 • 7
VII Standards
Top Mathematicians
• Money
• Geometry
• 7.G.1.1
Understanding shapes:
â€¢ Pairs of angles (linear, supplementary, complementary, adjacent, vertically opposite) (verification and simple proof of vertically opposite angles)
â€¢ Properties of parallel lines with transversal (alternate, corresponding, interior, exterior angles)
• 7.G.1.2
Properties of triangles:
â€¢ Angle sum property (with notions of proof & verification through paper folding, proofs using property of parallel lines, difference between proof and verification.)
â€¢ Exterior angle property
â€¢ Sum of two sides of a it's third side
â€¢ Pythagoras Theorem (Verification only)
• 7.G.1.3
Symmetry
â€¢ Recalling reflection symmetry
â€¢ Idea of rotational symmetry, observations of rotational symmetry of 2-D objects. (90°, 120°, 180°)
â€¢ Operation of rotation through 90° and 180° of simple figures.
â€¢ Examples of figures with both rotation and reflection symmetry (both operations)
â€¢ Examples of figures that have reflection and rotation symmetry and vice-versa
• 7.G.1.4
Representing 3-D in 2-D:
â€¢ Drawing 3-D figures in 2-D showing hidden faces.
â€¢ Identification and counting of vertices, edges, faces, nets (for cubes cuboids, and cylinders, cones).
â€¢ Matching pictures with objects (Identifying names)
â€¢ Mapping the space around approximately through visual estimation.
• 7.G.1.5
Congruence
â€¢ Congruence through superposition (examples-blades, stamps, etc.)
â€¢ Extend congruence to simple geometrical shapes e.g. triangles, circles.
â€¢ Criteria of congruence (by verification) SSS, SAS, ASA, RHS
• 7.G.1.6
Construction (Using scale, protractor, compass)
â€¢ Construction of a line parallel to a given line from a point outside it. (Simple proof as remark with the reasoning of alternate angles)
â€¢ Construction of simple triangles. Like given three sides, given a side and two angles on it, given two sides and the angle between them.
• The Number System
• 7.NS.1.1
Knowing our Numbers: Integers
â€¢ Multiplication and division of integers (through patterns). Division by zero is meaningless
â€¢ 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.
â€¢ Word problems including integers (all operations)
• 7.NS.1.2
Fractions and rational numbers:
â€¢ Multiplication of fractions
â€¢ Fraction as an operator
â€¢ Reciprocal of a fraction
â€¢ Division of fractions
â€¢ Word problems involving mixed fractions
â€¢ Introduction to rational numbers (with representation on number line)
â€¢ Operations on rational numbers (all operations)
â€¢ Representation of rational number as a decimal.
â€¢ Word problems on rational numbers (all operations)
â€¢ Multiplication and division of decimal fractions
â€¢ Conversion of units (length & mass)
â€¢ Word problems (including all operations)
• 7.NS.1.3
Powers:
â€¢ Exponents only natural numbers.
â€¢ 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)
• Mensuration
• 7.MEN.1.1
Revision of perimeter, Idea of, Circumference of Circle
• 7.MEN.1.2
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
• Algebra
• 7.OA.1.1
Algebraic Expressions
â€¢ Generate algebraic expressions (simple) involving one or two variables
â€¢ Identifying constants, coefficient, powers
â€¢ Like and unlike terms, degree of expressions e.g., x²y etc. (exponent ≤3, number of variables)
â€¢ Addition, subtraction of algebraic expressions (coefficients should be integers).
â€¢ Simple linear equations in one variable (in contextual problems) with two operations (avoid complicated coefficients)
• Ratios and Proportional Relationships
• 7.RP.1.1a
Ratio and proportion (revision)
• 7.RP.1.1b
Unitary method continued, consolidation, general expression.
• 7.RP.1.1c
Percentage - an introduction.
• 7.RP.1.1d
Understanding percentage as a fraction with denominator 100
• 7.RP.1.1e
Converting fractions and decimals into percentage and vice-versa.
• 7.RP.1.1f
Application to profit and loss (single transaction only)
• 7.RP.1.1g
Application to simple interest (time period in complete years).
• Data Handling
• 7.DH.1.1a
Collection and organisation of data â€“ choosing the data to collect for a hypothesis testing.
• 7.DH.1.1b
Mean, median and mode of ungrouped data â€“ understanding what they represent.
• 7.DH.1.1c
Constructing bargraphs
• 7.DH.1.1d
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.