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Skills available for South Africa grade 9 maths curriculum

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9.1 Numbers, Operations and Relationships

9.1.1 Whole numbers
- 9.1.1.a Properties of numbers
  - 9.1.1.a.1 Describe the real number system by recognising, defining and distinguishing properties of:
    - 9.1.1.a.1.1 natural numbers
      - Classify numbers (9-A.1)
    - 9.1.1.a.1.2 whole numbers
      - Classify numbers (9-A.1)
    - 9.1.1.a.1.3 integers
      - Classify numbers (9-A.1)
    - 9.1.1.a.1.4 rational numbers
      - Classify numbers (9-A.1)
    - 9.1.1.a.1.5 irrational numbers
      - Classify numbers (9-A.1)
- 9.1.1.b Calculations using whole numbers
  - 9.1.1.b.1 Revise calculations using all four operations on whole numbers, estimating and using calculators where appropriate
    - Add, subtract, multiply and divide integers (9-B.1)
- 9.1.1.c Calculation techniques
  - 9.1.1.c.1 Use a range of techniques to perform and check written and mental calculations of whole numbers including:
    - 9.1.1.c.1.1 long division
      - Add, subtract, multiply and divide integers (9-B.1)
    - 9.1.1.c.1.2 adding, subtracting and multiplying in columns
      - Add, subtract, multiply and divide integers (9-B.1)
    - 9.1.1.c.1.3 estimation
    - 9.1.1.c.1.4 rounding off and compensating
      - Add, subtract, multiply and divide integers (9-B.1)
    - 9.1.1.c.1.5 using a calculator
      - Add, subtract, multiply and divide integers (9-B.1)
- 9.1.1.d Multiples and factors
  - 9.1.1.d.1 Use prime factorisation of numbers to find LCM and HCF
- 9.1.1.e Solving problems
  - 9.1.1.e.1 Solve problems in contexts involving
    - 9.1.1.e.1.1 ratio and rate
    - 9.1.1.e.1.2 direct and indirect proportion
  - 9.1.1.e.2 Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:
    - 9.1.1.e.2.1 profit, loss, discount and VAT
    - 9.1.1.e.2.2 budgets
    - 9.1.1.e.2.3 accounts
      - Simple interest (9-D.6)
      - Compound interest (9-D.7)
    - 9.1.1.e.2.4 loans
    - 9.1.1.e.2.5 Simple interest
      - Simple interest (9-D.6)
    - 9.1.1.e.2.6 hire purchase
    - 9.1.1.e.2.7 exchange rates
    - 9.1.1.e.2.8 commission
      - Percent of a number: VAT, discount and more (9-D.8)
      - Multi-step problems with percents (9-D.10)
    - 9.1.1.e.2.9 rentals
    - 9.1.1.e.2.10 compound interest
      - Compound interest (9-D.7)
9.1.2 Exponents
- 9.1.2.a Comparing and representing numbers in exponential form
  - 9.1.2.a.1 Revise compare and represent integers in exponential form
    - 9.1.2.a.1.1 compare and represent numbers in scientific notation
  - 9.1.2.a.2 Extend scientific notation to include negative exponents
    - Convert between standard and scientific notation (9-T.1)
    - Compare numbers written in scientific notation (9-T.2)
- 9.1.2.b Calculations using numbers in exponential form
  - 9.1.2.b.1 Revise the following general laws of exponents:
    - 9.1.2.b.1.1 a to the m power x aⁿ = a to the m power + ⁿ
      - Multiplication with exponents (9-S.4)
      - Multiply monomials (9-U.2)
    - 9.1.2.b.1.2 a to the m power ÷ aⁿ = a to the m power – ⁿ, if m > n
    - 9.1.2.b.1.3 (a to the m power)ⁿ = a to the m power x ⁿ (a x t)ⁿ = aⁿ x tⁿ
      - Powers of monomials (9-U.5)
    - 9.1.2.b.1.4 a° = 1
      - Exponents with integer bases (9-S.1)
      - Exponents with decimal and fractional bases (9-S.2)
  - 9.1.2.b.2 Extend the general laws of exponents to include:
    - 9.1.2.b.2.1 integer exponents
    - 9.1.2.b.2.2 a to the –m power = 1/a to the m power
  - 9.1.2.b.3 Perform calculations involving all four operations using numbers in exponential form, using the laws of exponents
- 9.1.2.c Solving problems
  - 9.1.2.c.1 Solve problems in contexts involving numbers in exponential form, including scientific notation
    - Compound interest (9-D.7)
9.1.3 Integers
- 9.1.3.a Calculations with integers
  - 9.1.3.a.1 Revise:
    - 9.1.3.a.1.1 perform calculations involving all four operations with integers
    - 9.1.3.a.1.2 perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers
- 9.1.3.b Properties of integers
  - 9.1.3.b.1 Revise:
    - 9.1.3.b.1.1 Commutative, associative and distributive properties of addition and multiplication for integers
    - 9.1.3.b.1.2 additive and multiplicative inverses for integers
      - Properties of equality (9-I.4)
- 9.1.3.c Solving problems
  - 9.1.3.c.1 Solve problems in contexts involving multiple operations with integers
    - Word problems: mixed review (9-Z.1)
    - Consecutive integer problems (9-Z.3)
9.1.4 Common fractions
- 9.1.4.a Calculations with fractions
  - 9.1.4.a.1 All four operations with common fractions and mixed numbers
  - 9.1.4.a.2 All four operations, with numbers that involve the squares, cubes, square roots and cube roots of common fractions
    - Evaluate numerical expressions involving rational numbers (9-B.6)
    - Exponents with decimal and fractional bases (10-I.2)
- 9.1.4.b Calculation techniques
  - 9.1.4.b.1 Revise:
    - 9.1.4.b.1.1 convert mixed numbers to common fractions in order to perform calculations with them
      - Add and subtract rational numbers (9-B.4)
      - Multiply and divide rational numbers (9-B.5)
    - 9.1.4.b.1.2 use knowledge of multiples and factors to write fractions in the simplest form before or after calculations
    - 9.1.4.b.1.3 use knowledge of equivalent fractions to add and subtract common fractions
      - Add and subtract rational numbers (9-B.4)
    - 9.1.4.b.1.4 use knowledge of reciprocal relationships to divide common fractions
      - Multiply and divide rational numbers (9-B.5)
- 9.1.4.c Solving problems
  - 9.1.4.c.1 Solve problems in contexts involving common fractions, mixed numbers and percentages
- 9.1.4.d Equivalent forms
  - 9.1.4.d.1 Revise equivalent forms between:
    - 9.1.4.d.1.1 common fractions where one denominator is a multiple of another
      - Write fractions in lowest terms (8-D.2)
    - 9.1.4.d.1.2 common fraction and decimal fraction forms of the same number
      - Convert between decimals and fractions (9-A.4)
    - 9.1.4.d.1.3 common fraction, decimal fraction and percentage forms of the same number
      - Convert between percents, fractions and decimals (9-D.1)
9.1.5 Decimal fractions
- 9.1.5.a Calculations with decimal fractions
  - 9.1.5.a.1 Multiple operations with decimal fractions, using a calculator where appropriate
  - 9.1.5.a.2 Multiple operations with or without brackets, with numbers that involve the squares, cubes, square roots and cube roots of decimal fractions
    - Evaluate numerical expressions involving rational numbers (9-B.6)
    - Exponents with decimal and fractional bases (10-I.2)
- 9.1.5.b Calculation techniques
  - 9.1.5.b.1 Use knowledge of place value to estimate the number of decimal places in the result before performing calculations
  - 9.1.5.b.2 Use rounding off and a calculator to check results where appropriate
    - Round decimals and mixed numbers (8-D.4)
- 9.1.5.c Solving problems
  - 9.1.5.c.1 Solve problems in context involving decimal fractions
    - Word problems: mixed review (9-Z.1)
    - Word problems with money (9-Z.2)
- 9.1.5.d Equivalent forms
  - 9.1.5.d.1 Revise equivalent forms between:
    - 9.1.5.d.1.1 common fraction and decimal fraction forms of the same number
      - Convert between decimals and fractions (9-A.4)
    - 9.1.5.d.1.2 common fraction, decimal fraction and percentage forms of the same number
      - Convert between percents, fractions and decimals (9-D.1)

9.2 Patterns, Functions and Algebra

9.2.1 Numeric and geometric patterns
- 9.2.1.a Investigate and extend patterns
  - 9.2.1.a.1 Investigate and extend numeric and geometric patterns looking for relationships between numbers, including patterns:
    - 9.2.1.a.1.1 represented in physical or diagram form
    - 9.2.1.a.1.2 not limited to sequences involving a constant difference or ratio
    - 9.2.1.a.1.3 of learner's own creation
    - 9.2.1.a.1.4 represented in tables
      - Complete a function table from an equation (9-O.9)
    - 9.2.1.a.1.5 represented algebraically
      - Evaluate variable expressions for number sequences (9-N.4)
      - Complete a function table from an equation (9-O.9)
  - 9.2.1.a.2 Describe and justify the general rules for observed relationships between numbers in own words or in algebraic language
9.2.2 Functions and relationships
- 9.2.2.a Input and output values
  - 9.2.2.a.1 Determine input values, output values or rules for patterns and relationships using:
- 9.2.2.b Equivalent forms
  - 9.2.2.b.1 Determine, interpret and justify equivalence of different descriptions of the same relationship or rule presented:
    - 9.2.2.b.1.1 verbally
    - 9.2.2.b.1.2 in flow diagrams
    - 9.2.2.b.1.3 in tables
      - Relations: convert between tables, graphs, mappings and lists of points (9-O.1)
      - Write an equation in y=mx+c form from a table (9-Q.9)
    - 9.2.2.b.1.4 by formulae
    - 9.2.2.b.1.5 by equations
    - 9.2.2.b.1.6 by graphs on a Cartesian plane
9.2.3 Algebraic expressions
- 9.2.3.a Algebraic language
  - 9.2.3.a.1 Revise the following done in Grade 8:
    - 9.2.3.a.1.1 recognize and identify conventions for writing algebraic expressions
    - 9.2.3.a.1.2 identify and classify like and unlike terms in algebraic expressions
      - Model polynomials with algebra tiles (9-V.2)
    - 9.2.3.a.1.3 recognize and identify coefficients and exponents in algebraic expressions
      - Identify terms and coefficients (8-W.9)
  - 9.2.3.a.2 Recognize and differentiate between monomials, binomials and trinomials
    - Identify monomials (9-U.1)
    - Polynomial vocabulary (9-V.1)
- 9.2.3.b Expand and simplify algebraic expressions
  - 9.2.3.b.1 Revise the following done in Grade 8, using the commutative, associative and distributive laws for rational numbers and laws of exponents to:
    - 9.2.3.b.1.1 add and subtract like terms in algebraic expressions
    - 9.2.3.b.1.2 multiply integers and monomials by:
      - 9.2.3.b.1.2.a monomials
        
        Multiply monomials (9-U.2)
      - 9.2.3.b.1.2.b binomials
        
        Multiply a polynomial by a monomial (9-V.6)
      - 9.2.3.b.1.2.c trinomials
        
        Multiply a polynomial by a monomial (9-V.6)
    - 9.2.3.b.1.3 divide the following by integers or monomials:
      - 9.2.3.b.1.3.a monomials
        
        Divide monomials (9-U.3)
      - 9.2.3.b.1.3.b binomials
      - 9.2.3.b.1.3.c trinomials
    - 9.2.3.b.1.4 simplify algebraic expressions involving the above operations
    - 9.2.3.b.1.5 Determine the squares, cubes, square roots and cube roots of single algebraic terms or like algebraic terms
      - Square and cube roots of monomials (8-AA.10)
      - Powers of monomials (9-U.5)
    - 9.2.3.b.1.6 Determine the numerical value of algebraic expressions by substitution
      - Evaluate variable expressions involving integers (9-B.3)
      - Evaluate variable expressions involving rational numbers (9-B.7)
  - 9.2.3.b.2 Extend the above algebraic manipulations to include:
    - 9.2.3.b.2.1 Multiply integers and monomials by polynomials
      - Multiply a polynomial by a monomial (9-V.6)
    - 9.2.3.b.2.2 Divide polynomials by integers or monomials
    - 9.2.3.b.2.3 The product of two binomials
    - 9.2.3.b.2.4 The square of a binomial
      - Multiply two binomials: special cases (9-V.9)
- 9.2.3.c Factorize algebraic expressions
  - 9.2.3.c.1 Factorize algebraic expressions that involve:
    - 9.2.3.c.1.1 common factors
      - Sort factors of expressions (8-W.10)
      - Factorise out a monomial (9-W.2)
    - 9.2.3.c.1.2 difference of two squares
      - Factorise quadratics: differences of squares (9-W.6)
    - 9.2.3.c.1.3 trinomials of the form:
      - 9.2.3.c.1.3.a x² + bx + c
        
        Factorise quadratics with leading coefficient 1 (9-W.3)
      - 9.2.3.c.1.3.b ax² + bx + c, where a is a common factor.
  - 9.2.3.c.2 Simplify algebraic expressions that involve the above factorisation processes.
  - 9.2.3.c.3 Simplify algebraic fractions using factorisation.
9.2.4 Algebraic equations
- 9.2.4.a Equations
  - 9.2.4.a.1 Revise the following done in Grade 8:
    - 9.2.4.a.1.1 set up equations to describe problem situations
      - Write variable equations (9-J.4)
      - Write an equation in y=mx+c form from a word problem (9-Q.10)
    - 9.2.4.a.1.2 analyse and interpret equations that describe a given situation
    - 9.2.4.a.1.3 solve equations by inspection
      - Does x satisfy the equation? (9-J.5)
    - 9.2.4.a.1.4 using additive and multiplicative inverses
    - 9.2.4.a.1.5 using laws of exponents
      - Solve equations involving squares and square roots (8-F.9)
    - 9.2.4.a.1.6 determine the numerical value of an expression by substitution.
    - 9.2.4.a.1.7 use substitution in equations to generate tables of ordered pairs
      - Complete a function table from an equation (9-O.9)
  - 9.2.4.a.2 Extend solving equations to include:
    - 9.2.4.a.2.1 using factorisation
    - 9.2.4.a.2.2 equations of the form: a product of factors = 0
      - Solve a quadratic equation using the zero product property (10-O.4)
9.2.5 Graphs
- 9.2.5.a Interpreting graphs
  - 9.2.5.a.1 Revise the following done in Grade 8:
    - 9.2.5.a.1.1 analyse and interpret global graphs of problem situations, with a special focus on the following trends and features:
      - 9.2.5.a.1.1.a linear or non-linear
        
        Identify linear functions (9-Q.1)
      - 9.2.5.a.1.1.b constant, increasing or decreasing
      - 9.2.5.a.1.1.c maximum or minimum
      - 9.2.5.a.1.1.d discrete or continuous
  - 9.2.5.a.2 Extend the above with special focus on the following features of linear graphs:
    - 9.2.5.a.2.1 x-intercept and y-intercept
      - Find the gradient and y-intercept of a linear equation (9-Q.5)
      - Standard form: find x- and y-intercepts (9-Q.16)
    - 9.2.5.a.2.2 gradient
- 9.2.5.b Drawing graphs
  - 9.2.5.b.1 Revise the following done in Grade 8:
    - 9.2.5.b.1.1 draw global graphs from given descriptions of a problem situation, identifying features listed above.
    - 9.2.5.b.1.2 use tables of ordered pairs to plot points and draw graphs on the Cartesian plane
      - Complete a table and graph a linear function (9-Q.13)
  - 9.2.5.b.2 Extend the above with special focus on:
    - 9.2.5.b.2.1 drawing linear graphs from given equations
    - 9.2.5.b.2.2 determining equations from given linear graphs
      - Write an equation in y=mx+c form from a graph (9-Q.7)
      - Point-gradient form: write an equation from a graph (9-Q.22)

9.3 Space and Shape (Geometry)

9.3.1 Geometry of 2D shapes
- 9.3.1.a Classifying 2D shapes
  - 9.3.1.a.1 Revise properties and definitions of triangles in terms of their sides and angles, distinguishing between:
    - 9.3.1.a.1.1 equilateral triangles
      - Classify triangles (8-O.2)
    - 9.3.1.a.1.2 isosceles triangles
      - Classify triangles (8-O.2)
    - 9.3.1.a.1.3 right-angled triangles
      - Classify triangles (8-O.2)
  - 9.3.1.a.2 Revise and write clear definitions of quadrilaterals in terms of their sides, angles and diagonals, distinguishing between:
    - 9.3.1.a.2.1 parallelogram
      - Classify quadrilaterals (9-F.2)
    - 9.3.1.a.2.2 rectangle
      - Classify quadrilaterals (9-F.2)
    - 9.3.1.a.2.3 square
      - Classify quadrilaterals (9-F.2)
    - 9.3.1.a.2.4 rhombus
      - Classify quadrilaterals (9-F.2)
    - 9.3.1.a.2.5 trapezium
      - Classify quadrilaterals (9-F.2)
    - 9.3.1.a.2.6 kite
      - Classify quadrilaterals (9-F.2)
- 9.3.1.b Similar and congruent triangles
  - 9.3.1.b.1 Through investigation, establish the minimum conditions for congruent triangles
    - Congruent triangles: SSS, SAS and ASA (9-F.11)
  - 9.3.1.b.2 Through investigation, establish the minimum conditions for similar triangles
    - Similarity rules for triangles (10-Y.7)
- 9.3.1.c Solving problems
  - 9.3.1.c.1 Solve geometric problems involving unknown sides and angles in triangles and quadrilaterals, using known properties of triangles and quadrilaterals, as well as properties of congruent and similar triangles.
9.3.2 Geometry of 3D objects
- 9.3.2.a Classifying 3D objects
  - 9.3.2.a.1 Revise properties and definitions of the 5 Platonic solids in terms of the shape and number of faces, the number of vertices and the number of edges
    - Three-dimensional figure vocabulary (10-U.1)
  - 9.3.2.a.2 Recognize and describe the properties of:
    - 9.3.2.a.2.1 spheres
      - Three-dimensional figure vocabulary (10-U.1)
    - 9.3.2.a.2.2 cylinders
      - Three-dimensional figure vocabulary (10-U.1)
- 9.3.2.b Building 3D models
  - 9.3.2.b.1 Use nets to create models of geometric solids, including:
    - 9.3.2.b.1.1 cubes
      - Nets of three-dimensional figures (9-F.7)
    - 9.3.2.b.1.2 prisms
      - Nets of three-dimensional figures (9-F.7)
    - 9.3.2.b.1.3 pyramids
      - Nets of three-dimensional figures (9-F.7)
    - 9.3.2.b.1.4 cylinders
      - Nets of three-dimensional figures (9-F.7)
9.3.3 Geometry of straight lines
- 9.3.3.a Angle relationships
  - 9.3.3.a.1 Revise and write clear descriptions of the relationship between angles formed by:
    - 9.3.3.a.1.1 perpendicular lines
      - Identify complementary, supplementary, vertical, adjacent and congruent angles (8-O.8)
    - 9.3.3.a.1.2 intersecting lines
      - Identify complementary, supplementary, vertical, adjacent and congruent angles (8-O.8)
    - 9.3.3.a.1.3 parallel lines cut by a transversal
      - Transversal of parallel lines (9-F.5)
  - 9.3.3.a.2 Solving problems
    - 9.3.3.a.2.1 Solve geometric problems using the relationships between pairs of angles described above
      - Find measures of complementary, supplementary, vertical and adjacent angles (8-O.9)
      - Transversal of parallel lines (9-F.5)
9.3.4 Transformation Geometry
- 9.3.4.a Transformations
  - 9.3.4.a.1 Recognize, describe and perform transformations with points, line segments and simple geometric figures on a co-ordinate plane, focusing on:
    - 9.3.4.a.1.1 reflection in the X-axis or Y-axis
    - 9.3.4.a.1.2 translation within and across quadrants
    - 9.3.4.a.1.3 reflection in the line y = x
  - 9.3.4.a.2 Identify what the transformation of a point is, if given the co-ordinates of its image
    - Identify reflections, rotations and translations (9-F.19)
- 9.3.4.b Enlargements and reductions
  - 9.3.4.b.1 Use proportion to describe the effect of enlargement or reduction on area and perimeter of geometric figures
    - Area and perimeter of similar figures (9-F.14)
    - Perimeter, area and volume: changes in scale (9-F.18)
  - 9.3.4.b.2 Investigate the co-ordinates of the vertices of figures that have been enlarged or reduced by a given scale factor
    - Dilations and scale factors (9-F.22)
9.3.5 Construction of geometric figures
- 9.3.5.a Constructions
  - 9.3.5.a.1 Accurately construct geometric figures appropriately using a compass, ruler and protractor, including bisecting angles of a triangle
  - 9.3.5.a.2 Construct angles of 30°, 45°, 60° and their multiples without using a protractor
    - Construct an equilateral triangle or regular hexagon (9-G.6)
- 9.3.5.b Investigating properties of geometric figures
  - 9.3.5.b.1 By construction, investigate the angles in a triangle, focusing on the relationship between the exterior angle of a triangle and its interior angles
  - 9.3.5.b.2 By construction, investigate sides, angles and diagonals in quadrilaterals, focusing on:
    - 9.3.5.b.2.1 the diagonals of rectangles, squares, parallelograms, rhombi and kites
    - 9.3.5.b.2.2 exploring the sum of the interior angles of polygons
  - 9.3.5.b.3 By construction, explore the minimum conditions for two triangles to be congruent

9.4 Measurement

9.4.1 Area and perimeter of 2D shapes
- 9.4.1.a Area and perimeter
  - 9.4.1.a.1 Use appropriate formulae and conversions between SI units, to solve problems and calculate perimeter and area of:
    - 9.4.1.a.1.1 polygons
      - Perimeter (9-F.3)
      - Area (9-F.4)
    - 9.4.1.a.1.2 circles
      - Perimeter (9-F.3)
      - Area (9-F.4)
  - 9.4.1.a.2 Investigate how doubling any or all of the dimensions of a 2D figure affects its perimeter and its area
    - Area and perimeter of similar figures (9-F.14)
9.4.2 Surface area and volume of 3D objects
- 9.4.2.a Surface area and volume
  - 9.4.2.a.1 Use appropriate formulae and conversions between SI units to solve problems and calculate the surface area, volume and capacity of:
    - 9.4.2.a.1.1 cubes
      - Volume (8-U.7)
      - Surface area of prisms and cylinders (8-U.8)
    - 9.4.2.a.1.2 rectangular prisms
      - Volume (8-U.7)
      - Surface area of prisms and cylinders (8-U.8)
    - 9.4.2.a.1.3 triangular prisms
      - Volume (8-U.7)
      - Surface area of prisms and cylinders (8-U.8)
    - 9.4.2.a.1.4 cylinders
      - Volume (8-U.7)
      - Surface area of prisms and cylinders (8-U.8)
  - 9.4.2.a.2 Investigate how doubling any or all the dimensions of right prisms and cylinders affects their volume
    - Volume and surface area of similar solids (9-F.17)
    - Perimeter, area and volume: changes in scale (9-F.18)
9.4.3 The Theorem of Pythagoras
- 9.4.3.a Solve problems using the Theorem of Pythagoras
  - 9.4.3.a.1 Use the Theorem of Pythagoras to solve problems involving unknown lengths in geometric figures that contain right-angled triangles
    - Pythagoras' theorem (9-F.23)
    - Pythagoras' theorem: word problems (9-F.24)

9.5 Data Handling

9.5.1 Collect, organize and summarize data
- 9.5.1.a Collect data
  - 9.5.1.a.1 Pose questions relating to social, economic, and environmental issues
  - 9.5.1.a.2 Select and justify appropriate sources for the collection of data
  - 9.5.1.a.3 Distinguish between samples and populations, and suggest appropriate samples for investigation
    - Identify representative, random and biased samples (8-CC.6)
    - Identify biased samples (9-BB.3)
  - 9.5.1.a.4 Select and justify appropriate methods for collecting data
    - Identify representative, random and biased samples (8-CC.6)
    - Identify biased samples (9-BB.3)
- 9.5.1.b Organize and summarize data
  - 9.5.1.b.1 Organize numerical data in different ways in order to summarize by determining:
    - 9.5.1.b.1.1 measures of central tendency
      - Mean, median, mode and range (9-BB.1)
    - 9.5.1.b.1.2 measures of dispersion, including extremes and outliers
  - 9.5.1.b.2 Organize data according to more than one criteria
9.5.2 Represent data
- 9.5.2.a Represent data
  - 9.5.2.a.1 Draw a variety of graphs by hand/technology to display and interpret data including:
    - 9.5.2.a.1.1 bar graphs and double bar graphs
      - Create bar graphs, line graphs and histograms (9-M.2)
    - 9.5.2.a.1.2 histograms with given and own intervals
      - Create bar graphs, line graphs and histograms (9-M.2)
    - 9.5.2.a.1.3 pie charts
      - Interpret pie charts (9-M.3)
    - 9.5.2.a.1.4 broken-line graphs
      - Create bar graphs, line graphs and histograms (9-M.2)
    - 9.5.2.a.1.5 scatter plots
9.5.3 Interpret, analyse, and report data
- 9.5.3.a Interpret data
  - 9.5.3.a.1 Critically read and interpret data represented in a variety of ways
  - 9.5.3.a.2 Critically compare two sets of data related to the same issue
    - Interpret bar graphs, line graphs and histograms (9-M.1)
    - Interpret box-and-whisker plots (9-M.5)
- 9.5.3.b Analyse data
  - 9.5.3.b.1 Critically analyse data by answering questions related to:
    - 9.5.3.b.1.1 data collection methods
      - Identify representative, random and biased samples (8-CC.6)
      - Identify biased samples (9-BB.3)
    - 9.5.3.b.1.2 summary of data
    - 9.5.3.b.1.3 sources of error and bias in the data
      - Identify biased samples (9-BB.3)
- 9.5.3.c Report data
  - 9.5.3.c.1 Summarize data in short paragraphs that include
    - 9.5.3.c.1.1 drawing conclusions about the data
    - 9.5.3.c.1.2 making predictions based on the data
    - 9.5.3.c.1.3 making comparisons between two sets of data
    - 9.5.3.c.1.4 identifying sources of error and bias in the data
    - 9.5.3.c.1.5 choosing appropriate summary statistics for the data (mean, median, mode, range)
    - 9.5.3.c.1.6 the role of extremes and outliers in the data
9.5.4 Probability
- 9.5.4.a Probability
  - 9.5.4.a.1 Consider situations with equally probable outcomes, and:
    - 9.5.4.a.1.1 determine probabilities for compound events using two-way tables and tree diagrams
    - 9.5.4.a.1.2 determine the probabilities for outcomes of events and predict their relative frequency in simple experiments
      - Theoretical probability (9-AA.1)
      - Experimental probability (9-AA.2)
    - 9.5.4.a.1.3 compare relative frequency with probability and explains possible differences
      - Experimental probability (9-AA.2)

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9.1 Numbers, Operations and Relationships

9.1.1 Whole numbers

9.1.1.a Properties of numbers

9.1.1.a.1 Describe the real number system by recognising, defining and distinguishing properties of:

9.1.1.a.1.1 natural numbers

9.1.1.a.1.2 whole numbers

9.1.1.a.1.3 integers

9.1.1.a.1.4 rational numbers

9.1.1.a.1.5 irrational numbers

9.1.1.b Calculations using whole numbers

9.1.1.b.1 Revise calculations using all four operations on whole numbers, estimating and using calculators where appropriate

9.1.1.c Calculation techniques

9.1.1.c.1 Use a range of techniques to perform and check written and mental calculations of whole numbers including:

9.1.1.c.1.1 long division

9.1.1.c.1.2 adding, subtracting and multiplying in columns

9.1.1.c.1.3 estimation

9.1.1.c.1.4 rounding off and compensating

9.1.1.c.1.5 using a calculator

9.1.1.d Multiples and factors

9.1.1.d.1 Use prime factorisation of numbers to find LCM and HCF

9.1.1.e Solving problems

9.1.1.e.1 Solve problems in contexts involving

9.1.1.e.1.1 ratio and rate

9.1.1.e.1.2 direct and indirect proportion

9.1.1.e.2 Solve problems that involve whole numbers, percentages and decimal fractions in financial contexts such as:

9.1.1.e.2.1 profit, loss, discount and VAT

9.1.1.e.2.2 budgets

9.1.1.e.2.3 accounts

9.1.1.e.2.4 loans

9.1.1.e.2.5 Simple interest

9.1.1.e.2.6 hire purchase

9.1.1.e.2.7 exchange rates

9.1.1.e.2.8 commission

9.1.1.e.2.9 rentals

9.1.1.e.2.10 compound interest

9.1.2 Exponents

9.1.2.a Comparing and representing numbers in exponential form

9.1.2.a.1 Revise compare and represent integers in exponential form

9.1.2.a.1.1 compare and represent numbers in scientific notation

9.1.2.a.2 Extend scientific notation to include negative exponents

9.1.2.b Calculations using numbers in exponential form

9.1.2.b.1 Revise the following general laws of exponents:

9.1.2.b.1.1 a to the m power x an = a to the m power + n

9.1.2.b.1.2 a to the m power ÷ an = a to the m power – n, if m > n

9.1.2.b.1.3 (a to the m power)n = a to the m power x n (a x t)n = an x tn

9.1.2.b.1.4 a° = 1

9.1.2.b.2 Extend the general laws of exponents to include:

9.1.2.b.2.1 integer exponents

9.1.2.b.2.2 a to the –m power = 1/a to the m power

9.1.2.b.3 Perform calculations involving all four operations using numbers in exponential form, using the laws of exponents

9.1.2.c Solving problems

9.1.2.c.1 Solve problems in contexts involving numbers in exponential form, including scientific notation

9.1.3 Integers

9.1.3.a Calculations with integers

9.1.3.a.1 Revise:

9.1.3.a.1.1 perform calculations involving all four operations with integers

9.1.3.a.1.2 perform calculations involving all four operations with numbers that involve the squares, cubes, square roots and cube roots of integers

9.1.3.b Properties of integers

9.1.3.b.1 Revise:

9.1.3.b.1.1 Commutative, associative and distributive properties of addition and multiplication for integers

9.1.3.b.1.2 additive and multiplicative inverses for integers

9.1.3.c Solving problems

9.1.3.c.1 Solve problems in contexts involving multiple operations with integers

9.1.4 Common fractions

9.1.4.a Calculations with fractions

9.1.4.a.1 All four operations with common fractions and mixed numbers

9.1.4.a.2 All four operations, with numbers that involve the squares, cubes, square roots and cube roots of common fractions

9.1.4.b Calculation techniques

9.1.4.b.1 Revise:

9.1.4.b.1.1 convert mixed numbers to common fractions in order to perform calculations with them

9.1.4.b.1.2 use knowledge of multiples and factors to write fractions in the simplest form before or after calculations

9.1.4.b.1.3 use knowledge of equivalent fractions to add and subtract common fractions

9.1.4.b.1.4 use knowledge of reciprocal relationships to divide common fractions

9.1.4.c Solving problems

9.1.4.c.1 Solve problems in contexts involving common fractions, mixed numbers and percentages

9.1.4.d Equivalent forms

9.1.4.d.1 Revise equivalent forms between:

9.1.2.b.1.1 a to the m power x aⁿ = a to the m power + ⁿ

9.1.2.b.1.2 a to the m power ÷ aⁿ = a to the m power – ⁿ, if m > n

9.1.2.b.1.3 (a to the m power)ⁿ = a to the m power x ⁿ (a x t)ⁿ = aⁿ x tⁿ