MINIMUM LEVELS OF LEARNING IN MATHEMATICS
Introduction
Objectives of Primary Mathematics One of the major objectives of teaching primary mathematics is to enable children to solve speedily and accurately the numerical and spatial problems which they encounter at home, in the school and in the community. Primary mathematics should help children develop understanding of key mathematical concepts at each level through appropriate experiences with things from the physical world and the immediate environment. It should help children develop an understanding from the concrete to the abstract, from the specific to the general. The mathematics curriculum at the primary stage should, therefore, be directed to achieve the following objectives:
Ability to
- perform computations, with speed and accuracy
- translate verbal statements (a) in mathematical form using appropriate symbols, and (b) diagramatically
- make reasonably good approximations and estimate measurements
- apply mathematical concepts and skills to solve simple problems of day-to-day life
- think logically
- recognize order and pattern.
Note to Minimum Learning Competencies 1. The key mathematical concepts for each class are not listed in order of instructional sequence but have been classified under the following five areas of mathematical competencies:
(i) Understanding Whole Numbers and Numerals.
(ii) Ability to Add, Subtract, Multiply and Divide Whole Numbers.
(iii) Ability to use and solve simple problems of daily life relating to Units of Money, Length, Weight, Capacity, Area and Time.
(iv) Ability to use Fractions, Decimals and Percentage.
(v) Understanding of Geometrical Shapes and Spatial Relationships.
2. There is a separate section entitled Readiness for Primary Mathematics which precedes the above five areas. These are not to be viewed as
MINIMUM LEVELS OF LEARNING IN MATHEMATICS 19
experiences to be given only at the beginning of Class I, but rather spread over Class I and Class II as developing readiness for the concepts and problem-solving which are to follow in Classes III-V.
3. The key mathematical competencies have been listed primarily to include for the most part concepts and application of skills which will help all children acquire certain minimum levels of functional mathematics Mastery of these competencies will help children at present and in their later life to apply mathematical concepts and skills to solve problems relating to daily life. Therefore, these key mathematical competencies have included mental mathematical skills, estimation skills and the understanding of shapes and spatial relationships.
4. Concrete objects and mathematical equipment need to be used throughout the primary stage in mathematics, especially wherever new key concepts have to be gained. Though not always stated in conjunction with each skill/concept in the minimum learning competencies, it is imperative that this approach should be consistently followed. It has been stated in Class I as indicative and to highlight the significance of the experiential approach in the teaching and learning of mathematics. Such experiential learning will also enable children to find pleasure and excitement in the study of mathematics.
5. It should be noted that while it has not been stated, children need to revise the earlier stage of mathematical concepts before proceedings further. This revision has not been indicated with each concept.
6. In a few cases, the same mathematical competency has been repeated in two classes. This implies that while instruction and practice in the competency should be given in both classes, mastery should only be expected in the higher class.
Readiness for Primary Mathematics 1. Arrange objects in order according to size, length, thickness, weight and volume and use vocabulary describing the relationship, e.g. 'bigger than', 'smaller than', 'the same as', 'heavier', 'heaviest', etc.
2. Classify groups of objects according to various properties, e.g. size, Shape, length, etc.
3. Compare positions of things and persons in terms of the distance given point of reference and use vocabulary describing the relationships, e.g. 'near', 'far', 'nearest', etc.
4. Perceive and reproduce simple patterns relating to shape, colour, position and quantity.
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Statement of MLLs in Mathematics
Areas Class I Class II Class III Class IV Class V
1 Under- 1.1.1. Counts from 1-20 * 1.2.1. Demonstrates 1.3.1. Recognizes and 1.4.1. Recognizes and 1.5.1. Recognizes and
standing using objects and understanding of place writes numerals from writes numerals from writes numerals from
Whole pictures value of 2-digit numbers 100-1,000 1,000-10,000 10,000-1,00,00,000
Numbers by expanding numbers (One crore)
and between 10-99 into 10's
Numerals and ones, and by
expressing the expanded
form as a 2-digit number
*1.1.2. Recognizes 1.2.2. States the place 1.3.2. Writes numbers 1.4.2. Writes number 1.5.2. Writes number
numerals and matches value of the digits names from 1-100 names up to 10,000 names up to 1,00,00,000
numbers to numerals within a 2-digit (One crore)
from 1-100 numeral
1.1.3. Identifies zero 1.2.3. Demonstrates 1.3.3. Demonstrates 1.4.3. Demonstrates 1.5.3. Demonstrates
as the number represen- understanding of understanding of understanding of understanding of place
ting nothing or the ordinal numbers place value of 3-digit place value of 4- value of 5 and 6-digit
absence of objects in 1-10 (e.g. 1st, numbers by expanding digit numbers by numbers by expanding
a collection 2nd, 3rd) numbers between 100- expanding numbers numbers between
999 into 100's, 10's between 1,000-9, 10,000-9,99,999
and ones, and by 999 into 1,000's, into 1,00,000's,
expressing the expan- 100's, 10's and ones 10,000's, 1,000's,
ded form as a 3-digit and by expressing 100's, 10's and ones,
number the expanded form and by expressing the
as a 4-digit number expanded form as a
5 or 6-digit number
* Competencies marked with an indicate that these competencies should also be evaluated using concrete objects, pictures or
relevant mathematical apparatus.
Areas Class I Class II class III class IV Class V
1.1.4. Demonstrates 1.2.4. Finds the 1.3.4. States the place 1.4.4. Arranges 1.5.4. Arranges numbers
understanding of place number of objects in value of the digits within numbers from from 10,000-1,00,000
value by expanding a given set by coun- a 3-digit numeral 1,000-10,000 in in ascending and
numbers 10-20 into ting in 2s, 5s, or ascending and descending order
tens and ones, and by 10's (set of objects descending order
expressing the expanded not exceeding 100)
form as a two-digit
number
1.1.5. States the place 1.3.5. Arranges numbers 1.4.5 Identifies 1.5.5. Identifies the
value of the digits in from 100-1,000 in the numeral/numerals numeral/numerals before,
the numbers 10-20 ascending and descend- before, after or after or between any
ing order between any numeral/ numeral/numerals
numerals between between 10,000-
1,000-10,000 1,00,000
1.1.6. Arranges 1.3.6. Identifies the 1.4.6. Compares 1.5.6. Compares
numbers from 1-100 numeral/numerals numbers from 1,000- numbers from 10,000
in ascending and before, after or between 10,000 using the 9,99,999 using the
descending order any numeral/numerals signs >, <, = signs >, <, =
between 100-1,000
1.1.7. Identifies the 1.3.7. Compares 1.4.7. Demonstrates 1.5.7. Calculates
numeral/numerals numbers from 100-1,000 understanding of Highest Common
before after or using the signs >, <, = multiples and factors Factor (HCF) of 2
between any numeral/ of a number numbers not exceeding
numerals between 1-100 100
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Areas Class I Class II Class III Class IV Class V
1.3.8. Demonstrates 1.4.8. Demonstrates 1.5.8. Calculates
1.1.8. Compares understanding of even understanding of prime Lowest Common
numbers from 1-100 and odd numbers numbers up to 50 Multiple (LCM) of 2
using the words 'more or 3 numbers each of
than', 'less than', 'the which do not exceed 10
some as', 'greatest',
'least'
1.1.9. Writes the 1.3.9. Demonstrates
numerals from 1-100 understanding of
ordinal numbers 11-100
2. Ability *2.1.1. Adds numbers 2.2.1. Adds two or 2.3.1. Adds two or three 2.4.1. Adds two or 2.5.1. Adds two to four
to Add, 0-18 with sum not three 2-digit numbers 3-digit numbers with three 4-digit numbers 5 and 6-digit numbers
Subtract, exceeding 18 without carrying and carrying and sum not with carrying and with sum not exceeding
Multiply with carrying and sum exceeding 999 exceeding 9,999 9,99,999
and Divide not exceeding 99
Whole
Numbers
2.1.2. Adds two 2.2.2. Subtracts 2-digit 2.3.2. Subtracts 3-digit 2.4.2. Subtracts 4- 2.5.2. Subtracts 5 and
numbers mentally with numbers without numbers with borrowing digit numbers with 6-digit numbers
sum not exceeding 9 borrowing and with borrowing
borrowing
Areas Class I Class II class III Class IV Class V
*2.1.3. Subtracts 2.2.3. Solves one step 2.3.3. Solves 1-2 steps 2.4.3. Solves 1-2 2.5.3. Multiplies a
numbers from 0-18 of daily life problems of daily life problems steps of daily life number by a number
to separate smaller involving skills involving skills 2.3.1 problems involving up to 3 digits with
number from a larger 2.2.1 and 2.2.2 and 2.3.2 skills 2.4.1-2.4.2 product not exceeding
number and to find 9,99,999
the difference
between two numbers
2.1.4. Subtracts 2.2.4. Adds two 2.3.4. Adds and sub- 2.4.4. Adds and sub- 2.5.4. Divides a 4-digit
mentally one single numbers mentally tracts mentally two tracts mentally two number by a 2-digit
digit number from between 0-18 with numbers that are whole numbers that are whole number without and
another single digit the sum not exceeding 100's, where no number 1000's, where no with remainder
number 18 in the operation number in the
exceeds 1,000 operation exceeds
10,000
2.1.5. Interprets and 2.2.5. Subtracts 2.3.5. Solves one step 2.4.5. Understands 2.5.5. Solves 1-2
writes the symbols numbers mentally of daily life problems various terms of steps of daily life
+, -, and = (Both numbers not mentally involving multiplication such problems involving
exceeding 18) addition and subtraction as multiple, multiplier any 2 of the 4 basic
with no number exceed- and product operations of addition,
ing 50 and no carrying/ subtraction, multipli-
borrowing cation and division using
not more than 6-digit
numbers at any stage in
the operations and using
one or more of skills
2.5.1-2.5.4