{"id":158,"date":"2016-06-02T16:49:15","date_gmt":"2016-06-02T16:49:15","guid":{"rendered":"http:\/\/nexeonsoft.com\/smartschool\/?page_id=158"},"modified":"2016-06-02T17:08:56","modified_gmt":"2016-06-02T17:08:56","slug":"6th-grade-7th-grade-maths-bridging-course","status":"publish","type":"page","link":"http:\/\/nexeonsoft.com\/smartschool\/6th-grade-7th-grade-maths-bridging-course\/","title":{"rendered":"6th grade 7th grade Maths Bridging course"},"content":{"rendered":"

6th<\/sup> grade 7th<\/sup> grade Maths Bridging course<\/p>\n

Level I<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
(i)\u00a0Knowing our Numbers:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nConsolidating 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)<\/td>\n<\/tr>\n
(ii)Playing with Numbers:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nSimplification 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.<\/td>\n<\/tr>\n
(iii)\u00a0Whole numbers<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nNatural 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.)<\/td>\n<\/tr>\n
(iv)\u00a0Negative Numbers and Intergers<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nHow 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.<\/td>\n<\/tr>\n
(v)\u00a0Fractions:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nRevision 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)<\/td>\n<\/tr>\n
Algebra<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
INTRODUCTION TO ALGEBRA<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Introduction to variable through patterns and through appropriate word problems and generalisations (example 5 X 1 = 5 etc.)
\n\u2022 Generate such patterns with more examples.
\n\u2022 Introduction to unknowns through examples with simple contexts (single perations)<\/td>\n<\/tr>\n
Ratio and Proportion<\/a><\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Concept of Ratio
\n\u2022 Proportion as equality of two ratios
\n\u2022 Unitary method (with only direct variation implied)
\n\u2022 Word problems<\/td>\n<\/tr>\n
Geometry<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
(i)\u00a0Basic geometrical ideas (2 -D)<\/a>:<\/strong><\/td>\n<\/tr>\n
<\/td>\nIntroduction to geometry. Its linkage with and reflection in everyday experience.
\n\u2022 Line, line segment, ray.
\n\u2022 Open and closed figures.
\n\u2022 Interior and exterior of closed figures.
\n\u2022 Curvilinear and linear boundaries
\n\u2022 Angle \u2014 Vertex, arm, interior and exterior,
\n\u2022 Triangle \u2014 vertices, sides, angles, interior and exterior, altitude and median
\n\u2022 Quadrilateral \u2014 Sides, vertices, angles, diagonals, adjacent sides and opposite sides (only convex quadrilateral are to be discussed), interior and exterior of a quadrilateral.
\n\u2022 Circle \u2014 Centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference, interior and exterior.<\/td>\n<\/tr>\n
(ii)\u00a0Understanding Elementary Shapes (2-D and 3-D)<\/a>:<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Measure of Line segment
\n\u2022 Measure of angles
\n\u2022 Pair of lines
\n– Intersecting and perpendicular lines
\n– Parallel lines
\n\u2022 Types of angles- acute, obtuse, right, straight, reflex, complete and zero angle
\n\u2022 Classification of triangles (on the basis of sides, and of angles)
\n\u2022 Types of quadrilaterals \u2013 Trapezium, parallelogram, rectangle, square, rhombus.
\n\u2022 Simple polygons (introduction) (Upto octagons regulars as well as non regular).
\n\u2022 Identification of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,prism (triangular), pyramid (triangular and square)
\nIdentification and locating in the surroundings
\n\u2022 Elements of 3-D figures. (Faces, Edges and vertices)
\n\u2022 Nets for cube, cuboids, cylinders, cones and tetrahedrons.<\/td>\n<\/tr>\n
(iii)\u00a0Symmetry:<\/a><\/strong>\u00a0<\/strong>(reflection)<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Observation and identification of 2-D symmetrical objects for reflection symmetry
\n\u2022 Operation of reflection (taking mirror images) of simple 2-D objects
\n\u2022 Recognising reflection symmetry (identifying axes)<\/td>\n<\/tr>\n
(iv)\u00a0Constructions<\/a><\/strong>\u00a0<\/strong>(using Straight edge Scale, protractor, compasses)<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Drawing of a line segment
\n\u2022 Construction of circle
\n\u2022 Perpendicular bisector
\n\u2022 Construction of angles (using protractor)
\n\u2022 Angle 60o<\/sup>, 120o<\/sup>\u00a0(Using Compasses)
\n\u2022 Angle bisector- making angles of 30o<\/sup>, 45o<\/sup>, 90o<\/sup>\u00a0etc. (using compasses)
\n\u2022 Angle equal to a given angle (using compass)
\n\u2022 Drawing a line perpendicular to a given line from a point a) on the line b) outside the line.<\/td>\n<\/tr>\n
Mensuration<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
CONCEPT OF PERIMETER AND INTRODUCTION TO AREA<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\nIntroduction 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 \u2013 and its special case \u2013 a square. Deducing the formula of the perimeter for a rectangle and then a square through pattern and generalisation.<\/td>\n<\/tr>\n
Data handling<\/a><\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\n(i) What is data – choosing data to examine a hypothesis?
\n(ii) Collection and organisation of data – examples of organising it in tally bars and a table.
\n(iii) Pictograph- Need for scaling in pictographs interpretation & construction.
\n(iv) Making bar graphs for given data interpreting bar graphs+.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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Level II<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Number System<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
(i)\u00a0Knowing our Numbers:Integers<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Multiplication and division of integers (through patterns). Division by zero is meaningless<\/td>\n<\/tr>\n
<\/td>\n\u2022 Properties of integers (including identities for addition & multiplication, commutative, associative, distributive) (through patterns).<\/td>\n<\/tr>\n
<\/td>\nThese 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.<\/td>\n<\/tr>\n
<\/td>\n\u2022 Word problems including integers (all operations)<\/td>\n<\/tr>\n
(ii)\u00a0Fractions and rational numbers:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Multiplication of fractions
\n\u2022 Fraction as an operator
\n\u2022 Reciprocal of a fraction
\n\u2022 Division of fractions
\n\u2022 Word problems involving mixed fractions
\n\u2022 Introduction to rational numbers (with representation on number line)
\n\u2022 Operations on rational numbers (all operations)
\n\u2022 Representation of rational number as a decimal.
\n\u2022 Word problems on rational numbers (all operations)
\n\u2022 Multiplication and division of decimal fractions
\n\u2022 Conversion of units (length & mass)
\n\u2022 Word problems (including all operations)<\/td>\n<\/tr>\n
(iii)\u00a0Powers:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Exponents only natural numbers.
\n\u2022 Laws of exponents (through observing patterns to arrive at generalisation.)<\/td>\n<\/tr>\n
<\/td>\n(i) am<\/sup>\u00a0an<\/sup>\u00a0am+n<\/sup>
\n(ii) (am<\/sup>)n<\/sup>\u00a0=amn<\/sup>
\n(iii) am<\/sup>\/an<\/sup>\u00a0= am-n<\/sup>, where m – n \u2208 \u039d<\/td>\n<\/tr>\n
Algebra<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
ALGEBRAIC EXPRESSIONS<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Generate algebraic expressions (simple) involving one or two variables
\n\u2022 Identifying constants, coefficient, powers
\n\u2022 Like and unlike terms, degree of expressions e.g., x2<\/sup>y etc. (exponent \u2264 3, number of variables )
\n\u2022 Addition, subtraction of algebraic expressions (coefficients should be integers).
\n\u2022 Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)<\/td>\n<\/tr>\n
Ratio and Proportion<\/a><\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022Ratio and proportion (revision)
\n\u2022 Unitary method continued, consolidation, general expression.
\n\u2022 Percentage- an introduction.
\n\u2022 Understanding percentage as a fraction with denominator 100
\n\u2022 Converting fractions and decimals into percentage and vice-versa.
\n\u2022 Application to profit and loss (single transaction only)
\n\u2022 Application to simple interest (time period in complete years).<\/td>\n<\/tr>\n
Geometry<\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
(i)\u00a0Understanding shapes:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)<\/td>\n<\/tr>\n
<\/td>\n\u2022 Properties of parallel lines with transversal (alternate,corresponding, interior, exterior angles)<\/td>\n<\/tr>\n
(ii)\u00a0Properties of triangles:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)
\n\u2022 Exterior angle property
\n\u2022 Sum of two sides of a it’s third side
\n\u2022 Pythagoras Theorem (Verification only)<\/td>\n<\/tr>\n
(iii)\u00a0Symmetry<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Recalling reflection symmetry
\n\u2022 Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90o<\/sup>, 120o<\/sup>, 180o<\/sup>)
\n\u2022 Operation of rotation through 90o<\/sup>\u00a0and 180o<\/sup>\u00a0of simple figures.
\n\u2022 Examples of figures with both rotation and reflection symmetry (both operations)
\n\u2022 Examples of figures that have reflection and rotation symmetry and vice-versa<\/td>\n<\/tr>\n
(iv)\u00a0Representing 3-D in 2-D:<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Drawing 3-D figures in 2-D showing hidden faces.
\n\u2022 Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
\n\u2022 Matching pictures with objects (Identifying names)
\n\u2022 Mapping the space around approximately through visual estimation.<\/td>\n<\/tr>\n
(v)\u00a0Congruence<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Congruence through superposition (examplesblades, stamps, etc.)
\n\u2022 Extend congruence to simple geometrical shapes e.g. triangles, circles.
\n\u2022 Criteria of congruence (by verification) SSS, SAS, ASA, RHS<\/td>\n<\/tr>\n
(vi)\u00a0Construction (Using scale, protractor, compass)<\/a><\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 Construction of a line parallel to a given line from a point outside it.(Simple proof as remark with the reasoning of alternate angles)
\n\u2022 Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.<\/td>\n<\/tr>\n
Mensuration<\/strong><\/td>\n<\/tr>\n
<\/td>\n\u2022 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.<\/td>\n<\/tr>\n
Data handling<\/a><\/strong>\u00a0<\/strong><\/td>\n<\/tr>\n
<\/td>\n(i) Collection and organisation of data \u2013 choosing the data to collect for a hypothesis testing.
\n(ii) Mean, median and mode of ungrouped data \u2013 understanding what they represent.
\n(iii) Constructing bargraphs
\n(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<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

of randomness.<\/p>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

6th grade 7th grade Maths Bridging course Level I (i)\u00a0Knowing 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 =, <, Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/pages\/158"}],"collection":[{"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/comments?post=158"}],"version-history":[{"count":2,"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/pages\/158\/revisions"}],"predecessor-version":[{"id":175,"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/pages\/158\/revisions\/175"}],"wp:attachment":[{"href":"http:\/\/nexeonsoft.com\/smartschool\/wp-json\/wp\/v2\/media?parent=158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}