6th grade 7th grade Maths Bridging course
Level I
| (i) Knowing our Numbers: | |
| Consolidating the sense of numbers up to 5 digits, Size, estimation of numbers, identifying smaller, larger, etc. Place value (recapitulation and extension), connectives: use of symbols =, <, > and use of brackets, word problems on number operations involving large numbers up to a maximum of 5 digits in the answer after all operations. This would include conversions of units of length & mass (from the larger to the smaller units), estimation of outcome of number operations. Introduction to a sense of the largeness of, and initial familiarity with, large numbers up to 8 digits and approximation of large numbers) | |
| (ii)Playing with Numbers: | |
| Simplification of brackets, Multiples and factors, divisibility rule of 2, 3, 4, 5, 6, 8, 9, 10, 11. (All these through observing patterns. Children would be helped in deducing some and then asked to derive some that are a combination of the basic patterns of divisibility.) Even/odd and prime/composite numbers, Co-prime numbers, prime factorisation, every number can be written as products of prime factors. HCF and LCM, prime factorization and division method for HCF and LCM, the property LCM X HCF = product of two numbers. All this is to be embedded in contexts that bring out the significance and provide motivation to the child for learning these ideas. | |
| (iii) Whole numbers | |
| Natural numbers, whole numbers, properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity), number line. Seeing patterns, identifying and formulating rules to be done by children. (As familiarity with algebra grows, the child can express the generic pattern.) | |
| (iv) Negative Numbers and Intergers | |
| How negative numbers arise, models of negative numbers, connection to daily life, ordering of negative numbers, representation of negative numbers on number line. Children to see patterns, identify and formulate rules. What are integers, identification of integers on the number line, operation of addition and subtraction of integers, showing the operations on the number line (addition of negative integer reduces the value of the number) comparison of integers, ordering of integers. | |
| (v) Fractions: | |
| Revision of what a fraction is, Fraction as a part of whole, Representation of fractions (pictorially and on number line), fraction as a division, proper, improper & mixed fractions, equivalent fractions, comparison of fractions, addition and subtraction of fractions (Avoid large and complicated unnecessary tasks). (Moving towards abstraction in fractions) Review of the idea of a decimal fraction, place value in the context of decimal fraction, inter conversion of fractions and decimal fractions (avoid recurring decimals at this stage), word problems involving addition and subtraction of decimals (two operations together on money, mass, length and temperature) | |
| Algebra | |
| INTRODUCTION TO ALGEBRA | |
| • Introduction to variable through patterns and through appropriate word problems and generalisations (example 5 X 1 = 5 etc.) • Generate such patterns with more examples. • Introduction to unknowns through examples with simple contexts (single perations) |
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| Ratio and Proportion | |
| • Concept of Ratio • Proportion as equality of two ratios • Unitary method (with only direct variation implied) • Word problems |
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| Geometry | |
| (i) Basic geometrical ideas (2 -D): | |
| Introduction to geometry. Its linkage with and reflection in everyday experience. • Line, line segment, ray. • Open and closed figures. • Interior and exterior of closed figures. • Curvilinear and linear boundaries • Angle — Vertex, arm, interior and exterior, • Triangle — vertices, sides, angles, interior and exterior, altitude and median • Quadrilateral — Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral. • Circle — Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior. |
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| (ii) Understanding Elementary Shapes (2-D and 3-D): | |
| • Measure of Line segment • Measure of angles • Pair of lines – Intersecting and perpendicular lines – Parallel lines • Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle • Classification of triangles (on the basis of sides, and of angles) • Types of quadrilaterals – Trapezium, parallelogram, rectangle, square, rhombus. • Simple polygons (introduction) (Upto octagons regulars as well as non regular). • Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,prism (triangular), pyramid (triangular and square) Identification and locating in the surroundings • Elements of 3-D figures. (Faces, Edges and vertices) • Nets for cube, cuboids, cylinders, cones and tetrahedrons. |
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| (iii) Symmetry: (reflection) | |
| • Observation and identification of 2-D symmetrical objects for reflection symmetry • Operation of reflection (taking mirror images) of simple 2-D objects • Recognising reflection symmetry (identifying axes) |
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| (iv) Constructions (using Straight edge Scale, protractor, compasses) | |
| • Drawing of a line segment • Construction of circle • Perpendicular bisector • Construction of angles (using protractor) • Angle 60o, 120o (Using Compasses) • Angle bisector- making angles of 30o, 45o, 90o etc. (using compasses) • Angle equal to a given angle (using compass) • Drawing a line perpendicular to a given line from a point a) on the line b) outside the line. |
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| Mensuration | |
| CONCEPT OF PERIMETER AND INTRODUCTION TO AREA | |
| Introduction and general understanding of perimeter using many shapes. Shapes of different kinds with the same perimeter. Concept of area, Area of a rectangle and a square Counter examples to different misconcepts related to perimeter and area. Perimeter of a rectangle – and its special case – a square. Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation. | |
| Data handling | |
| (i) What is data – choosing data to examine a hypothesis? (ii) Collection and organisation of data – examples of organising it in tally bars and a table. (iii) Pictograph- Need for scaling in pictographs interpretation & construction. (iv) Making bar graphs for given data interpreting bar graphs+. |
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Level II
| Number System | |
| (i) 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) | |
| (ii) 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) |
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| (iii) Powers: | |
| • Exponents only natural numbers. • Laws of exponents (through observing patterns to arrive at generalisation.) |
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| (i) am an am+n (ii) (am)n =amn (iii) am/an = am-n, where m – n ∈ Ν |
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| Algebra | |
| 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) |
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| Ratio and Proportion | |
| •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). |
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| Geometry | |
| (i) 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) | |
| (ii) 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) |
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| (iii) Symmetry | |
| • Recalling reflection symmetry • Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90o, 120o, 180o) • Operation of rotation through 90o and 180o 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 |
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| (iv) 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. |
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| (v) Congruence | |
| • Congruence through superposition (examplesblades, stamps, etc.) • Extend congruence to simple geometrical shapes e.g. triangles, circles. • Criteria of congruence (by verification) SSS, SAS, ASA, RHS |
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| (vi) 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. |
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| Mensuration | |
| • 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 handling | |
| (i) Collection and organisation of data – choosing the data to collect for a hypothesis testing. (ii) Mean, median and mode of ungrouped data – understanding what they represent. (iii) Constructing bargraphs (iv) 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 |
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of randomness.