can draw the line of best fit and use it to estimate results.

2] I can explain what the standard deviation of a set of data represents.

3] I can find the standard deviation of a set of data.

4] I can draw scatter diagrams using pairs of data and recognise different types of correlation. I can draw the line of best fit and use it to estimate results.

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

## Subject Focus: Data handling and chance – Statistics (Assistive Technology & Other Resources)

1] I can use assistive technology (

*e.g. tablets and computers)*and other learning resources to learn about statistics.