G1 Mathematics
Lessons in g1 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
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G1 Mathematics
- Number and proportionSuggested next · 11 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in number and proportion.
- Algebra and equationsSuggested next · 13 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in algebra and equations.
- Functions and graphsSuggested next · 2 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in functions and graphs.
- Geometry and reasoningSuggested next · 7 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 2 Mathematics 2021Build and connect the representations and methods in geometry and reasoning.
- Area, volume and mensurationSuggested next · 6 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in area, volume and mensuration.
- TrigonometrySuggested next · 2 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in trigonometry.
- Statistics and probabilitySuggested next · 5 lessonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020 · Normal (Technical) Secondary 2 Mathematics 2021 · Normal (Technical) Secondary 3–4 Mathematics 2022Build and connect the representations and methods in statistics and probability.
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Normal (Technical) Secondary 1 Mathematics 2020
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G1 Mathematics 2027
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Lessons in g1 mathematics. This course is still being developed; independent practice and assessment coverage is incomplete.
Learning goals
- Identify primes, factors and multiples
- Calculate with integers and rational numbers
- Compare and order numbers and representations
- Round, estimate and judge numerical accuracy
- Interpret integer power notation
- Represent and simplify ratios of quantities
- Share a quantity in a specified ratio
- Relate part-to-part ratios to part-to-whole fractions
- Model and solve direct or inverse proportional relationships
- Interpret a percentage relative to its base
- Calculate percentage changes and contextual amounts
- Recover a whole or original amount from a percentage part
- Use rate, speed, distance and time relationships
- Convert compatible measurement units
- Interpret algebraic notation and represented operations
- Evaluate an algebraic expression by substitution
- Represent a situation with algebraic expressions
- Express and use the general term of a sequence
- Simplify linear expressions by combining like terms
- Expand and factorise algebraic expressions
- Multiply and divide algebraic fractions with domain restrictions
- Change the subject of a formula
- Solve linear equations and check the solution
- Solve simultaneous equations by justified methods
- Solve quadratic equations by suitable methods
- Formulate, use and interpret a mathematical model
- Interpret and draw graphs of functions
- Read and plot ordered coordinate pairs
- Find and interpret a graph gradient
- Classify shapes by their properties
- Deduce unknown angles from geometric relationships
- Construct geometric figures from stated conditions
- Reason about congruence, similarity and scale factors
- Classify angles by their size
- Calculate and justify area and perimeter
- Calculate and justify volume and surface area
- Calculate circle, arc, sector and segment measures
- Use and justify Pythagoras’ theorem
- Use trigonometric ratios in right-angled triangles
- Read and interpret data displays
- Organise data and construct a suitable display
- Evaluate the purposes and limitations of data displays
- Calculate and interpret the arithmetic mean
- Find and interpret the mode and median
- Compare variability using appropriate measures
- Calculate event probabilities from an explicit sample space
Syllabus statements covered
- negative numbers and primes (exclude prime factorisation) • integers and their four operations • four operations on fractions and decimals (including negative fractions and decimals) • calculations with calculator, including squares, cubes, square roots and cube roots • representation and ordering of numbers on the number line • use of <, >, ⩽, ⩾ • approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) • use of index notation for integer powers • use of standard form A × 10^n, where n is an integer, and 1 ⩽ A < 10
- comparison between two or more quantities by ratio • dividing a quantity in a given ratio • ratios involving fractions and decimals • equivalent ratios • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion
- expressing percentage as a fraction or decimal • finding the whole given a percentage part • expressing one quantity as a percentage of another • comparing two quantities by percentage • percentages greater than 100% • finding one quantity given the percentage and the other quantity • increasing/decreasing a quantity by a given percentage • finding percentage increase/decrease
- rates and average rates (including the concepts of speed and average speed) • conversion of units (e.g. km/h to m/s)
- using letters to represent numbers • interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 ± y)/5 as (3 ± y) ÷ 5 or (1/5) × (3 ± y) • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic expressions • recognising and representing number sequences, including nth term for simple cases such as n + 3, 2n + 1 • addition and subtraction of linear expressions • simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2 • expansion of the product of two linear expressions • multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10) • changing the subject of a simple formula • finding the value of an unknown quantity in a given formula • factorisation of linear expressions ax + kay • factorisation of quadratic expressions x² + px + q. Exclude (a ± b)² = a² ± 2ab + b² and a² − b² = (a + b)(a − b), and addition/subtraction of algebraic fractions such as 1/x + 1/(x − 1).
- solving linear equations in one variable • solving simple fractional equations that reduce to linear equations, such as x/3 + (x − 2)/4 = 3 and 3/(x − 2) = 6 • graphs of linear equations in two variables ax + by = c • solving simultaneous linear equations in two variables by substitution and elimination or graphically • solving quadratic equations in one variable by formula • formulating a linear or quadratic equation in one variable or a pair of linear equations in two variables to solve problems
- Cartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables • linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c) • graphs of linear functions • the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) • graphs of quadratic functions and their properties ∗ positive or negative coefficient of x^2 ∗ maximum and minimum points ∗ symmetry
- right, acute, obtuse and reflex angles • vertically opposite angles, angles on a straight line and angles at a point • angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles • properties of triangles, special quadrilaterals • properties of perpendicular bisectors of line segments and angle bisectors • construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate
- line and rotational symmetry of plane figures • lines of symmetry • order of rotational symmetry • congruent and similar figures • properties of similar triangles and quadrilaterals: ∗ corresponding angles are equal ∗ corresponding sides are proportional
- area of triangle as ½ × base × height • area and circumference of circle • area of parallelogram and trapezium • problems involving perimeter and area of composite plane figures • volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere • conversion between cm^2 and m^2, and between cm^3 and m^3 • problems involving volume and surface area of composite solids • arc length as fraction of the circumference and sector area as fraction of the area of a circle
- use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths of three sides • use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles (including problems involving angles of elevation and depression)
- simple concepts in collecting, classifying and tabulating data • analysis and interpretation of: ∗ tables ∗ bar graphs ∗ pictograms ∗ line graphs ∗ pie charts ∗ dot diagrams ∗ histograms with equal class intervals ∗ cumulative frequency diagrams • purposes and use, advantages and disadvantages of the different forms of statistical representations • purposes and use of mean, mode and median • calculation of the mean, mode and median for a set of ungrouped data • percentiles, quartiles, range and interquartile range
- probability as a measure of chance • probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
- negative numbers and primes (exclude prime factorisation)
- integers and their four operations
- four operations on fractions and decimals (including negative fractions and decimals)
- calculations with calculator, including squares, cubes, square roots and cube roots
- representation and ordering of numbers on the number line
- use of <, >, ≤, ≥
- approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation)
- comparison between two or more quantities by ratio
- dividing a quantity in a given ratio
- ratios involving fractions and decimals
- equivalent ratios
- writing a ratio in its simplest form
- expressing percentage as a fraction or decimal
- finding the whole given a percentage part
- expressing one quantity as a percentage of another
- comparing two quantities by percentage
- percentages greater than 100%
- finding one quantity given the percentage and the other quantity
- increasing/decreasing a quantity by a given percentage
- finding percentage increase/decrease
- using letters to represent numbers
- interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y)
- evaluation of algebraic expressions and formulae
- recognising number sequences (including evaluating simple nth term like n + 3 and 2n + 1)
- translation of simple real-world situations into algebraic expressions
- right, acute, obtuse and reflex angles
- vertically opposite angles, angles on a straight line and angles at a point
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- line and rotational symmetry of plane figures
- lines of symmetry
- order of rotational symmetry
- area of triangle as ½ × base × height
- area and circumference of circle
- area of parallelogram and trapezium
- problems involving perimeter and area of composite plane figures
- volume and surface area of cube and cuboid
- conversion between cm² and m², and between cm³ and m³
- problems involving volume and surface area of composite solids
- simple concepts in collecting, classifying and tabulating data
- analysis and interpretation of: • tables • bar graphs • pictograms • line graphs • pie charts
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- direct and inverse proportion
- rates and average rates (including the concepts of speed and average speed)
- conversion of units (e.g. km/h to m/s)
- addition and subtraction of linear expressions
- simplification of linear expressions such as −2(3x − 5) + 4x; 2x/3 − 3(x − 5)/2
- solving linear equations in one variable
- formulating a linear equation in one variable to solve problems
- Cartesian coordinates in two dimensions
- graph of a set of ordered pairs as a representation of a relationship between two variables
- linear functions (y = ax + b)
- graphs of linear functions
- the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)
- properties of triangles and special quadrilaterals
- properties of perpendicular bisectors of line segments and angle bisectors
- construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractor where appropriate
- congruent and similar figures
- properties of similar triangles and quadrilaterals: • corresponding angles are equal • corresponding sides are proportional
- volume and surface area of prism and cylinder
- conversion between cm² and m², and between cm³ and m³
- use of Pythagoras’ theorem
- determining whether a triangle is right-angled given the lengths of three sides
- analysis and interpretation of: • dot diagrams • histograms with equal class intervals
- purposes and uses, advantages and disadvantages of the different forms of statistical representations
- purposes and uses of mean, mode and median
- calculation of the mean, mode and median for a set of ungrouped data
- probability as a measure of chance
- probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)
- use of index notation for integer powers
- use of standard form A × 10^n , where n is an integer, and 1 ≤ A < 10
- map scales (distance and area)
- recognising and representing number sequences (include finding an algebraic expression for the nth term for simple cases such as n + 3 and 2n + 1)
- expansion of the product of two linear expressions
- multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
- changing the subject of a simple formula
- finding the value of an unknown quantity in a given formula
- factorisation of linear expressions of the form ax + kay
- factorisation of quadratic expressions of the form x² + px + q. Exclude: use of (a ± b)² = a² ± 2ab + b² and a² − b² = (a + b)(a − b); addition and subtraction of algebraic fractions such as 1/x + 1/(x − 1)
- graphs of linear equations in two variables (ax + by = c )
- solving simple fractional equations that can be reduced to linear equations such as x/3 + (x − 2)/4 = 3; 3/(x − 2) = 6
- solving simultaneous linear equations in two variables by * substitution and elimination methods * graphical method
- formulating a pair of linear equations in two variables to solve problems
- solving quadratic equations in one variable by use of formula
- formulating a quadratic equation in one variable to solve problems
- quadratic functions (y = ax^2 + bx + c) <Sec 4>
- graphs of quadratic functions and their properties <Sec 4> • positive or negative coefficient of x^2 • maximum and minimum points • symmetry
- volume and surface area of pyramid, cone and sphere
- conversion between cm² and m², and between cm³ and m³
- arc length and sector area as fractions of the circumference and area of a circle
- use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles (including problems involving angles of elevation and depression)
- percentiles, quartiles, range and interquartile range
- analysis and interpretation of cumulative frequency diagrams