Math Games

Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two concentric circles. Data

Understanding shapes:
• Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)
• Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)

Properties of triangles:
• Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)
• Exterior angle property
• Sum of two sides of a it's third side
• Pythagoras Theorem (Verification only)

Symmetry
• Recalling reflection symmetry
• Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90°, 120°, 180°)
• Operation of rotation through 90° and 180° of simple figures.
• Examples of figures with both rotation and reflection symmetry (both operations)
• Examples of figures that have reflection and rotation symmetry and vice-versa

Representing 3-D in 2-D:
• Drawing 3-D figures in 2-D showing hidden faces.
• Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
• Matching pictures with objects (Identifying names)
• Mapping the space around approximately through visual estimation.

Congruence
• Congruence through superposition (examples-blades, stamps, etc.)
• Extend congruence to simple geometrical shapes e.g. triangles, circles.
• Criteria of congruence (by verification) SSS, SAS, ASA, RHS

Construction (Using scale, protractor, compass)
• Construction of a line parallel to a given line from a point outside it. (Simple proof as remark with the reasoning of alternate angles)
• Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.

Revision of perimeter, Idea of, Circumference of Circle

Area:
Concept of measurement using a basic unit area of a square, rectangle, triangle, parallelogram and circle, area between two rectangles and two concentric circles. Data

Knowing our Numbers: Integers
• Multiplication and division of integers (through patterns). Division by zero is meaningless
• Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns). These would include examples from whole numbers as well. Involve expressing commutative and associative properties in a general form. Construction of counterexamples, including some by children. Counter examples like subtraction is not commutative.
• Word problems including integers (all operations)

Fractions and rational numbers:
• Multiplication of fractions
• Fraction as an operator
• Reciprocal of a fraction
• Division of fractions
• Word problems involving mixed fractions
• Introduction to rational numbers (with representation on number line)
• Operations on rational numbers (all operations)
• Representation of rational number as a decimal.
• Word problems on rational numbers (all operations)
• Multiplication and division of decimal fractions
• Conversion of units (length & mass)
• Word problems (including all operations)

Powers:
• Exponents only natural numbers.
• Laws of exponents (through observing patterns to arrive at generalisation.)
- a^m x a^n= a^(m+n)
- (a^m)n = a^(mn)
- (a^m) /(a^n) = a^(m-n), where (m-n ∈ N)

Algebraic Expressions
• Generate algebraic expressions (simple) involving one or two variables
• Identifying constants, coefficient, powers
• Like and unlike terms, degree of expressions e.g., x²y etc. (exponent ≤3, number of variables)
• Addition, subtraction of algebraic expressions (coefficients should be integers).
• Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)

Ratio and proportion (revision)

Unitary method continued, consolidation, general expression.

Percentage - an introduction.

Understanding percentage as a fraction with denominator 100

Converting fractions and decimals into percentage and vice-versa.

Application to profit and loss (single transaction only)

Application to simple interest (time period in complete years).

Collection and organisation of data – choosing the data to collect for a hypothesis testing.

Mean, median and mode of ungrouped data – understanding what they represent.

Constructing bargraphs

Feel of probability using data through experiments. Notion of chance in events like tossing coins, dice etc. Tabulating and counting occurrences of 1 through 6 in a number of throws. Comparing the observation with that for a coin. Observing strings of throws, notion of randomness.