Curriculum for Excellence Benchmarks: Fourth Level
Skills available for Scotland Fourth Level maths objectives
Section
Print skill plan
Number, money and measure
Estimation and rounding
Rounds answers to a specified significant figure.
Rounds answers to a specified significant figure.
Demonstrates that the context of the question needs to be considered when rounding.
Demonstrates that the context of the question needs to be considered when rounding.
Demonstrates the impact of inaccuracy and error, for example, the impact of rounding an answer before the final step in a multi-step calculation.
Demonstrates the impact of inaccuracy and error, for example, the impact of rounding an answer before the final step in a multi-step calculation.
Uses a given tolerance to decide if there is an allowable amount of variation of a specified quantity, for example, dimensions of a machine part, 235 mm ± 1 mm.
Uses a given tolerance to decide if there is an allowable amount of variation of a specified quantity, for example, dimensions of a machine part, 235 mm ± 1 mm.
Number and number processes
Interprets and solves multi-step problems using the four operations.
Interprets and solves multi-step problems using the four operations.
Applies the correct order of operations in all calculations, including those with brackets.
Applies the correct order of operations in all calculations, including those with brackets.
Powers and roots
Shows understanding that square roots of whole numbers can have positive and negative values, for example, √9 = ± 3.
Shows understanding that square roots of whole numbers can have positive and negative values, for example, √9 = ± 3.
Uses knowledge of the inverse relationship between powers and roots to evaluate whole number roots of any appropriate number, ∛27 = 3.
Uses knowledge of the inverse relationship between powers and roots to evaluate whole number roots of any appropriate number, ∛27 = 3.
Uses knowledge of mathematical notation to express numbers in scientific notation.
Uses knowledge of mathematical notation to express numbers in scientific notation.
Fractions, decimal fractions and percentages
Chooses the most efficient form of fractions, decimal fractions or percentages when making calculations.
Rational numbers
Percentages
Chooses the most efficient form of fractions, decimal fractions or percentages when making calculations.
Rational numbers
Percentages
Uses calculations to support comparisons, decisions and choices.
Rational numbers
Consumer maths
Uses calculations to support comparisons, decisions and choices.
Rational numbers
Consumer maths
Calculates the percentage increase or decrease of a value.
Calculates the percentage increase or decrease of a value.
Applies addition, subtraction and multiplication skills to solve problems involving fractions and mixed numbers.
Addition and subtraction
Multiplication
Applies addition, subtraction and multiplication skills to solve problems involving fractions and mixed numbers.
Addition and subtraction
Multiplication
Uses knowledge of proportion to solve problems in real-life which involve changes in related quantities.
Ratios and rates
Proportions
Direct proportions
Uses knowledge of proportion to solve problems in real-life which involve changes in related quantities.
Ratios and rates
Proportions
Direct proportions
Money
Applies understanding of credit and debit in relation to earnings and deductions.
Applies understanding of credit and debit in relation to earnings and deductions.
Uses budgeting skills to manage income effectively and justifies spending and saving choices.
Uses budgeting skills to manage income effectively and justifies spending and saving choices.
Calculates net income by selecting appropriate information.
Calculates net income by selecting appropriate information.
Compares a range of personal finance products.
Compares a range of personal finance products.
Communicates the impact of financial decisions.
Communicates the impact of financial decisions.
Applies knowledge of currency conversion to determine best value.
Applies knowledge of currency conversion to determine best value.
Time
Demonstrates effective time management skills, for example, working with different time zones or making plans, including across midnight.
Demonstrates effective time management skills, for example, working with different time zones or making plans, including across midnight.
Carries out calculations involving speed, distance and time involving decimal fraction hours.
Carries out calculations involving speed, distance and time involving decimal fraction hours.
Calculates time durations across hours, days and months.
Calculates time durations across hours, days and months.
Measurement
Demonstrates understanding of the impact of truncation and premature rounding.
Demonstrates understanding of the impact of truncation and premature rounding.
Calculates the area of kites, parallelograms and trapeziums.
Parallelograms
Trapeziums
Calculates the area of kites, parallelograms and trapeziums.
Parallelograms
Trapeziums
Uses formulae and calculates the surface area of cylinders, cuboids and triangular prisms.
Uses formulae and calculates the surface area of cylinders, cuboids and triangular prisms.
Calculates the volume of triangular prisms and cylinders using formulae.
Calculates the volume of triangular prisms and cylinders using formulae.
Mathematics – its impact on the world, past, present and future
Contributes to discussions and presentations on the role of mathematics in everyday life and in the workplace.
Contributes to discussions and presentations on the role of mathematics in everyday life and in the workplace.
Investigates the mathematical skills required for a range of careers, including those in STEM subjects.
Investigates the mathematical skills required for a range of careers, including those in STEM subjects.
Patterns and relationships
Determines a general formula for the nth term to describe a sequence and uses it to solve related problems, linear examples only.
Determines a general formula for the nth term to describe a sequence and uses it to solve related problems, linear examples only.
Calculates the gradient of lines in a coordinate diagram.
Calculates the gradient of lines in a coordinate diagram.
Draws conclusions about the gradient of a line, for example, 'does the ramp meet building regulations?'.
Draws conclusions about the gradient of a line, for example, 'does the ramp meet building regulations?'.
Communicates the gradient of vertical and horizontal lines and states the equation of these lines as x = a or y = b or equivalent.
Communicates the gradient of vertical and horizontal lines and states the equation of these lines as x = a or y = b or equivalent.
Uses a given formula to plot a straight line onto a Cartesian diagram.
Uses a given formula to plot a straight line onto a Cartesian diagram.
Expressions and equations
Expands brackets using the distributive law and simplifies.
Distributive property
Equivalent expressions
Expands brackets using the distributive law and simplifies.
Distributive property
Equivalent expressions
Solves an extended range of linear equations involving the distributive law, for example, ax ± b = cx ± d, where a, b, c and d are integers.
Solves an extended range of linear equations involving the distributive law, for example, ax ± b = cx ± d, where a, b, c and d are integers.
Solves linear inequalities, including on simple closed intervals.
Understand inequalities
One-step inequalities
Two-step inequalities
Solves linear inequalities, including on simple closed intervals.
Understand inequalities
One-step inequalities
Two-step inequalities
Solves problems by expressing the given information appropriately as an equation, in-equation or formula.
Solves problems by expressing the given information appropriately as an equation, in-equation or formula.
Evaluates algebraic expressions involving a bracket.
Evaluates algebraic expressions involving a bracket.
Factorises expressions with a numeric common factor.
Factorises expressions with a numeric common factor.
Shape, position and movement
Properties of 2D shapes and 3D objects
Calculates the length of any side of a right-angled triangle using the Theorem of Pythagoras.
Missing lengths
Perimeter
Word problems
Calculates the length of any side of a right-angled triangle using the Theorem of Pythagoras.
Missing lengths
Perimeter
Word problems
Calculates the size of an angle in a right-angled triangle using trigonometry.
Trigonometric ratios
Angle measures
Calculates the size of an angle in a right-angled triangle using trigonometry.
Trigonometric ratios
Angle measures
Calculates the length of a side in a right-angled triangle using trigonometry.
Trigonometric ratios
Side lengths
Calculates the length of a side in a right-angled triangle using trigonometry.
Trigonometric ratios
Side lengths
Uses the formula C = πD or C = 2πr to calculate the circumference of a circle.
Uses the formula C = πD or C = 2πr to calculate the circumference of a circle.
Uses the formula A = πr2 to calculate the area of a circle.
Uses the formula A = πr2 to calculate the area of a circle.
Calculates diameter and radius of a circle when given the area or circumference.
Calculates diameter and radius of a circle when given the area or circumference.
Angle, symmetry and transformation
Describes rotational properties of shapes, pictures and patterns, including the order of rotation.
Describes rotational properties of shapes, pictures and patterns, including the order of rotation.
Uses knowledge of rotational symmetry to complete designs.
Uses knowledge of rotational symmetry to complete designs.
Uses a four-quadrant Cartesian grid to read and plot coordinates.
Uses a four-quadrant Cartesian grid to read and plot coordinates.
Applies understanding of translation to reflect or translate an object on a four-quadrant grid.
Translations
Reflections
Applies understanding of translation to reflect or translate an object on a four-quadrant grid.
Translations
Reflections
Uses similarity to find unknown lengths of 2D shapes.
Uses similarity to find unknown lengths of 2D shapes.
Applies knowledge of the relationship between the tangent and radius to calculate sizes of missing angles.
Applies knowledge of the relationship between the tangent and radius to calculate sizes of missing angles.
Applies knowledge of triangles, angles and circles, including semi-circles, to solve problems.
Triangles
Angles
Circles
Compound figures
Applies knowledge of triangles, angles and circles, including semi-circles, to solve problems.
Triangles
Angles
Circles
Compound figures
Identifies transformation by reflection or translation of a point or shape on a grid.
Identifies transformation by reflection or translation of a point or shape on a grid.
Information handling
Data and analysis
Interprets raw and graphical data.
Tables and charts
Bar graphs
Pie charts
Scatter plots
Interprets raw and graphical data.
Tables and charts
Bar graphs
Pie charts
Scatter plots
Uses statistical language, for example, correlations, to describe identified relationships.
Uses statistical language, for example, correlations, to describe identified relationships.
Calculates the mean, median, mode and range of a data set.
Calculates the mean, median, mode and range of a data set.
Selects the most appropriate statistical diagram to display a given data set, for example, stem and leaf.
Selects the most appropriate statistical diagram to display a given data set, for example, stem and leaf.
Justifies the most appropriate statistical diagram to display a given data set.
Justifies the most appropriate statistical diagram to display a given data set.
Uses different types of charts to display discrete, continuous and grouped data appropriately.
Uses different types of charts to display discrete, continuous and grouped data appropriately.
Ideas of chance and uncertainty
Calculates the probability and determines the expected occurrence of an event.
Calculates the probability and determines the expected occurrence of an event.
Applies knowledge and skills in calculating probability to make predictions.
Applies knowledge and skills in calculating probability to make predictions.