INDIA MATH CLASS VIII – EDmama India

A. Numbers and Counting

A.05. Calculate the highest common factor (HCF) of two or more numbers.
A.06. Calculate the lowest common multiple (LCM) of two or more numbers.
A.07. Solve word problems involving HCF and LCM.
A.08. Use prime factorization to simplify fractions.
A.09. Relate prime factorization to finding the square root and cube root of perfect squares and perfect cubes
A.01. Classify numbers as prime, composite, or neither.
A.02. Identify the factors of a given number.
A.03. Apply divisibility rules to determine if a number is divisible by another.
A.04. Determine the prime factorization of a number.

B. Integers

C. Operations with Integers

C.01. Model addition and subtraction of integers using counters or number lines.
C.02. State and apply the rules for adding and subtracting integers.
C.03. Add and subtract integers, including multiple integers in a single expression.
C.04. Apply the rules for multiplying and dividing integers.
C.05. Multiply and divide integers.
C.06. Evaluate numerical expressions involving integers, using the order of operations.
C.07. Solve word problems involving addition, subtraction, multiplication, and division of integers.
C.08. Understand and apply properties of integers in arithmetic operations.

D. Rational Numbers

D.01. Define and identify rational and irrational numbers.
D.02. Write fractions in lowest terms (simplify fractions).
D.03. Determine the lowest common denominator (LCD) for a set of fractions.
D.04. Convert between decimals and fractions or mixed numbers.
D.05. Round decimals and mixed numbers to a specified place value.
D.06. Compare and order rational numbers, including fractions, decimals, and mixed numbers.
D.07. Place rational numbers in order on a number line.
D.08. Explain why the square root of a non-perfect square is irrational.

E. Operations with Rational Numbers

E.01. Determine the reciprocal and multiplicative inverse of a rational number.
E.02. Add and subtract rational numbers, including fractions and decimals.
E.03. Apply addition and subtraction rules to simplify expressions with rational numbers.
E.04. Multiply and divide rational numbers, including fractions and decimals.
E.05. Apply multiplication and division rules to simplify expressions with rational numbers.
E.06. Apply addition, subtraction, multiplication, and division rules in multi-step problems involving rational numbers.
E.07. Evaluate numerical expressions involving rational numbers, using the order of operations.
E.08. Solve word problems involving addition, subtraction, multiplication, and division of rational numbers.
E.09. Justify steps taken when simplifying expressions with rational numbers

F. Exponents and Roots

F.01. Understand the meaning of exponents and their notation.
F.02. Evaluate powers with positive, negative, decimal, and fractional bases.
F.03. Solve equations with variable exponents by trial and error.
F.04. Understand and apply the concept of negative exponents.
F.05. Evaluate powers with negative exponents.
F.06. Apply the rules of multiplication and division with exponents (product rule, quotient rule).
F.07. Apply the power rule for exponents.
F.08. Evaluate expressions using properties of exponents.
F.09. Identify equivalent expressions involving exponents.
F.10. Determine square roots of perfect squares.
F.11. Identify positive and negative square roots.
F.12. Estimate positive and negative square roots.
F.13. Understand the relationship between squares and square roots.
F.14. Solve equations involving squares and square roots.
F.15. Determine cube roots of perfect cubes.
F.16. Estimate cube roots.
F.17. Solve equations involving cubes and cube roots.
F.18. Simplify expressions involving multiple exponents and roots.
F.19. Express numbers using fractional exponents and their relationship to roots.

G. Scientific Notation

H. Ratios, Rates and Proportions

H.01. Understand the concept of ratios and how to represent them.
H.02. Identify equivalent ratios.
H.03. Write an equivalent ratio for a given ratio.
H.04. Solve word problems involving equivalent ratios.
H.05. Determine and apply unit rates.
H.06. Compare ratios in word problems.
H.07. Determine if two ratios form a proportion.
H.08. Solve proportions.
H.09. Solve proportions in word problems.
H.10. Solve problems using scale drawings and proportions.
H.11. Calculate and interpret the rate of change.
H.12. Identify constant rates of change.
H.13. Apply ratios and proportions to estimate population size.
H.14. Identify examples of direct and inverse proportions.

I. Proportional Relationships

I.01. Identify proportional relationships from tables.
I.02. Determine the constant of proportionality from a table.
I.03. Write equations for proportional relationships based on tables.
I.04. Identify proportional relationships by graphing.
I.05. Determine the constant of proportionality from a graph.
I.06. Write equations for proportional relationships based on graphs.
I.07. Graph proportional relationships.
I.08. Interpret graphs of proportional relationships.
I.09. Write and solve equations for proportional relationships to solve problems.
I.10. Explain the relationship between the equation, table, and graph of a proportional relationship.

J. Percents

J.01. Convert between percents, fractions, and decimals.
J.02. Compare percents to fractions and decimals.
J.03. Find what percent one number is of another.
J.04. Solve word problems involving finding the percentage of a number.
J.05. Estimate percents of numbers.
J.06. Calculate percentages of numbers and money amounts.
J.07. Solve percent equations.
J.08. Determine the percent of change.
J.09. Solve word problems involving percent of change (increase or decrease).
J.10. Solve simple interest problems.
J.11. Solve compound interest problems.
J.12. Compare different percentage scenarios and select the best option.

K. Consumer Maths

K.01. Use price lists to determine the cost of items.
K.02. Calculate and compare unit prices to find the best deal.
K.03. Calculate the total price using unit prices.
K.04. Calculate VAT, discount, and mark-up using percentages.
K.05. Find the percent discount or mark-up.
K.06. Calculate the original price given the sale price and discount percentage.
K.07. Solve multi-step problems involving percentages in consumer contexts.
K.08. Estimate tips based on a percentage of the bill.
K.09. Analyze the impact of inflation on purchasing power.

L. Units of Measurement

M. Problem Solving

N. Coordinate Plane

O. Two-Dimensional Figures

O.01. Identify and classify polygons based on their properties.
O.02. Classify triangles based on their sides and angles.
O.03. Identify trapeziums (trapezoids).
O.04. Classify quadrilaterals (parallelograms, rhombuses, squares, rectangles).
O.05. Graph triangles and quadrilaterals on a coordinate plane.
O.06. Identify and apply the properties of parallelograms.
O.07. Identify and apply the properties of rhombuses.
O.08. Identify and apply the properties of squares and rectangles.
O.09. Find missing angles in triangles and quadrilaterals using angle properties.
O.10. Determine the sum of the interior angles of polygons.
O.11. Define and identify lines, line segments, and half lines (rays).
O.12. Identify complementary, supplementary, vertical, adjacent, and congruent angles.
O.13. Find measures of complementary, supplementary, vertical, and adjacent angles.
O.14. Understand and apply the properties of transversals of parallel lines.
O.15. Find lengths and measures of bisected line segments and angles.
O.16. Identify and label the parts of a circle (center, radius, diameter, chord, arc).
O.17. Identify symmetry in two-dimensional figures.
O.18. Count lines of symmetry in a figure.
O.19. Draw lines of symmetry in a figure.
O.20. Relate geometric shapes to algebraic equations.

P. Congruence and Similarity

Q. Constructions

Q.01. Construct the midpoint and perpendicular bisector of a line segment.
Q.02. Construct an angle bisector.
Q.03. Construct a congruent angle.
Q.04. Construct a perpendicular line to a given line through a point on the line.
Q.05. Construct a perpendicular line to a given line through a point not on the line.
Q.06. Construct parallel lines.
Q.07. Construct an equilateral triangle and a regular hexagon.
Q.08. Use geometric constructions to solve problems.

R. Pythagoras’ Theorem

S. Three-Dimensional Figures

T. Geometric Measurement

T.01. Calculate the perimeter of polygons.
T.02. Calculate the area of polygons, including triangles, quadrilaterals and composite shapes.
T.03. Calculate the area between two shapes.
T.04. Solve word problems involving area and perimeter.
T.05. Calculate the circumference and area of circles, semicircles, and quarter circles.
T.06. Solve word problems involving circles.
T.07. Calculate the volume of prisms and cylinders.
T.08. Calculate the surface area of prisms and cylinders.
T.09. Determine the effect of changes in scale on perimeter, area, and volume.
T.10. Calculate the volume and surface area of similar solids.
T.11. Relate geometric measurements to algebraic equations.

U. Number Sequences

U.01. Define arithmetic and geometric sequences
U.02. Identify arithmetic and geometric sequences.
U.03. Determine the common difference in an arithmetic sequence.
U.04. Generate terms of an arithmetic sequence.
U.05. Determine the common ratio in a geometric sequence.
U.06. Generate terms of a geometric sequence.
U.07. Solve mixed review problems involving number sequences.
U.08. Solve word problems involving number sequences.
U.09. Evaluate variable expressions for number sequences.
U.10. Write variable expressions (formulas) for arithmetic sequences.
U.11. Write variable expressions (formulas) for geometric sequences.
U.12. Find a specific term in a sequence given the formula

V. Expressions and Properties

V.01. Write variable expressions to represent mathematical relationships.
V.02. Write variable expressions from diagrams.
V.03. Write variable expressions to solve word problems.
V.04. Evaluate one-variable expressions by substituting values for variables.
V.05. Evaluate multi-variable expressions.
V.06. Evaluate absolute value expressions.
V.07. Evaluate radical expressions.
V.08. Evaluate rational expressions.
V.09. Identify terms and coefficients in algebraic expressions.
V.10. Sort factors of expressions.
V.11. Identify and apply properties of addition and multiplication (commutative, associative, distributive, identity, inverse).
V.12. Multiply expressions using the distributive property.
V.13. Simplify variable expressions using properties of operations.
V.14. Add and subtract like terms in algebraic expressions.
V.15. Add, subtract, and multiply linear expressions.
V.16. Identify factors of linear expressions.
V.17. Identify equivalent linear expressions.
V.18. Apply algebraic expressions to solve geometric problems.

W. One-Variable Equations

W.01. Verify which value of x satisfies a given equation.
W.02. Translate word problems into algebraic equations.
W.03. Model and solve equations using algebra tiles.
W.04. Write and solve equations that represent diagrams.
W.05. State and apply the properties of equality (addition, subtraction, multiplication, division).
W.06. Solve one-step equations using inverse operations.
W.07. Solve two-step equations using inverse operations.
W.08. Solve multi-step equations involving the distributive property and combining like terms.
W.09. Solve equations involving like terms on both sides.
W.10. Solve equations by completing the solution steps.
W.11. Solve equations in word problems.
W.12. Create your own equations based on given solutions.

X. Monomials and Polynomials

X.01. Define and identify monomials.
X.02. Model polynomials with algebra tiles.
X.03. Add and subtract polynomials using algebra tiles.
X.04. Add and subtract polynomials algebraically.
X.05. Add polynomials to find the perimeter of geometric figures.
X.06. Multiply monomials using the product of powers rule.
X.07. Divide monomials using the quotient of powers rule.
X.08. Simplify expressions involving multiplication and division of monomials.
X.09. Simplify expressions involving powers of monomials.
X.10. Determine square and cube roots of monomials.
X.11. Multiply polynomials using algebra tiles.
X.12. Multiply polynomials algebraically, including using the distributive property and FOIL method.
X.13. Multiply polynomials to find area.
X.14. Divide polynomials by a monomial.

Y. Factorising

Y.01. Determine the highest common factor (HCF) of monomials.
Y.02. Factorise out a monomial from a polynomial.
Y.03. Factorise quadratic expressions with a leading coefficient of 1.
Y.04. Factorise quadratic expressions with other leading coefficients.
Y.05. Factorise quadratic expressions that are special cases (difference of squares, perfect square trinomials).
Y.06. Factorise quadratic expressions using algebra tiles.
Y.07. Factorise polynomials by grouping.
Y.08. Factorise polynomials completely, using a combination of techniques.
Y.09. Apply factoring to simplify rational expressions.

Z. Data and Graphs

Z.01. Read and interpret data presented in tables.
Z.02. Read and interpret bar graphs.
Z.03. Construct bar graphs to represent data.
Z.04. Read and interpret line graphs.
Z.05. Construct line graphs to represent data.
Z.06. Read and interpret line plots (dot plots).
Z.07. Construct line plots (dot plots) to represent data.
Z.08. Read and interpret stem-and-leaf plots.
Z.09. Construct stem-and-leaf plots to represent data.
Z.10. Read and interpret histograms.
Z.11. Construct histograms to represent data.
Z.12. Create frequency charts to organize data.
Z.13. Read and interpret pie charts (circle graphs).
Z.14. Calculate central angles for pie charts.
Z.15. Choose the best type of graph to represent a given set of data.
Z.16. Explain the advantages and disadvantages of different data representations.

AA. Statistics

BB. Probability

BB.01. Calculate the probability of simple events.
BB.02. Calculate the probability of opposite, mutually exclusive, and overlapping events.
BB.03. Determine experimental probability based on observations.
BB.04. Make predictions based on experimental probability.
BB.05. Determine the number of possible outcomes in compound events.
BB.06. Apply the counting principle to calculate the number of outcomes.
BB.07. Calculate the probability of compound events.
BB.08. Distinguish between independent and dependent events.

Course Content

A. Numbers and Counting

A.05. Calculate the highest common factor (HCF) of two or more numbers.

A.06. Calculate the lowest common multiple (LCM) of two or more numbers.

A.07. Solve word problems involving HCF and LCM.

A.08. Use prime factorization to simplify fractions.

A.09. Relate prime factorization to finding the square root and cube root of perfect squares and perfect cubes

A.01. Classify numbers as prime, composite, or neither.

A.02. Identify the factors of a given number.

A.03. Apply divisibility rules to determine if a number is divisible by another.

A.04. Determine the prime factorization of a number.

B. Integers

B.01. Represent integers on a number line.

B.02. Graph integers on horizontal and vertical number lines.

B.03. Compare and order integers using inequality symbols.

B.04. Find the absolute value of an integer.

B.05. Solve real-world problems involving ordering of integers.

B.06. Describe real world situations using integers.

C. Operations with Integers

C.01. Model addition and subtraction of integers using counters or number lines.

C.02. State and apply the rules for adding and subtracting integers.

C.03. Add and subtract integers, including multiple integers in a single expression.

C.04. Apply the rules for multiplying and dividing integers.

C.05. Multiply and divide integers.

C.06. Evaluate numerical expressions involving integers, using the order of operations.

C.07. Solve word problems involving addition, subtraction, multiplication, and division of integers.

C.08. Understand and apply properties of integers in arithmetic operations.

D. Rational Numbers

D.01. Define and identify rational and irrational numbers.

D.02. Write fractions in lowest terms (simplify fractions).

D.03. Determine the lowest common denominator (LCD) for a set of fractions.

D.04. Convert between decimals and fractions or mixed numbers.

D.05. Round decimals and mixed numbers to a specified place value.

D.06. Compare and order rational numbers, including fractions, decimals, and mixed numbers.

D.07. Place rational numbers in order on a number line.

D.08. Explain why the square root of a non-perfect square is irrational.

E. Operations with Rational Numbers

E.01. Determine the reciprocal and multiplicative inverse of a rational number.

E.02. Add and subtract rational numbers, including fractions and decimals.

E.03. Apply addition and subtraction rules to simplify expressions with rational numbers.

E.04. Multiply and divide rational numbers, including fractions and decimals.

E.05. Apply multiplication and division rules to simplify expressions with rational numbers.

E.06. Apply addition, subtraction, multiplication, and division rules in multi-step problems involving rational numbers.

E.07. Evaluate numerical expressions involving rational numbers, using the order of operations.

E.08. Solve word problems involving addition, subtraction, multiplication, and division of rational numbers.

E.09. Justify steps taken when simplifying expressions with rational numbers

F. Exponents and Roots

F.01. Understand the meaning of exponents and their notation.

F.02. Evaluate powers with positive, negative, decimal, and fractional bases.

F.03. Solve equations with variable exponents by trial and error.

F.04. Understand and apply the concept of negative exponents.

F.05. Evaluate powers with negative exponents.

F.06. Apply the rules of multiplication and division with exponents (product rule, quotient rule).

F.07. Apply the power rule for exponents.

F.08. Evaluate expressions using properties of exponents.

F.09. Identify equivalent expressions involving exponents.

F.10. Determine square roots of perfect squares.

F.11. Identify positive and negative square roots.

F.12. Estimate positive and negative square roots.

F.13. Understand the relationship between squares and square roots.

F.14. Solve equations involving squares and square roots.

F.15. Determine cube roots of perfect cubes.

F.16. Estimate cube roots.

F.17. Solve equations involving cubes and cube roots.

F.18. Simplify expressions involving multiple exponents and roots.

F.19. Express numbers using fractional exponents and their relationship to roots.

G. Scientific Notation

G.01. Convert numbers between standard and scientific notation.

G.02. Compare numbers written in scientific notation.

G.03. Multiply numbers written in scientific notation.

G.04. Divide numbers written in scientific notation.

G.05. Perform addition and subtraction with numbers in scientific notation.

G.06. Apply scientific notation to solve real-world problems involving very large or very small numbers.

H. Ratios, Rates and Proportions

H.01. Understand the concept of ratios and how to represent them.

H.02. Identify equivalent ratios.

H.03. Write an equivalent ratio for a given ratio.

H.04. Solve word problems involving equivalent ratios.

H.05. Determine and apply unit rates.

H.06. Compare ratios in word problems.