SCOPE AND SEQUENCE
WHAT ARE WE GOING TO LEARN?
GLO BAL THINKERS
Secondary Education
Mathematics
YEAR 1 YEAR 2
1 Natural numbers
• Numeral systems
• Large numbers
• Rounding natural numbers
• Basic operations with natural numbers
• Expressions with combined operations
2 Powers and roots
• Powers
• Powers of base 10. Uses
• Calculations with powers
• Square roots
3 Divisibility
• The relation of divisibility
• Multiples and divisors of a number
• Prime and composite numbers
• Decomposing a number into its prime factors
• Lowest common multiple
• Greatest common divisor
4 Integers
• Positive and negative numbers
• The set of integers
• Addition and subtraction with integers
• Addition and subtraction with brackets
• Multiplication and division of integers
• Combined operations
• Powers and roots of integers
5 Decimals
• The structure of decimals
• Addition, subtraction and multiplication with decimals
• Dividing decimals
• Square roots and decimal numbers
6 Fractions
• What are fractions?
• The relationship between fractions and decimals
• Equivalent fractions
• Some problems with fractions
7 Operating with fractions
• Reducing to a common denominator
• Adding and subtracting fractions
• Multiplying and dividing fractions
• Combined operations
• Some problems with fractions
8 Proportionality and percentages
• Proportionality between magnitudes
• Direct proportionality problems
• Inverse proportionality problems
• Percentages
• Percentage increases and decreases
9 Algebra
• Letters instead of numbers
• Algebraic expressions
• Equations
• First methods for solving equations
• Solving first-degree equations with one unknown
• Solving problems through equations
10 Lines and angles
• Basic elements of geometry
• Two important lines
• Angles
• Angle measures
• Operating with angle measures
• Angular relationships
• Angles in polygons
• Angles in a circumference
11 Geometric shapes
• Polygons and other plane shapes
• Symmetry in plane shapes
• Triangles
• Quadrilaterals
• Regular polygons and circumferences
• Cordovan triangle and related shapes
• Pythagorean theorem
• Applications of the Pythagorean theorem
• Three-dimensional shapes
• Polyhedra
• Solids of revolution
12 The metric system
• Magnitudes and measures
• The metric system
• Units of measurement for fundamental magnitudes
• Conversion of units
• Complex and simple amounts
• Measuring surface areas
13 Areas and perimeters
• Measuring quadrilaterals
• Measuring triangles
• Measuring polygons
• Measuring circles
• Calculating areas using the Pythagorean theorem
14 Graphs of functions
• Cartesian coordinates
• Points that provide information
• Points that are related
• Interpreting graphs
• Linear functions. Equation and representation
15 Statistics
• Statistical analysis process
• Frequency and frequency tables
• Statistical graphs
• Statistical parameters
• Position parameters
1 Natural numbers
• The set of natural numbers
• Operating with natural numbers
• The relation of divisibility
• Prime and composite numbers
• Lowest common multiple of two or more numbers
• Greatest common divisor of two or more numbers
2 Integers
• Positive and negative numbers
• The Z set of integers
• Operating with integers
• Powers of integers
• Roots of integers
3 Decimal numbers and fractions
• Decimal numbers
• Representing and ordering decimal numbers
• Operating with decimal numbers
• The square root of a decimal number
• Fractions
• Fractions and decimal numbers
4 Operating with fractions
• Adding and subtracting fractions
• Multiplying and dividing fractions
• Problems with fractions
• Powers and fractions
5 Proportionality and percentages
• Ratios and proportions
• Directly proportional magnitudes
• Inversely proportional magnitudes
• Problems of compound proportionality
• Problems of proportional distribution
• Percentages
• Problems with percentages
• Bank interest
6 Algebra
• Algebra: What do we use it for?
• Algebraic expressions
• Polynomials
• Notable products
7 Equations
• Equations: meaning and use
• Equations: elements and terminology
• Transposing terms
• Solving simple equations
• Equations with denominators
• General method for solving first-degree equations
• Solving problems using equations
• Second-degree equations
• Solving second-degree equations
8 Systems of equations
• First-degree equations with two unknowns
• Systems of linear equations
• Methods for solving linear systems
• Solving problems using systems of equations
9 Pythagorean theorem
• Pythagorean theorem
• Calculating a side when two are known
• Applications of the Pythagorean theorem
10 Similarity
• Similar shapes
• Plans, maps and models
• How to build similar shapes
• Thales’ theorem
• Similarity of right-angled triangles
• Applications of the similarity of triangles
11 Geometric shapes
• Prisms
• Pyramids
• Truncated pyramids
• Regular polyhedra
• Plane sections of polyhedra
• Cylinders
• Cones
• Truncated cones
• Spheres
• Sections of spheres, cylinders and cones
12 Measuring volume
• Units of volume
• Cavalieri’s principle
• Volume of a prism and a cylinder
• Volume of a pyramid and a truncated pyramid
• Volume of a cone and a truncated cone
• Volume of a sphere
13 Functions
• The concept of function
• Increase, decrease, maximums and minimums
• Functions shown in tables of values
• Functions from their equation
• Proportionality functions: y = mx
• The slope of a line
• Linear functions: y = mx + n
• Constant functions: y = k
14 Statistics
• Making a table and its graph
• Location parameters
• Dispersion parameters
• Position parameters
• Two-way tables
15 Chance and probability
• Random events
• Probability of an event
• Assigning probabilities to regular experiments
• Some strategies for calculating probabilities
1 Numbers to count, numbers for measurements
• Natural numbers
• Other ways of counting
• Integers
• Fractions
• Operations with fractions
• Decimal numbers
• Fractions and decimals with the calculator
2 Powers and roots
• Exponentiation
• Scientific notation
• Exact roots
• Radicals
3 Arithmetic problems
• Approximations and errors
• Calculating with percentages
• Compound interest
• Common problems
• Compound proportion in arithmetic problems
4 Progressions
• Sequences
• Arithmetic progressions
• Geometric progressions
• Surprising geometric progressions
5 Algebraic language
• Algebraic expressions
• Monomials
• Polynomials
• Identities
• Dividing polynomials
• Factorising polynomials
• Algebraic fractions
6 Equations
• Equations. Solving an equation
• First-degree equations
• Second-degree equations
• Polynomial equations with a degree greater than two
• Solving problems using equations
7 Systems of equations
• Linear equations with two unknowns
• Systems of linear equations
• Equivalent systems
• Types of systems by number of solutions
• Methods for solving systems
• Systems of non-linear equations
• Solving problems using systems
8 Characteristics of functions
• Functions and graphs
• Important aspects of functions
• Analytical expression of a function
9 Linear and quadratic functions
• Proportionality function y = mx
• Linear function y = mx + n
• Applying linear functions. Movement problems
• Studying two linear functions together
• Parabolas and quadratic functions
10 Metric problems in plane geometry
• Angle relationships
• Similar triangles. Thales’ theorem
• Similar shapes. Scales
• Pythagorean theorem
• Algebraic applications of the Pythagorean theorem
• Areas of polygons
• Areas of curved shapes
11 Geometric shapes
• Regular and semiregular polyhedra
• Truncating regular polyhedra
• Planes of symmetry of a shape
• Axes of rotation of a shape
• Surface area of geometric shapes
• Volume of geometric shapes
• Geographic coordinates
12 Geometric transformations
• Geometric transformations
• Motions on the plane
• Translations
• Rotations. Shapes with a centre of rotation
• Axial symmetries. Shapes with axes of symmetry
• Composition of motions
• Mosaics, friezes and rosettes
13 Statistical tables and graphs
• The statistical process
• Statistical variables
• Population and sample
• Making a frequency table
• Using the right type of graph
14 Statistical parameters
• Two types of statistical parameters
• Calculating –x and σ in frequency tables
• Joint interpretation of –x and σ
• Position parameters: median and quartiles
• Using a calculator to get –x and σ
• Statistics in the media
15 Chance and probability
• Random events
• Probability of an event
• Probability in regular experiments. Laplace’s law
• Probability in irregular experiments. Law of large numbers
• Probabilities in compound experiments
1 Real numbers
• Irrational numbers
• Real numbers: the real number line
• Sections of the real number line: intervals and half-lines
• Roots and radicals
• Approximate numbers. Errors
• Numbers in scientific notation. Error control
• Logarithms
2 Polynomials and algebraic fractions
• Polynomials. Operations
• Ruffini’s rule
• Root of a polynomial. Finding roots
• Factorising polynomials
• Divisibility of polynomials
• Algebraic fractions
3 Equations, inequations and systems
• Equations
• Systems of linear equations
• Systems of non-linear equations
• Inequations with one unknown
4 Functions. Characteristics
• Basic concepts
• How functions are presented
• Domain of definition
• Continuous functions. Discontinuities
• Increase, maximums and minimums
• Tendency and periodicity
5 Basic functions
• Linear functions
• Quadratic functions. Parabolas
• Absolute value functions
• Inversely proportional functions
• Radical functions
• Exponential functions
• Logarithmic functions
6 Similarity. Applications
• Similarity
• Similarity of triangles
• Similarity of right-angled triangles
• Applications of the similarity of triangles
• Similarity of rectangles. Applications
7 Trigonometry
• Trigonometric ratios of an acute angle
• Basic trigonometric relationships
• Using a calculator in trigonometry
• Solving right-angled triangles
• Solving oblique-angled triangles
• Trigonometric ratios of 0° to 360°
• Angles of any measurement. Trigonometric ratios
• Trigonometric functions. The radian
8 Analytic geometry
• Vectors in the plane
• Operating with vectors
• Vectors which represent points
• Midpoint of a segment
• Aligned points
• Equations of a straight line
• Straight lines. Parallelism and perpendicularity
• Straight lines parallel to the coordinate axes
• Relative positions of two straight lines
• Distance between two points
• Equation of a circumference
9 Statistics
• Statistics and statistical methods
• Frequency tables
• Statistical parameters: –x and σ
• Position parameters for isolated data
• Position parametersfor grouped data
• Box-and-whisker plots
• Statistical inference
10 Bivariate distributions
• Bivariate distributions
• Correlation value
• Using the line of best fit to make estimations
11 Combinatorics
• Product-based strategies
• Variations and permutations (the order matters)
• When the order does not matter. Combinations
12 Calculating probability
• Random events
• Probability of events. Characteristics
• Probability in single experiments
• Probability in compound experiments
• Creating individual experiments
• Creating dependent experiments
• Contingency tables
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