English Syllabus for all Levels

Level K

• Introduction to numbers
• Counting numbers up to 100 – forward and backward.
• Skip Counting by 2s, 5s & 10s.
• Finding missing numbers.
• Compare numbers > < =
• Writing before and after numbers.
• Sorting numbers – Ascending and Descending order.
• Single digit additions.
• Single digit subtractions.
• Finding missing addends in addition equations.
• Place values – One, tens and hundreds.
• Number Forms – Expanded and Standard forms.
• Introduction to Two-digit additions.
• Introduction to Two-digit subtractions.
• Story problems – Addition & Subtraction.

Level A

Number and Operations in Base 10.
• Counting numbers by 2s, 5s & 10s.
• Rounding (10s & 100)
• Place values
• Arithmetic Sequence
• Math mountain equations
• Addition Fact Families
• Commutative Properties of Addition
• Mental Math addition
• Regrouping Addition and Subtraction.
• Finding missing addends in addition, subtraction equations.
• Multiplication: 2-digit & 3-digit with 2, 3, & 4.
• Geometry: Recognizing 2D & 3D shapes
Basic properties of 2D shapes. (Sides, Angles & Vertices)
• Money Problems – pennies, nickels, dimes & quarters.
• Time (Clock): Current time
     Elapsed time
Story problems – Addition, Subtraction & Multiplication.
Math Puzzles.

Level B

  • Regrouping 3 – 4-digit addition and subtraction.
  • Multiplication: Multiplying 3-, 4- and 5-digit numbers by a single digit.
  • Introduction to Division Concept: Simple division and long   division by 2, 3, 4 & 5.
  • Mental math multiplication with 10s & 100s
  • Mental Math addition.
  • Mental Math multiplication (with tens eg. 23*20) .
  • Introduction to numbers with place values up to 999.
  • Rounding 10s & 100s.
  • Fact Families: Addition, Multiplication.
  • Math Mountain equations.
  • Arithmetic Sequence.
  • Finding missing addends in equations.
  • Fractions: Basics of Fractions (shaded, unshaded, and whole)
             Dividing Shapes into equal parts and writing fractions.
                      Determining Fractions in Number line.
                     Equivalent Fractions.
                     Comparing Fractions with Like denominators.
                     Comparing Fractions with Unlike denominators.
                    Adding Fractions.
                    Subtracting Fractions.
  • Geometry: Introduction to Lines of symmetry.
    2D & 3D Properties.
  • Measurements – Metric system
             US customary system
             Units Conversion
  • Story Word Problems : One or two step word problems.
  • Time (Add, Subtract & Elapsed time)
  • Money & Time Problems.
  • Math Puzzles
  • Advanced Money Word problems

Level C

  •  Review of 3 & 4 – digit addition and subtraction.
  • Review of 3 digits by 1 digit multiplication.
  • Review of simple division and long division below 1000.
  • Review of Place values up to 100.
  • Place values
  • Rounding (10s & 100s)
  • Missing numbers with rule
  • Missing numbers in equations
  • Time (Add, Subtract & Elapsed time)
  • Money
  • Introduction to numbers with place values up to 1,000,000.
  • Multiplication of 3 & 4 – digit numbers with 2-digit number.
  • Division with 4 & 5 – digit dividends.
  • Introduction to Numbers – Natural numbers, Whole numbers, Prime & Composite numbers.
  • Introduction to Multiples, Factors & Factor pairs.
  • Prime Factorization.
  • Exponents.
  • Properties – Commutative, Associative, Identity, Zero, & Distributive properties
  • Multi step Story problems (addition, subtraction, multiplication & division).
  • Fractions:
         Basics of Fractions (shaded, unshaded, and whole)
         Dividing Shapes into equal parts and writing fractions.
         Determining Fractions in Number line.
         Equivalent Fractions.
         Comparing Fractions with Like denominators.
         Comparing Fractions with Unlike denominators.
         Adding Fractions.
         Subtracting Fractions.
         Word problems.
  • Introduction to Types of fractions (Proper, Improper & Mixed number).
  • Locating the wholes and fractions on a number line.
  • Conversion between improper fraction and mixed number.
  • Introduction to basic algebraic equations.
  • Geometry – 2D & 3D Shapes Properties and Axis of symmetry.
         Lines, rays, segments, angles, triangles, quadrilaterals and polygons.
         Area & Perimeter Problems – (Rectangle, Square & Irregular shapes)
         Word Problems on finding Area and Perimeter.
  • Measurements – Metric system
         US customary system
         Units Conversion
  • Money & Time Problems
  • Math Puzzles
  • Word Problems

Level D

  • Review of number system – Prime & Composite numbers.
  • Review of Multiples, Factors & Factor Pairs.
  • Review of Prime Factorization.
  • Review of multiplication & division with 3 & 4 digit numbers.
  • Review of Money & Time.
  • Review of Equations and Expressions.
  • Multiplication of 5 & 6 digit numbers with 1-digit & 2-digit numbers.
  • Division with 5 & 6 digit dividends with 1-digit & 2-digit divisors.
  • Divisibility rules for 2, 3, 4, 5, 6, 8, 9,10 & 12.
  • Finding Least Common Multiple (LCM) using different methods.
  • Finding Greatest Common Factor (GCF) using different methods.
  • Fractions
         Converting Mixed to Improper and vice versa.
         Adding and subtracting fractions and mixed numbers.
         Multiplication & Division of fractions.
         Adding and subtracting more than 2 fractions using LCM method.
         Word problems on Fractions
  • Introduction to decimals
          Decimal numbers – Addition, Subtraction, Multiplication & Division.
          Converting fractions to decimals and vice versa.
  • Introduction to Integers – Numeric expressions.
  • Order of Operation – Solving numeric expressions using PEMDAS.
  • Introduction to Algebra
         Algebraic expressions: Terms, Variables, Coefficients, Constants.
         Solving one step equations
         Simplifying the terms.
         Simplify the algebraic expressions.
  • Introduction to Ratios
         Find the Ratios
         Simplest form of ratios.
         Equivalent Ratios
  • Introduction to Geometry
         Finding area and perimeter of square, rectangle, Parallelogram, triangle &
         Irregular shapes.
         Types of Angles.
  • Measurements – Metric System and US Customary System
         Types of Units
         Conversion of units
  • Multi step Story problems (addition, subtraction, multiplication & division).
  • Challenging Word Problems

Level E

  • Review of Prime Factorization.
  • Review of Divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10 & 12.
  • Review of Least Common Multiple (LCM) using different methods.
  • Review of Greatest Common Factor (GCF) using different methods.
  • Review of Fractions
         Multiplication and Division of fractions.
         Adding and subtracting more than 2 fractions using LCM method.
  • Review of Numeric expressions using Order of Operations (PEDMAS).
  • Number System
         Rational & Irrational numbers.
         Decimal numbers – Addition, Subtraction, Multiplication & Division.
         Converting fractions to decimals and vice versa.
         Operations with Integers.
  • Introduction to Algebra
         Term, Variable, Coefficient & Constant.
         Solving single variable algebraic expressions.
         Solving algebraic equations using addition, subtraction, multiplication & division
    methods.
         Solving two-step & multi-step equations.
        Applying Distributive property to algebraic equations.
        Story problems involving algebra.
  • Ratios & Proportions.
         Introduction to simple Ratios.
        Finding missing Ratios.
         Introduction to Proportions.
         Finding missing variable in  Proportion equations.
         Word problems on Ratios & Proportions.
  • Rate Problems.
         Introduction to Rate & unit rates.
         Word problems on rate.
  • Distance, Speed & Time.
         Introduction to Distance, Speed & Time Formula.
         Solving problems using Formula.
  • Geometry.
         Lines.
         Area & Perimeter of Square, Rectangle, Triangle, Parallelogram, Trapezoid &
         Circle.
         Area & Perimeter of regular Polygons.
         Area & Perimeter of 3D shapes (cube, prism & cylinder).
         Volume of 3D shapes.
         Finding Surface area.
  • Percentages

Level F (Algebra 1)

  • Introduction to Polynomials
         Adding and subtracting Polynomials.
         Multiplying and Dividing Polynomials.
         Simplifying the multiple polynomial expressions.
  • Functions
         Domain and Range.
         Independent and dependent variables.
         Writing Function Rules.
         Represent functions as graphs.
  • Linear Equations & Inequalities
         Introduction to coordinate planes.
         Graph using intercepts.
         Finding Slope and Rate of Change.
  • Absolute value equations & inequalities
  • Compound Inequalities
  • Graphing linear equations and inequalities.
  • Exponents
  • Special Products formulas
         Solving equations using Zero-Product property.
         Factoring Trinomials.
  • Quadratic equations.
         Understanding Quadratic equations
         Solving Quadratic equations by factoring.
  • System of Linear Equations.
         Graphing method of solving equations
         Elimination method of solving equations
         Substitution method of solving equations

Level G (Geometry)

  • Inductive reasoning
  • Conjecture
  • Counter example
  • Conditional Statements – Hypothesis & Conclusion
  • Truth Value
  • Related Conditional statements – Conditional, Converse, Inverse, & Contrapositive
  • Conjunction & Disjunction
  • Biconditional (if and only if)
  • Deductive reasoning (Law of Detachment & Law of Syllogism)
  • Properties of Equality
         (Addition, Subtraction, Multiplication, Division, Reflexive, Symmetric, Transitive,
          Substitution)
  • Properties of Congruence
         (Reflexive, Symmetric, & Transitive)
  • Parallel and Skew lines
  • Transversal
  • Angle pairs formed by Transversals
         Alternate interior angles
         Same-side interior angles
         Corresponding angles
         Alternate exterior angles
  • Formulas
         Midpoint
         Distance
         Midsegment
  • Postulates:
         1) Angles
                        Corresponding Angles Postulate
                        Converse of the Corresponding Angles Postulate
                        Parallel Postulate
                        Perpendicular Postulate
         2) Triangles
                        Side-Side-Side (SSS) Postulate
                       Side-Angle-Side (SAS) Postulate
                       Angle-Side-Angle (ASA) Postulate
                       Angle-Angle-Side (AAS) Postulate
                       Hypotenuse-Leg (HL) Theorem
  • Theorems:
         1) Angles
                      Vertical Angles Theorem
                     Congruent Supplements Theorem
                     Congruent Complements Theorem
                      All right angles are congruent
                      If two angles are congruent and supplementary, then each angle is a right angle.
                      Alternate Interior Angles Theorem
                      Same-Side Interior Angles theorem
                      Alternate Exterior Angles Theorem
                     Converse of the Alternate Interior Angles Theorem
                     Converse of the Same-Side Interior Angles theorem
                     Converse of the Alternate Exterior Angles Theorem
                     If two lines are parallel to the same line, then they are parallel to each other
                     If two lines are perpendicular to the same line, then they are parallel to each
                    other.
                    If a line is perpendicular to one of two parallel lines, then it is also perpendicular
                    to the other.
         2) Triangles
                   Triangle Angle Sum Theorem
                   Triangle Exterior Angle Theorem
                   Third Angles Theorem
                   Isosceles Triangle Theorem
                   Converse of the Isosceles Triangle Theorem
                   Triangle Midsegment Theorem
                   Perpendicular Bisector Theorem
                   Converse of the Perpendicular Bisector Theorem
                   Angle Bisector Theorem
                   Converse of the Angle Bisector Theorem
                   Congruency of Perpendicular Bisectors Theorem
                   Congruency of Angle Bisectors Theorem

Level H (Algebra 2)

  • Linear Models
  •  Scatter Plots
  •  Relations and Functions
  •  Absolute Value Functions and Graphs
  •  Two Variable Inequalities
  •  Graphing Linear Inequalities
  •  Quadratic Functions and Transformations
  •  Standard Form of a Quadratic Function
  •  Factoring Quadratic Expressions
  •  Completing the Square
  •  The Quadratic Formula
  •  Complex Numbers
  •  Quadratic Systems
  •  Polynomials & Polynomial functions:
             Polynomial Functions
             Polynomials, Linear Factors, and Zeros
             Solving Polynomial Equations
             Dividing Polynomials
            Rational Root Theorem
            Conjugate Root Theorem
            The fundamental Theorem of Algebra
            Binomial Theorem
            Pascal’s Triangle
  •  Radical Function & Rational Exponents
           Roots and Radical Expressions
           Multiplying and Dividing Radical Expressions
           Adding and Subtracting Radical Expressions
           Multiplying Radical Expressions
           Multiplying Conjugates
           Rationalizing the Denominator
           Rational Exponents
           Solving Square Root Equations
           Solving Other Radical Equations
           Function Operations
           Inverse Relations and Functions
           Graphing Radical Functions