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 (0/00) and parts per million (ppm).
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 nth term of a quadratic sequence, e.g. 6, 11, 18, 27, ... ⇒ nth term = n2 + 2n + 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.
2] I can derive and use the nth term of a quadratic sequence, e.g. 6, 11, 18, 27, ... ⇒ nth term = n2 + 2n + 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.
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 (Constructions)
1] I can construct the circumscribed and the inscribed circle of a triangle.
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 (Coordinate Geometry)
1] I can find the coordinates of vertices of the cube and cuboid in 3D space.
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 (Assistive Technology & Other Resources)
1] I can write and use procedures in LOGO.
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.
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.
