# TFI Knowledge Base/Maths/Numbers and Operations

### Std 1.1

1.1 Students understand how to name, represent and use numbers to 100. Using concrete objects, they appreciate the sizes of these numbers and build their mental images.

### Std 1.2

They count and group objects in ones and tens and understand that a 2-digit number has a tens value and a ones value and build an understanding of the concept of place value (in base ten number system) i.e. the place of a digit gives its value. They are able to represent numbers on an abacus i.e. decompose and compose numbers using place-value. They use place value to order numbers to 100 in ascending and descending order (excluding symbols).

### Std 1.6

Using concrete objects and pictures, they understand the meaning and use the terms addition/subtraction. They understand the commutative nature of addition (without using the term) and its use to calculate efficiently. They understand the effect of zero in addition and subtraction and know the symbols for the two operations and the symbol ‘=’.

### Std 1.7

They are able to add/subtract using concrete objects and skeletal number line (with divisions marked).

### Std 1.10

They know the cases in which addition and subtraction are applied and that they cannot subtract a larger number from a smaller number (as of now). They can identify the operation, represent the problems by mathematical expressions, interpret and solve them.

### Std 1.11

They understand the inverse relation between addition and subtraction and can give subtraction corresponding to an addition and vice-versa in number sentences using symbols +,-,= .

### Std 1.12

They understand that sets of objects, pictures, numbers representing them or expressions like 2+3 are all equivalent in the sense of their number.

### Std 2.1

Students understand and learn how to name and represent numbers to 1000 and note the pattern in their representation. They appreciate relative sizes of the numbers by regarding 10 as a unit or hundred as a unit (in concrete manipulation or mental images).

### Std 2.2

They compose and decompose (expand) numbers using place value. They recognize representations using ones blocks, tens blocks, hundreds blocks and write numbers for these representations.

### Std 2.3

They compare and order the numbers on a partial number line and understand their relative position. They order them in ascending and descending order using symbols >, <, = .

### Std 2.4

They count backward and forward starting from any number to 1000. They know ordinal numbers to 20 and use them in different contexts.

### Std 2.5

They are able to add and subtract numbers up to three digits without and with composing/decomposing in expanded form (so that they can understand the concept of composing and decomposing well) as well as short form.

### Std 2.6

They know, understand and use commutative and associative properties of addition (without using the terms) and inverse relationship between addition and subtraction.

### Std 2.7

They are able to understand the meaning of multiplication (repeated addition) and division (equal sharing, grouping) and their effect using concrete objects, pictures. They understand inverse relation between multiplication and division using concrete objects.

### Std 2.9

They understand that multiplication and division are based on multiplication tables and understand, construct and learn multiplication tables of 2 to 5 and 10.

### Std 2.10

They understand and correctly use vertical algorithm for multiplication and division for up to three digit numbers by one-digit numbers without and with composing/decomposing including those in which remainder is left behind. They know the terms related to division (dividend, divisor, quotient and remainder).

### Std 2.12

They summarize the cases for all four basic operations. They identify operations, write expressions, solve and interpret the results for a mixed bag of problems in meaningful contexts.

### Std 2.13

They know and recognize odd and even numbers.

### Std 2.14

They understand using concrete material and pictures- the meaning of fraction as part of a whole or of a collection where whole or collection is divided into equal parts. They recognize and name the following fractions of a whole or a small set of objects - half, one-third, one fourth etc. and two-third, three-fourth using concrete objects and pictures. They know their symbolical representation and the terms numerator and denominator. They compare and order these fractions using concrete objects and pictures. They are explained the representation of these fractions on a number line. They understand concretely, pictorially that when all fractional parts are included such as two halves or four one-fourths, the result is the whole or the complete set.

### Std 2.15

Estimation - estimate number of objects in a set of upto 50 objects, count and compare the estimate with the actual number - check reasonableness of addition/subtraction answers

### Std 3.1

Students extend naming and representation of numbers to 10000. They understand the cyclical pattern in which the digits change as the numbers increase and realize that counting can go on endlessly in this fashion. They deepen their understanding of whole numbers, their representation and their relative sizes.

### Std 3.2

They understand the place-value structure of the base-ten number system and are able to efficiently decompose (expand) and compose numbers using place value. They recognize equivalent expanded representations for the same number and compare and order the numbers.

### Std 3.3

They recognize representations using ones blocks, tens blocks, hundreds blocks and thousands blocks and write numbers for the same correctly.

### Std 3.5

They are able to fluently carry out addition and subtraction of numbers up to 4-digits.

### Std 3.6

They understand the meaning and effect of multiplication and division and the cases in which they are applied. They understand commutative, associative and distributive properties of multiplication (without using the terms) and are able to use them.

### Std 3.7

They construct and learn multiplication tables of 6, 7, 8, 11 and 12.

### Std 3.8

They understand the effect of multiplication by 1, 10, 100 and division by 1 and also by 10, 100 if the number ends in zeroes i.e. the answer is a whole number. They use this and distributive property of multiplication over addition to understand and use vertical multiplication and division algorithm to multiply and divide by numbers of 2 or more digits without and then with composing or decomposing. They understand the relation, dividend = divisor x quotient + remainder.

### Std 3.9

They understand the effect of 0 and 1 in multiplication and division.

### Std 3.10

They understand inverse relation between multiplication and division and use it to check results.

### Std 3.11

They appreciate the usefulness and purpose of multiplication and division besides addition and subtraction. They develop the ability to correctly choose suitable operations for a mixed bag of problems (a problem may involve more than one operation), write expressions for the problems, solve, check reasonableness of answers and interpret the results.

### Std 3.12

They understand properties of sum and product of odd and even numbers.

### Std 3.14

They understand the meaning and concept of fractions as part of a whole or a collection where the whole or collection is divided into equal parts using concrete objects and pictures. They understand naming and notation of fractions and know the terms- numerator and denominator.

### Std 3.17

They understand the relative sizes of unit fractions (1 or 2 to 1 or 12) and other simple fractions (2 or 3, ¾) using one long object (e.g. sugarcane), a collection of say 12 objects or their pictures. They are explained the representation of these fractions on a number line

### Std 3.20

They thus understand that decimals are fractions and know decimal and fraction equivalents of tenth, hundredth etc /]]

### Std 3.25

Estimation - estimate number of objects in a set of upto 100 objects, count and compare the estimate with the actual number - use properties of operations and their mutual relation to check reasonableness of results

### Std 4.1

Students deepen their understanding of whole numbers by knowing number representation to 100000 and may be, beyond. They summarize the decimal numeration system and understand the relative sizes of the numbers.

### Std 4.2

They decompose and compose numbers using place value and are able to efficiently compare and order.

### Std 4.3

They are able to efficiently apply the appropriate operation and fluently carry out addition and subtraction of whole numbers upto five digits and beyond.

### Std 4.4

They are able to apply and more accurately compute multiplication and division of whole numbers (with whole number quotients). They use the relation, dividend = divisor x quotient + remainder.

### Std 4.8

They efficiently apply the appropriate operations for problems (with multiple operations and unitary method) from a mixed bag and fluently and accurately carry out the computations, check reasonableness of results and interpret the results.

### Std 4.10

They deepen understanding of whole numbers by knowing about factors, multiples, prime and composite numbers. They know prime factors to 50 and express a number as a product of prime factors (not using exponents).

### Std 4.11

They know about common factors and common multiples and Least Common Multiple (LCM) and its relevance in solving addition/subtraction of fractions and other simple problems.

### Std 4.12

They understand the meaning of proper/improper fractions and mixed numbers concretely, pictorially and symbolically. They convert improper fractions to mixed numbers and vice-versa and understand their equivalence.

### Std 4.14

Using LCM, they are also able to compare unlike fractions with denominators less than 12 or 20 (for the sake of simplicity) and add/subtract them. They compare or add/subtract mixed numbers by comparing or adding/subtracting whole parts and then fractional parts (like or unlike).

### Std 4.15

They summarize methods of comparing and adding/subtracting fractions and mixed numbers.

### Std 4.16

They compare like/unlike decimals to thousandth place and beyond. They understand and know addition/subtraction of like/unlike decimals to thousandth place and beyond.

### Std 4.18

Estimation - estimate number of objects in a set of upto 500 objects and count and compare the estimate with the actual number - understand meaning and purpose of round numbers i.e. why rounded solutions may be appropriate and when they are called for - know how to round 2-digit number to the nearest 10, 3-digit number to the nearest 100 and 4-digit number to the nearest 1000

### Std 5.1

Students know number representation of very large numbers as crores and beyond in the Indian system. They also know the International system of naming numbers. They understand the relative sizes of the numbers. They decompose and compose numbers using place value and are able to efficiently compare and order.

### Std 5.2

They efficiently apply the appropriate operation and carry out addition and subtraction and also multiplication and division with large whole numbers.

### Std 5.4

They know applications of LCM (other than adding/subtracting fractions) through simple problems e.g 3 bells ring at intervals of 7, 10, 14 minutes respectively, they begin by ringing together. After how long will they ring together again?

### Std 5.6

Besides parts of a whole or a collection when whole or collection is divided in equal parts, they understand fraction from another point of view also as – division of two whole numbers. They understand equivalence of these interpretations and associate a proper fraction to a number between 0 and 1 on the number line.

### Std 5.7

They know representation of a whole number as a fraction and a decimal and understand that division can be regarded as multiplication by reciprocal.

### Std 5.8

They understand the meaning and effect of multiplication and division of fractions by a whole number, by a fraction or a mixed number/improper fraction and know how to carry out multiplication and division of fractions by these.

### Std 5.9

They understand the meaning and effect of movement of decimal when number is multiplied or divided by 10, 100, 1000. They understand the meaning and effect of multiplication and division of decimals by a whole number, by a decimal alone and by a number with both whole and decimal components. They know how to manipulate the decimal point while multiplying and dividing a decimal number by a whole number, a decimal, and a number with both components.

### Std 5.10

They master unitary method to solve multiplication and division problems involving any of whole numbers, fractions or decimals.

### Std 5.11

They summarize the four operations and their effects with whole numbers, decimals and fractions

### Std 5.13

They understand the equivalence of the concepts of fractions and decimals. They know that all decimals can be represented in fractional form and all fractions in decimal form by dividing the numerator by the denominator including terminating and repeating decimals.

### Extra Topics

Profit/Loss, Recipricols, prime/composite numbers