Hafa Math Academy

Singapore Curriculum

Primary 1 - 2Primary 3 - 4Primary 5 - 6Secondary 1Secondary 2Secondary 3Secondary 4Higher 1Higher 2
Counting and Cardinality
  1.  Know number names and the count sequence.
  2.  Count to tell the number of objects.
  3.  Compare numbers.
Operations and Algebraic Thinking
  1. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. 
  2. Add and subtract within 20.
  3. Work with equal groups of objects to gain foundations for multiplication.
Number and Operations in Base Ten
  1. Work with numbers 11-19 to gain foundations for place value.
  2. Use place value understanding and properties of operations to add and subtract.
Measurement and Data
  1. Describe and compare measurable attributes.
  2. Classify objects and count the number of objects in each category.
  3. Measure and estimate lengths in standard units.
  4. Relate addition and subtraction to length.
  5. Work with time and money.
  6. Represent and interpret data.
Geometry
  1. Identify and describe shapes.
  2. Analyze, compare, create, and compose shapes.
  3. Reason with shapes and their attributes.
Operations and Algebraic Thinking
  1. Represent and solve problems involving multiplication and division.
  2. Understand properties of multiplication and the relationship between multiplication and division.
  3. Multiply and divide within 100.
  4. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
  5. Write and interpret numerical expressions.
  6. Analyze patterns and relationships.
Number and Operations in Base Ten
  1. Use place value understanding and properties of operations to perform multi-digit arithmetic.
  2. Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations - Fractions
  1. Develop understanding of fractions as numbers.
  2. Use equivalent fractions as a strategy to add and subtract fractions.
  3. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
  1. Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.
  2. Represent and interpret data.
  3. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
  4. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
Geometry
  1. Reason with shapes and their attributes.
  2. Graph points on the coordinate plane to solve real-world and mathematical problems.
  3. Classify two-dimensional figures into categories based on their properties.
Ratios and Proportional Relationships
  1. Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
  1. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  2. Multiply and divide multi-digit numbers and find common factors and multiples.
  3. Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
  1. Apply and extend previous understandings of arithmetic to algebraic expressions.
  2. Reason about and solve one-variable equations and inequalities.
  3. Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
  1. Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
  1. Develop understanding of statistical variability.
  2. Summarize and describe distributions.
Number Theory
  1. Understanding exponents and square roots.
  2. Use properties of rational and irrational numbers.
Operations with Integers
  1. Understanding integers and representing on a number line.
  2. Evaluate numerical expressions involving integers.
Ratios and Proportional Relationships
  1. Understand ratio concepts and use ratio reasoning to solve problems.
  2. Graphing proportional relationships.
Equations ,Inequalities and Functions
  1. Complete the table for two variable relationship and graph the equation.
  2. Solve inequalities and interpret on the number line.
  3. Identify linear and non-linear functions.
Congruence and Similarity
  1. Measure side lengths and angles of congruent figures.
  2. Solve congruent statements and corresponding parts.
Geometry
  1. Perform operations on composite figures with triangles, semicircles and quarter circles.
  2. Perform operations on volume and surface area of 3D shapes.
Statistics and Probability
  1. Interpret charts to find mean, median, mode and range.
  2. Perform operations on probability with compound events.
Rational Number, Integers and Exponents
  1. Evaluate expressions involving rational numbers, integers and exponents.
  2. Perform operations on reciprocals and multiplicative inverses.
  3. Solve equations involving cubes and cube roots.
Arithmetic with Polynomials and Rational Functions
  1. Perform arithmetic operations on polynomials
  2. Understand the relationship between zeros and factors of polynomials
  3. Use polynomial identities to solve problems
  4. Rewrite rational functions
Reasoning with Equations and Inequalities
  1. Understand solving equations as a process of reasoning and explain the reasoning
  2. Solve equations and inequalities in one variable
  3. Solve systems of equations
  4. Represent and solve equations and inequalities graphically
Quadratic expressions and equations
  1. Solve a quadratic equations by factorizing.
Pythagoras Theorem
  1. Find the missing hypotenuse and leg length of a right angle triangle using Pythagoras theorem.
Statistics and Probability
  1. Interpret charts to find mean, median, mode and range.
  2. Perform operations on probability with compound events.
Data and Graphs
  1. Create and interpret line plots, stem and leaf plots, histogram, bar graphs, frequency charts, box and whisker plots, pie charts etc.
Polynomials
  1. Identify monomials, binomials and polynomials.
  2. Add and subtract polynomials using algebra tiles.
  3. Analyze and factorize polynomials.
Simultaneous Equations
  1. Identify the solution to the simultaneous equations.
  2. Solve simultaneous equations using elimination, substitution and graphical method.
Linear, Quadratic, and Exponential Models
  1. Construct and compare linear and exponential models and solve problems
  2. Interpret expressions for functions in terms of the situation they model
Trigonometric Functions
  1. Extend the domain of trigonometric functions using the unit circle
  2. Model periodic phenomena with trigonometric functions
  3. Prove and apply trigonometric identities
Geometry
  1. Perform operations on reflection, rotation and translation of objects.
  2. Model area of sectors, arcs , chords, tangent lines.
  3. Prove and apply trigonometric identities
Functions: Linear, Quadratic, Exponential
  1. Identify linear, quadratic and exponential functions from graphs.
  2. Perform operations on describing linear and exponential growth and decay.
Congruence
  1. Experiment with transformations in the plane
  2. Understand congruence in terms of rigid motions
  3. Prove geometric theorems
  4. Make geometric constructions
Similarity, Right Triangles, and Trigonometry
  1. Understand similarity in terms of similarity transformations
  2. Prove theorems involving similarity
  3. Define trigonometric ratios and solve problems involving right triangles
  4. Apply trigonometry to general triangles
Circles
  1. Understand and apply theorems about circles
  2. Find arc lengths and areas of sectors of circles
Expressing Geometric Properties with Equations
  1. Translate between the geometric description and the equation for a conic section
  2. Use coordinates to prove simple geometric theorems algebraically
Geometric Measurement and Dimension
  1. Explain volume formulas and use them to solve problems
  2. Visualize relationships between two-dimensional and three-dimensional objects
Vectors
  1. Find the component form of a vector from its magnitude and direction angle.
  2. Graphing a resultant vector using the triangle/parallelogram method.
Derivatives
  1. Perform operations on derivatives of polynomials.
  2. Find derivatives of rational/exponential functions using different rules.
Complex Numbers
  1. Perform arithmetic operations with complex numbers
  2. Represent complex numbers and their operations on the complex plane
  3. Use complex numbers in polynomial identities and equations
Vector and Matrix Quantities
  1. Represent and model with vector quantities.
  2. Perform operations on vectors.
  3. Perform operations on matrices and use matrices in applications.
Interpreting Categorical and Quantitative Data
  1. Summarize, represent, and interpret data on a single count or measurement variable
  2. Summarize, represent, and interpret data on two categorical and quantitative variables
  3. Interpret linear models
Functions: Linear, Quadratic, Exponential
  1. Identify linear, quadratic and exponential functions from graphs.
  2. Perform operations on describing linear and exponential growth and decay.
Trigonometric Functions
  1. Extend the domain of trigonometric functions using the unit circle
  2. Model periodic phenomena with trigonometric functions
  3. Prove and apply trigonometric identities
Parabolas and Hyperbolas
  1. Find focus or directrix, vertex, axis of symmetry of a parabola.
  2. Write equations of parabolas in vertex form from graphs.
  3. Write equations of hyperbolas in standard form from graphs.
Conditional Probability and the Rules of Probability
  1. Understand independence and conditional probability and use them to interpret data
  2. Use the rules of probability to compute probabilities of compound events in a uniform probability model
Using Probability to Make Decisions
  1. Calculate expected values and use them to solve problems
  2. Use probability to evaluate outcomes of decisions
Derivatives
  1. Perform operations on derivatives of polynomials.
  2. Find derivatives of rational/exponential functions using different rules.
Functions and Quadratic Functions
  1. Identify inverse functions and relations.
  2. Describe families of functions and relations.
  3. Solve quadratic functions by factorising, completing the square and quadratic formula.
Simultaneous equations and non-linear inequalities
  1. Determine the number of solutions to simultaneous equations in three variables.
  2. Solve systems of linear and absolute value inequalities by graphing.
Matrices and Vectors
  1. Solve matrix equations using inverses.
  2. Linear combinations of 2 dimensional and 3 dimensional vectors.
Complex Numbers, Argand Plane and Polar form
  1. Perform all four operations on complex numbers.
  2. Find absolute value, midpoints and distance in the argand plane.
  3. Convert complex numbers between rectangular and polar form.
Limits and Rational Functions
  1. Finding limits involving rationalization and factorization.
  2. Find the limit at a vertical asymptote of rational functions.
Calculate Derivatives
  1. Finding derivatives of polynomials, rational and trigonometric functions.
  2. Perform operations on finding the derivatives using product and quotient rules.
Probability Distributions
  1. Identify discrete and continuous random variables.
  2. Write the probability distribution for a game of chance.
  3. Use normal distribution to approximate binomial distribution.
Statistics
  1. Identify biased samples, perform operations on finding variance and standard deviation.
  2. Analyse a regression line using statistics of a data set.

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