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Number and Algebra
Whole numbers up to 100.
Ordinal numbers up to 10th.
Addition of numbers with sums up to 20
Place value in any 2-digit number.
Addition of numbers, with sums up to 100
Subtraction of numbers where both numbers are less than 100.
Repeating patterns
Fractions 1/2 and 1/4.
The denominations and values of Philippine coins and bills up to ₱100.
Addition of money where the sum is up to ₱100 and subtraction of money where both amounts are less than ₱100.
Whole numbers up to 1000.
Place value in any 3-digit number.
Addition of numbers with sums up to 1000.
The denominations and values of Philippine coins and bills up to ₱1000, and the addition of amounts of money with sums up to ₱1000.
Subtraction of numbers where both numbers are less than 1000.
Increasing patterns and decreasing patterns.
Multiplication and division of whole numbers using the 2, 3, 4, 5, and 10 multiplication tables.
Odd and even numbers.
Unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, and 8.
Ordinal numbers up to 100th.
Addition and subtraction of numbers of up to 4 digits and money up to ₱10 000.
Multiplication using 6, 7, 8, and 9 multiplication tables.
Properties of multiplication
Multiplication of numbers with and without regrouping
Estimation of products of two numbers by first rounding to the nearest multiple of 10.
Generation of repeating and increasing patterns, and repeating and decreasing patterns.
Division using the 6, 7, 8, and 9 multiplication tables.
Division of 2- to 4-digit numbers.
Estimation of quotients by first rounding the divisor and dividend to the nearest multiple of 10.
Addition and subtraction of similar fractions.
Whole numbers up to 1 000 000.
Addition of numbers with sums up to 1 000 000 and subtraction of numbers where both numbers are less than 1 000 000.
Multiplication of whole numbers with products-up to 1 000 000, division of up to 4-digit numbers by up to 2-digit numbers, and the MDAS rules.
Addition and subtraction of similar fractions, including mixed numbers.
Dissimilar and equivalent fractions.
Factors and multiples of numbers up to 100.
Addition and subtraction of dissimilar fractions.
Simple patterns.
Decimal numbers and their relationship to fractions.
The GMDAS rules for operations with numbers
Multiplication of fractions.
Division of fractions.
Decimal numbers with decimal parts up to ten thousandths.
Addition and subtraction of decimal numbers.
Divisibility rules.
Prime and composite numbers.
Multiplication and division of decimal numbers.
GMDAS rules when performing three or more operations with fractions and decimals.
The four operations with decimals.
The four operations with different combinations of fractions, whole numbers, and mixed numbers.
Ratio and proportion.
Percentages, and their relationships with fractions and decimals.
Exponential form, including calculation using the GEMDAS rules.
Common factors, greatest common factors, common multiples, and least common multiples.
Application of percentages.
Use of rates.
Rational numbers.
Square roots of perfect squares, cube roots of perfect cubes, and irrational numbers.
Sets and subsets, and the union and intersection of sets using Venn diagrams
Subset of real numbers.
The set of integers, and comparing and ordering integers.
The four operations with integers.
Simplification of numerical expressions involving integers
Absolute value of an integer.
The solution of simple equations.
The evaluation of algebraic expressions following substitution.
The rearrangement of a formula to make a different variable the subject of the formula
Operations using scientific notation.
Algebraic expressions and operations with monomials, binomials, and multinomials.
Special products for binomials, and factorization of polynomials.
Rational algebraic expressions and equations.
Rules for obtaining terms in sequences
Plotting points, and finding distance and the midpoint of line segments on the Cartesian coordinate plane.
Earning money, profit and loss, ‘best buys’, buying on terms.
Linear equations in one variable.
Linear equations in two variables and their graphs.
Systems of linear equations in two variables.
Relations and functions.
Graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros
Quadratic equations and graphs of quadratic functions.
The solution of quadratic equations
Direct and inverse variation.
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