# India/Knowledge Base/Maths/Arithmetic

## Contents

## Grade 1

### Lesson Plans

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### Resources

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### Standards

Here are some standards, objectives etc for use as reference. You can click on any of the objctives to create a lesson plan out of it.

**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 ‘=’.

- SWBAT combine quantities in 2 separate groups up to 10 (EI K.5)
- SWBAT use pictures to represent an addition problem and use an addition problem to represent given pictures (make the connection between the two)
- SWBAT remove quantities in 2 groups up to 10 (EI K.5)
- SWBAT use pictures to represent a subtraction problem use a subtraction problem to represent given pictures (make the connection between the two)
- SWBAT demonstrate understanding of the commutative property of addition by writing two addition problems to (ex. 3 +5 and 5+3) to represent the same situation

**Std 1.7**
They are able to add/subtract using concrete objects and skeletal number line (with divisions marked).

- SWBAT add 1-digit numbers up to a sum of 10 (EI K.5)
- SWBAT subtract 1 digit numbers less than 10 (EI K.5)
- SWBAT add 1 digit numbers up to a sum of 20

**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.

## Grade 2

### Lesson Plans

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### Resources

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### Standards

Here are some standards, objectives etc for use as reference. You can click on any of the objctives to create a lesson plan out of it.

**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.

- SWBAT add two single digit numbers(EI 1.8)
- SWBAT identify and create visual representations of addition
- SWBAT identify that additing 0 results in the same numer
- SWBAT add 2 2-digit numbers without carryover
- SWBAT identify and create visual representations of subtraction (counting forwards, counting backwards, crossing out)
- SWBAT subtract a 1 digit number from a 1 digit number
- SWBAT identify that subtracting 0 results in the same number
- SWBAT subtract 2 digit numbers from each other without borrowing
- SWBAT add numbers involving carrover
- SWBAT subtract up to 2-digit numbers involving borrowing

**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.

- SWBAT use the inverse relation between addition and subtraction to fill in missing quantities in equations (in arithmetic problems)
- SWBAT use the inverse relation between addition and subtraction to determine missing quantities in situations (in word problems)

**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.

- SWBAT identify and create visual representations of multiplication
- SWBAT identify repeated addition expressions that correspond with multiplication problems (and vice versa)
- SWBAT apply the commutative property of multiplication

**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.

- SWBAT solve simple word problems using addition
- SWBAT solve simple word problems using subtraction
- SWBAT solve word problems using addition or subtraction and involving carry-over/borrowing.
- SWBAT solve simple word problems using multiplication
- SWBAT solve application questions based on addition/subtraction (for example, questions based on buying items at a store, etc.)
- SWBAT solve application questions based on multiplication (for example, questions based on buying items at a store, etc.)

## Grade 3

### Lesson Plans

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### Resources

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### Standards

Here are some standards, objectives etc for use as reference. You can click on any of the objctives to create a lesson plan out of it.

**Std 3.5**
They are able to fluently carry out addition and subtraction of numbers up to 4-digits.

- SWBAT add numbers up to 3 digits without carryover
- SWBAT add numbers up to 3 digits with carryover
- SWBAT subtract numbers up to 3 digits without borrowing
- SWBAT subtract numbers up to 3 digits with borrowing
- SWBAT add more than 2 numbers, up to 3 digits each
- SWBAT create (multiple) addition or subtraction expressions that result in a given quantity.
- SWBAT use the inverse relation between addition and subtraction to fill in missing quantities in equations (in arithmetic problems)

**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.

- SWBAT show and identify visual representations of multiplication
- SWBAT show and identify visual representations of division
- SWBAT apply the commutative and associative property of multiplication
- SWBAT identify repeated addition expressions that correspond with multiplication problems (and vice versa)

**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.

- SWBAT multiply numbers up to 3 digits by 1 digit
- SWBAT identify the divisor, divident, quotient, and remainder (EI 2.10)
- SWBAT divide numbers up to 2 digits by 1 digit (based on simple division facts, not long division)
- SWBAT multiply a number by 10
- SWBAT divide a number by 10 (no decimal in the answer).

**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.

- SWBAT solve multiplication problems with a missing number (ex. 5 x ___ = 45 )
- SWBAT solve division problems with a missing number (ex. ___ divide by 8 = 7 )
- SWBAT identify and apply multiplication and division as inverse operations

**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.

- SWBAT solve word problems involving addition or subtraction up to 3 digits
- SWBAT solve word problems involving multiplication
- SWBAT solve word problems involving division.
- SWBAT solve word problems involving finding missing values (based on addition or subtraction)
- SWBAT solve application based questions based on addition or subtraction (for example, questions based on buying items at a store, etc.)
- SWBAT solve application based questions based on multiplication or division (for example, questions based on buying items at a store or based on pictures, etc.)

**Std 3.12**
They understand properties of sum and product of odd and even numbers.

## Grade 4

### Lesson Plans

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### Resources

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### Standards

Here are some standards, objectives etc for use as reference. You can click on any of the objctives to create a lesson plan out of it.

**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.

- SWBAT add numbers up to 5 digits without carryover SWBAT add numbers up to 5 digits with carryover SWBAT subtract numbers up to 5 digits without borrowing
- SWBAT subtract numbers up to 5 digits with borrowing.
- SWBAT use apply inverse operations to solve addition/subtraction problems with a missing number

**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.

- SWBAT multiply numbers up to 4 digits (several steps to build up to)
- SWBAT multiply numbers by 10/100/1000
- SWBAT divide numbers up to 4 digits by 2 digits (several steps to build up to)
- SWBAT divide numbers by 10/100/1000
- SWBAT solve word problems involving multiplication/division.
- SWBAT identify and apply the relation dividend = divisor x quotient + remainder to check their answers.
- SWBAT apply inverse operations to find missing numbers in multiplication/division problems

**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.

## Grade 5

### Lesson Plans

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### Resources

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### Standards

Here are some standards, objectives etc for use as reference. You can click on any of the objctives to create a lesson plan out of it.

**Std 5.2**
They efficiently apply the appropriate operation and carry out addition and subtraction and also multiplication and division with large whole numbers.

- SWBAT add 3 numbers including large numbers.
- SWBAT subtract large numbers
- SWBAT solve word problems involving addition/subtraction including those with large numbers
- SWBAT multiply numbers up to a 5-digit by a 3-digit number
- SWBAT divide numbers up to a 5-digit by a 2-digit number
- SWBAT solve word problems involving multiplication/division.

**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 5.10**
They master unitary method to solve multiplication and division problems involving any of whole numbers, fractions or decimals.

- SWBAT solve proportion problems by finding the unit rate
- SWBAT solve proportion problems by multiplying/dividing (scaling)

**Std 5.11**
They summarize the four operations and their effects with whole numbers, decimals and fractions

- SWBAT test for divisibility of a number by 2, 3, 5, 10. (4th EI, 5th IGCSE)
- SWBAT add/subtract fractions with unlike denominators
- SWBAT add/subtract mixed numbers with unlike denominators
- SWBAT add/subtract with decimals to the same decimal place
- SWBAT add/subtract with decimals to different decimal places
- SWBAT multiply a decimal by an integer
- SWBAT multiply a decimal by a decimal

## Grade 6

### Lesson Plans

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### Standards

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## Grade 7

### Lesson Plans

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## Grade 8

### Lesson Plans

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## Grade 9

### Lesson Plans

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## Grade 10

### Lesson Plans

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