grade9 pixelmath

L1 Lesson 1.1 Demonstrate an understanding of: Representationof natural numbers, integers, rational numbers onthe number line

Lesson 1.2Demonstrate an understanding of: Representationof terminating/ non – terminating recurringdecimals, on the number line through successivemagnification

Lesson 1.3 Demonstrate an understanding of: Rationalnumbers as recurring/ terminating decimals

Lesson 1.4 Understand definition of the nth root of a realnumber

Lesson 1.5 Demonstrate an understanding of: Law ofexponents with integral powers

Lesson 1.6 Demonstrate an understanding of: Rationalexponents with positive real bases

Challenging Questions integrating the aboveconceptsLesson 1.7

Chapter : 2.Polynomials

L2 Lesson 2.1 Demonstrate an understanding of A polynomial inone variable with examples and counter examples

Lesson 2.2Demonstrate an understanding of Coefficients of apolynomial, terms of a polynomial and zeropolynomial, degree of a polynomial, constant,linear, quadratic and cubic polynomials

Lesson 2.3 Demonstrate an understanding of Monomials,binomials, trinomials

Lesson 2.4 Demonstrate an understanding of Factors andMultiples

Lesson 2.5 Demonstrate an understanding of Zeros of apolynomial

Lesson 2.6 Demonstrate an understanding of The RemainderTheorem with examples

Lesson 2.7 Demonstrate an understanding of Statement andproof of the Factor Theorem

Lesson 2.8Demonstrate an understanding of Factorization ofax^2 + bx +c, a ≠0, where a, b and c are realnumbers; and of cubic polynomials using the Factor Theorem

Lesson 2.9Algebraic expressions and identities, verificationof identities and their use in factorization ofpolynomials

Lesson 2.10 Challenging Questions integrating the aboveconcepts

Chapter : 4.Linear Equations in Two Variables

L4 Lesson 4.1Demonstrate an understanding of: Equation in twovariables (review /recall of linear equations in onevariable)

Lesson 4.2 Demonstrate an understanding of: Word problemson linear equations in one variable

Lesson 4.3 Demonstrate an understanding of: Linearequations of the type: ax +by +c = 0

Lesson 4.4Demonstrate an understanding of: A linearequation in two variables has infinitely manysolutions, each solution written as an orderedpair of real numbers, plotting them shows theylie in a line

Chapter : 3.Coordinate Geometry

L3 Lesson 3.1Demonstrate an understanding of: The Cartesianplane, coordinates of a point, names and termsassociated with the coordinate plane, notations,plotting points in the plane

Lesson 3.2 Demonstrate an understanding of: X coordinate(abscissa) and Y coordinate (ordinate)

Lesson 3.3 Demonstrate an understanding of: Four quadrants

Lesson 3.4

Demonstrate an understanding of: Graph of linearequations in two variables

Lesson 4.6Demonstrate an understanding of: Examples/wordproblems from real life including problems onRatio and Proportion

Challenging Questions integrating the aboveconcepts

Chapter : 5.Introduction to Euclid’s Geometry

L5 Lesson 5.1 Demonstrate an understanding of: The history ofGeometry in India and Euclid’s Geometry

Lesson 5.2Demonstrate an understanding of: Euclid’smethod of formalizing observed phenomenon intorigorous mathematics

Lesson 5.3 Demonstrate an understanding of: Euclid’sdefinitions, Axioms and Postulates

Lesson 5.4 Demonstrate an understanding of: Euclid’s fivepostulates

Lesson 5.5 Demonstrate an understanding of: Equivalentversions of Euclid’s fifth postulate

Lesson 5.6Show the relationship between axiom andtheorem, for example: Axiom1: Given two distinctpoints, there exists one and only one line throughthem

Lesson 5.7Show the relationship between axiom andtheorem, for example: Theorem 2: Two distinctlines cannot have more than one point in common

Lesson 5.8 Challenging Questions integrating the aboveconcepts

Chapter : 7.Triangles

L7 Lesson 7.1 Demonstrate an understanding of: Congruence oftriangles

Lesson 7.2Demonstrate an understanding of: Criteria forcongruence of triangles (SAS congruence, ASAcongruence, SSS congruence, RHs – Right angleHypotenuse Side congruence)

Lesson 7.3 Understand that: The angles opposite to equalsides of a triangle are equal

Lesson 7.4 Understand that: The sides opposite to equalangles of a triangle are equal

Lesson 7.5 Demonstrate an understanding of inequalities intriangles

L14

L15

Collection of data, presentation of data - tabularform, ungrouped / groupedLesson 14.1

Lesson 14.2 Bar graphs, histograms (with varying baselengths)

Lesson 14.3Frequency polygons, qualitative analysis of datato choose the correct form of presentation for thecollected data

Lesson 14.4 Mean, median, mode of ungrouped data

Lesson 14.5 Challenging Questions integrating the aboveconcepts

Chapter : 8.Quadrilaterals

L8 Lesson 8.1 Demonstrate an understanding of: Angle sumproperty of a quadrilateral

Lesson 8.2 Demonstrate an understanding of: Types ofquadrilaterals

Lesson 8.3Properties of parallelograms (A quadrilateral is aparallelogram if a pair of its opposite sides isparallel and equal)

Lesson 8.4 Understand that the diagonal divides aparallelogram into two congruent triangles

Lesson 8.5 In a parallelogram opposite sides are equal, andconversely

Lesson 8.6 In a parallelogram opposite angles are equal, andconversely

Lesson 8.7 In a parallelogram, the diagonals bisect each otherand conversely

Understand the Mid – Point TheoremLesson 8.8

Lesson 8.9 Challenging Questions integrating the aboveconcepts

Chapter : 11.Constructions

L11 Demonstrate an understanding of basicconstructions: A circleLesson 11.1

Lesson 11.2Demonstrate an understanding of basicconstructions: A perpendicular bisector of a linesegment

Lesson 11.3 Demonstrate an understanding of basicconstructions: A bisector of a given angle

Construction of angles of measure 60°, 90°, 45°etc., equilateral trianglesLesson 11.4

Lesson 11.5Construction of a triangle given its base,sum/difference of the other two sides and onebase angle

Lesson 11.6 Construction of a triangle of given perimeter andbase angles

Lesson 11.7Challenging Questions integrating the aboveconcepts

Chapter : 9.Area of Parallelograms and Triangles

L9 Lesson 9.1 Review concept of area, recall area of rectangle

Lesson 9.2 Understand Parallelograms on the same base andbetween the same parallels have the same area

Lesson 9.3Demonstrate an understanding of triangles on thesame or equal base and between the sameparallels are equal in area

Lesson 9.4 Challenging Questions integrating the aboveconcepts

Chapter : 10.Circles

L10 Demonstrate an understanding of Centre of circle,plane of the circle, radius and diameter

Demonstrate an understanding of Interior of thecircle

Demonstrate an understanding of Major arc

Demonstrate an understanding of Minor arc

Demonstrate an understanding of Exterior of thecircle

Chapter : 6.Lines and Angles

L6 Lesson 6.1 Demonstrate an understanding of: Line segment

Lesson 6.2 Demonstrate an understanding of: Collinearpoints and non collinear points

Lesson 6.3 Demonstrate an understanding of: Angle: armsand vertex

Lesson 6.4 Demonstrate an understanding of: Types ofangles: acute, right, obtuse, straight and reflex

Chapter : 12.Heron’s Formula

L12 Lesson 12.1 Area of a triangle with its sides as a, b and c iscalculated by using Heron’s formula

Lesson 12.2Area of a quadrilateral whose sides and onediagonal are given, can be calculated by dividingthe quadrilateral into two triangles and using theHeron’s formula

Lesson 12.3 Challenging Questions integrating the aboveconcepts

Chapter : 13.Surface Area and Volume

L13 Lesson 13.1 Surface areas and volumes of: Cubes

Lesson 13.2 Surface areas and volumes of: Cuboids

Lesson 13.3 Surface areas and volumes of: Spheres (includinghemispheres)

Lesson 13.4 Surface areas and volumes of: Right circularcylinders/cones

Lesson 13.5 Challenging Questions integrating the aboveconcepts

Lesson 15.1Develop an understanding of: Repeatedexperiments and observed frequency approachto probability

Lesson 15.2 Develop an understanding of: Focus on empiricalprobability

Lesson 15.3 Develop an understanding of: The experiments tobe drawn from real - life situations

Develop an understanding of: The probability ofan event lies between 0 and 1 (0 and 1 inclusive)

Challenging Questions integrating the aboveconcepts

Lesson 15.4

Lesson 15.5

Chapter : 14.Statistics

Chapter : 15.Probability

Lesson 6.5 Demonstrate an understanding of:Complementary and Supplementary angles

Lesson 6.6 Demonstrate an understanding of: Adjacentangles

Lesson 6.7 Demonstrate an understanding of: Verticallyopposite angles

Lesson 6.8Intersecting and non intersecting lines - If twolines intersect, vertically opposite angles areequal

Lesson 6.9Parallel lines and transversal - Angles formed andtheir axioms: angles formed includecorresponding angles, alternate angles andinterior angles.

Lesson 6.10 Lines parallel to the same line

Lesson 6.11 Angle sum property of a triangle: proof andproblems based on it

Lesson 6.12 Exterior angle of a triangle equal to the sum of thetwo opposite interior angles

Lesson 6.13 Word problems on all the above

Lesson 6.14 Challenging Questions integrating the aboveconcepts

Lesson 4.5

Lesson 4.7 Equations of lines parallel to the x - axis andy-axis: Represent solution on number line

Equations of lines parallel to the x - axis andy-axis: Represent solution on the Cartesian Plane

Lesson 4.9 Challenging Questions integrating the aboveconcepts

Lesson 4.8

Lesson 10.1

Lesson 10.2

Lesson 10.4

Lesson 10.5

Demonstrate an understanding of Circumference

Demonstrate an understanding of Major segment

Lesson 10.6

Lesson 10.3

Demonstrate an understanding of Minor segment

Demonstrate an understanding that there is oneand only one circle passing through three givennon-collinear points

Understand that equal chords of a circle subtendequal angles at the center and its converse

Understand that the perpendicular from the centerof a circle to a chord bisects the chord andconversely, the line drawn through the center of a circle to bisect a chord is perpendicular to the chord

Lesson 10.7

Lesson 10.8

Lesson 10.10

Understand that equal chords of a circle (or ofcongruent circles) are equidistant from the center(or their respective centers) and conversely

Lesson 10.12

Lesson 10.11

Lesson 10.9

Demonstrate an understanding that the anglesubtended by an arc at the center is double theangle subtended by it at any point on theremaining part of the circle

The sum of either of the pair of the oppositeangles of a cyclic quadrilateral is 180° and itsconverse

Understand that the angles in the same segmentof a circle are equal

If a line segment joining two points subtendsequal angle at two other points lying on the sameside of the line containing the segment, the fourpoints lie on a circle

Lesson 10.13

Lesson 10.15

Problem involving proofs of above and based onthe proofs finding an angle and other relatedterms

Lesson 10.17

Lesson 10.16

Lesson 10.14

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Chapter : 1.Number System

LESSON LEVELS CONCEPT

GRADE9

Lesson 7.6 Word problems on all the above

Lesson 7.7 Challenging Questions integrating the above concepts

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