Adding two 1-digit numbers

Horizontal addition of two 2-digit numbers

Vertical addition of 2-digit numbers with carryover

Introduces elementary subtraction using a number line

100s of word problems to apply the arithmetic skills learned in the level

Vertical subtraction of 2 numbers

Vertical addition of 2 numbers up to 1000s 

Reinforces skills of carry and borrow by using harder problems

Word problems introduce concepts of money, distance and time

Developing skills in subtraction by subtraction of 2 numbers up to 4 digits. 

Word problems develop real world skills dealing with money, distance, weight and time

Introduces multiplication as repeated addition

Teaches multiplication tables up to 12 times 12

Vertical multiplication skills of 1-digit, 2-digit and 3-digit numbers are developed fully

100s of word problems to apply these skills 

Division introduced as the inverse of multiplication

Explanation of concepts such as quotient and remainder

At the end of this level, children will be able to do long division of a 4-digit number by a 2-digit number

Order of operations skills using the PEMDAS rule are mastered

Associative and commutative rules

Fractions are introduced

Mixed fractions, improper fractions are introduced

LCM concept is introduced

At the end of this level students will be able to add, subtract, multiply and divide 2 fractions, including mixed numbers

Complex arithmetic using multiple fractions  and integers is introduced 

Application of the PEMDAS rule is reinforced through 100s of problems

Word problems to help understand fractions in the real world like ratios and proportions, speed, flow rates are introduced

Introduces decimals 

Negative numbers introduced

4 operations with combinations of positive and negative numbers 

Exponents are introduced 

Complex arithmetic of multiple positive and negative numbers including decimals, integers and fractions is mastered

Students start doing Algebra with the evaluation of expressions with 1 and/or 2 variables

Simplification of algebraic expressions

Solving linear equations in 1 variable with integer, decimal and fractional coefficients

Fractional equations 

100s of word problems, where students have to frame equations from information in the questions

Algebraic equations with variables are introduced as a precursor to solving simultaneous equations

Students master solving simultaneous equations in 2 and 3 variables using the process of eliminations

Develop skills to check if the solution is correct

Introduces inequalities with1 variable

Starts with single inequality and progresses to systems of inequalities

Multiplication of two algebraic expressions

Introduces polynomials in 1 and/or 2 variables

Expansion of polynomial expressions

Factoring of polynomials with degree up to 4

Master solving quadratic equations

Functions and graphing of functions 

Solving linear equations and inequalities using graphs

Pythagoras theorem and triples 

Factor and remainder theorem