Primary 1 - 2Primary 3 - 4Primary 5 - 6Secondary 1Secondary 2Secondary 3Secondary 4Higher 1Higher 2

Counting and Cardinality

**Know number names and the count sequence.**-
**Count to tell the number of objects.** -
**Compare numbers.**

Operations and Algebraic Thinking

**Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.****Add and subtract within 20.****Work with equal groups of objects to gain foundations for multiplication.**

Number and Operations in Base Ten

**Work with numbers 11-19 to gain foundations for place value.****Use place value understanding and properties of operations to add and subtract.**

Measurement and Data

**Describe and compare measurable attributes.****Classify objects and count the number of objects in each category.****Measure and estimate lengths in standard units.****Relate addition and subtraction to length.****Work with time and money.****Represent and interpret data.**

Geometry

**Identify and describe shapes.****Analyze, compare, create, and compose shapes.****Reason with shapes and their attributes.**

Operations and Algebraic Thinking

**Represent and solve problems involving multiplication and division.****Understand properties of multiplication and the relationship between multiplication and division.****Multiply and divide within 100.****Solve problems involving the four operations, and identify and explain patterns in arithmetic.****Write and interpret numerical expressions.****Analyze patterns and relationships.**

Number and Operations in Base Ten

**Use place value understanding and properties of operations to perform multi-digit arithmetic.****Perform operations with multi-digit whole numbers and with decimals to hundredths.**

Number and Operations - Fractions

**Develop understanding of fractions as numbers.****Use equivalent fractions as a strategy to add and subtract fractions.****Apply and extend previous understandings of multiplication and division to multiply and divide fractions.**

Measurement and Data

**Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.****Represent and interpret data.****Geometric measurement: understand concepts of area and relate area to multiplication and to addition.****Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.**

Geometry

**Reason with shapes and their attributes.****Graph points on the coordinate plane to solve real-world and mathematical problems.****Classify two-dimensional figures into categories based on their properties**.

Ratios and Proportional Relationships

**Understand ratio concepts and use ratio reasoning to solve problems.**

The Number System

**Apply and extend previous understandings of multiplication and division to divide fractions by fractions.****Multiply and divide multi-digit numbers and find common factors and multiples.****Apply and extend previous understandings of numbers to the system of rational numbers.**

Expressions and Equations

**Apply and extend previous understandings of arithmetic to algebraic expressions.****Reason about and solve one-variable equations and inequalities.****Represent and analyze quantitative relationships between dependent and independent variables.**

Geometry

**Solve real-world and mathematical problems involving area, surface area, and volume.**

Statistics and Probability

**Develop understanding of statistical variability.****Summarize and describe distributions.**

Number Theory

**Understanding exponents and square roots.**

**Use properties of rational and irrational numbers.**

Operations with Integers

**Understanding integers and representing on a number line.**

**Evaluate numerical expressions involving integers.**

Ratios and Proportional Relationships

**Understand ratio concepts and use ratio reasoning to solve problems.****Graphing proportional relationships.**

Equations ,Inequalities and Functions

**Complete the table for two variable relationship and graph the equation.**

**Solve inequalities and interpret on the number line.**

**Identify linear and non-linear functions.**

Congruence and Similarity

**Measure side lengths and angles of congruent figures.**

**Solve congruent statements and corresponding parts.**

Geometry

**Perform operations on composite figures with triangles, semicircles and quarter circles.****Perform operations on volume and surface area of 3D shapes.**

Statistics and Probability

**Interpret charts to find mean, median, mode and range.**

**Perform operations on probability with compound events.**

Rational Number, Integers and Exponents

**Evaluate expressions involving rational numbers, integers and exponents.**

**Perform operations on reciprocals and multiplicative inverses.**

**Solve equations involving cubes and cube roots.**

Arithmetic with Polynomials and Rational Functions

**Perform arithmetic operations on polynomials****Understand the relationship between zeros and factors of polynomials****Use polynomial identities to solve problems****Rewrite rational functions**

Reasoning with Equations and Inequalities

**Understand solving equations as a process of reasoning and explain the reasoning****Solve equations and inequalities in one variable****Solve systems of equations****Represent and solve equations and inequalities graphically**

Quadratic expressions and equations

**Solve a quadratic equations by factorizing.**

Pythagoras Theorem

**Find the missing hypotenuse and leg length of a right angle triangle using Pythagoras theorem.**

Statistics and Probability

**Interpret charts to find mean, median, mode and range.**

**Perform operations on probability with compound events.**

Data and Graphs

**Create and interpret line plots, stem and leaf plots, histogram, bar graphs, frequency charts, box and whisker plots, pie charts etc.**

Polynomials

**Identify monomials, binomials and polynomials.**

**Add and subtract polynomials using algebra tiles.**

**Analyze and factorize polynomials.**

Simultaneous Equations

**Identify the solution to the simultaneous equations.**

**Solve simultaneous equations using elimination, substitution and graphical method.**

Linear, Quadratic, and Exponential Models

**Construct and compare linear and exponential models and solve problems****Interpret expressions for functions in terms of the situation they model**

Trigonometric Functions

**Extend the domain of trigonometric functions using the unit circle****Model periodic phenomena with trigonometric functions****Prove and apply trigonometric identities**

Geometry

**Perform operations on reflection, rotation and translation of objects.**

**Model area of sectors, arcs , chords, tangent lines.**

**Prove and apply trigonometric identities**

Functions: Linear, Quadratic, Exponential

**Identify linear, quadratic and exponential functions from graphs.****Perform operations on describing linear and exponential growth and decay.**

Congruence

**Experiment with transformations in the plane****Understand congruence in terms of rigid motions****Prove geometric theorems****Make geometric constructions**

Similarity, Right Triangles, and Trigonometry

**Understand similarity in terms of similarity transformations****Prove theorems involving similarity****Define trigonometric ratios and solve problems involving right triangles****Apply trigonometry to general triangles**

Circles

**Understand and apply theorems about circles****Find arc lengths and areas of sectors of circles**

Expressing Geometric Properties with Equations

**Translate between the geometric description and the equation for a conic section****Use coordinates to prove simple geometric theorems algebraically**

Geometric Measurement and Dimension

**Explain volume formulas and use them to solve problems****Visualize relationships between two-dimensional and three-dimensional objects**

Vectors

**Find the component form of a vector from its magnitude and direction angle.**

**Graphing a resultant vector using the triangle/parallelogram method.**

Derivatives

**Perform operations on derivatives of polynomials.**

**Find derivatives of rational/exponential functions using different rules.**

Complex Numbers

**Perform arithmetic operations with complex numbers****Represent complex numbers and their operations on the complex plane****Use complex numbers in polynomial identities and equations**

Vector and Matrix Quantities

**Represent and model with vector quantities.****Perform operations on vectors.****Perform operations on matrices and use matrices in applications.**

Interpreting Categorical and Quantitative Data

**Summarize, represent, and interpret data on a single count or measurement variable****Summarize, represent, and interpret data on two categorical and quantitative variables****Interpret linear models**

Functions: Linear, Quadratic, Exponential

**Identify linear, quadratic and exponential functions from graphs.****Perform operations on describing linear and exponential growth and decay.**

Trigonometric Functions

**Extend the domain of trigonometric functions using the unit circle****Model periodic phenomena with trigonometric functions****Prove and apply trigonometric identities**

Parabolas and Hyperbolas

**Find focus or directrix, vertex, axis of symmetry of a parabola.**

**Write equations of parabolas in vertex form from graphs.****Write equations of hyperbolas in standard form from graphs.**

Conditional Probability and the Rules of Probability

**Understand independence and conditional probability and use them to interpret data****Use the rules of probability to compute probabilities of compound events in a uniform probability model**

Using Probability to Make Decisions

**Calculate expected values and use them to solve problems****Use probability to evaluate outcomes of decisions**

Derivatives

**Perform operations on derivatives of polynomials.**

**Find derivatives of rational/exponential functions using different rules.**

Functions and Quadratic Functions

**Identify inverse functions and relations.**

**Describe families of functions and relations.****Solve quadratic functions by factorising, completing the square and quadratic formula.**

Simultaneous equations and non-linear inequalities

**Determine the number of solutions to simultaneous equations in three variables.****Solve systems of linear and absolute value inequalities by graphing.**

Matrices and Vectors

**Solve matrix equations using inverses.**

**Linear combinations of 2 dimensional and 3 dimensional vectors.**

Complex Numbers, Argand Plane and Polar form

**Perform all four operations on complex numbers.**

**Find absolute value, midpoints and distance in the argand plane.****Convert complex numbers between rectangular and polar form.**

Limits and Rational Functions

**Finding limits involving rationalization and factorization.**

**Find the limit at a vertical asymptote of rational functions.**

Calculate Derivatives

**Finding derivatives of polynomials, rational and trigonometric functions.**

**Perform operations on finding the derivatives using product and quotient rules.**

Probability Distributions

**Identify discrete and continuous random variables.**

**Write the probability distribution for a game of chance.****Use normal distribution to approximate binomial distribution.**

Statistics

**Identify biased samples, perform operations on finding variance and standard deviation.**

**Analyse a regression line using statistics of a data set.**

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