1. CONFIDENTIAL1 Today we will discuss about the topic: Patterns to multiply by 2, 10, 100 Good Afternoon! Let’s Warm up:. 1) 4 x 3 = x 2) 2 x 1 = 3) 7 x 0 = 4) 6 x 5 =

2. CONFIDENTIAL2 REVIEW Let’s discuss what we did in the last session.  Factor: Number that is multiplied to give a product  Product: Number that is obtained by multiplying numbers.  Multiplication by a whole number is REPEATED ADDITION

3. CONFIDENTIAL3 REVIEW There are several properties of multiplication. 1) COMMUTATIVE PROPERTY: We can change the order of the factors and the product stays the same. EXAMPLE:4 x 3 = 12 3 x 4 = 12 2) IDENTITY PROPERTY: We can multiply a number by 1 and the product is the number. EXAMPLE: 3 x 1 = 3 3) ZERO PROPERTY: We can multiply a number by 0 and the product is zero. EXAMPLE: 7 x 0 = 0

4. CONFIDENTIAL4 Let’s learn few terms before we proceed!  Multiple: It is the product of a number and any whole number. 4 and 6 are both multiples of 2.  Even numbers: Whole numbers that are divisible by 2 are even numbers. Like the numbers 2, 4, 6, 8 and 10. These numbers are the multiples of 2.  Odd numbers: Whole numbers that are not divisible by 2 are odd numbers. Like the numbers 1, 3, 5, 7, and 9. These numbers are not the multiples of 2.

5. CONFIDENTIAL5  Prime numbers: Numbers whose factors are only 1 and the number itself are prime numbers. Like the numbers 1, 2, 3, 5, 7, 11, 13 and 17 are prime numbers.  Composite numbers: All the non-prime numbers except 0 and 1, are Composite Numbers.

6. CONFIDENTIAL6 We can multiply by the means of Skip Counting also. By Skip Counting we mean that we can find the multiples of any number by hopping equal steps on the number line. 0 123456 222  Here the numbers are taking 3 jumps each of 2 steps.

7. CONFIDENTIAL7 Find: 2 x 5 We use Skip Count by 2 five times to find the result for this purpose. 0 123456 22222 78910  The numbers 2, 4, 6, 8 and 10 are multiples of 2. These numbers are obtained by multiplying a number times 2. The product is 10.

8. CONFIDENTIAL8 We take a problem that is : 3 x 4 Let’s see here: 0 12345678910 3333 12 11 The product is 12.  Here the numbers are taking 4 jumps each of 3 steps. We use Skip Count by 3 four times to find the result for this purpose.

9. CONFIDENTIAL9 There are other strategies that can be used for multiplication. Find the value of 7 x 3. Use a Known Fact 7 groups of 3 = 7 groups of 2 plus 7 7 x 3 = 7 x 2 + 7 = 14 + 7 = 21 7 x 3 = 21

10. CONFIDENTIAL10 Double a Known Fact Find the value of 8 x 6. 8 x 6 = (4 x 6 ) + (4 x 6) = 24 + 24 = 48 8 x 6 = 48 8 groups of 6 = 4 groups of 6 + 4 groups of 6

11. CONFIDENTIAL11 We can make a multiplication table by skip counting on the number line. 05101520253035404550 5 5 55555 5 55 The multiplication table of 5 would be like this: 0 1 2 3 4 5 6 7 8 910 0 5 1520253035404550 RULE: 5 x n, where ‘n’ is any whole number

12. CONFIDENTIAL12 05101520253035404550 10 We can make multiplication table of 10 in a similar way : The multiplication table of 10 would be like this: 0 1 2 3 4 5 6 7 8 910 0 2030405060708090100 RULE: 10 x n, where ‘n’ is any whole number

13. CONFIDENTIAL13 0100 Now make a multiplication table of 100 in a similar way : Fill in the blanks with appropriate values : 0 1 2 3 4 5 6 7 8 9 10 01005001000 RULE: 10 x n, where ‘n’ is any whole number 200300400500

14. CONFIDENTIAL14 Now we will explore about the square numbers. Square numbers: The numbers which are obtained by multiplying a number by itself are square numbers. Like, 4 x 4 = 16 Number Square Number

15. CONFIDENTIAL15 We will try to understand this with the help of a model Find 4 x 4 : Shade the square on the graph with 4 rows and 4 squares in each row. Then count the number of squares.

16. CONFIDENTIAL16 Number of Rows x Number of squares in each row Square number 4x416 Record the number of squares in a table. Thus, 4 x 4 = 16 Can you find out the value of 3x3 with the help of the model given below?

17. CONFIDENTIAL17 We look into the Multiplication Table and its patterns now: x 0123456789101112 00000000000000 10123456789101112 2024681012141618202224 30369121518212427303336 404812162024283236404448 5051015202530354045505560 6061218243036424854606672 7071421283542495663707784 8081624324048566472808896 90918273645546372819099108 100 2030405060708090100110120 110 2233445566778899110121132 120 24364860728496108120132144 In the table, the pattern of the square numbers are shown within the yellow squares.

18. CONFIDENTIAL18 Find the value of the following expressions from the Multiplications Table. 3 x 8 = 5 x 7 = 12 x 4 = 6 x 6 =

19. CONFIDENTIAL19 BREAK

20. CONFIDENTIAL20 GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw- puzzles/12-piece-jigsaw/050205food.html

21. CONFIDENTIAL21 Assignments 0 1 2 3 4 5 6 7 8 910 0 7355670 RULE: 7 x n, where ‘n’ is any whole number 1) Fill in the correct values to complete the table of 7 with the help of Multiplication Table.

22. CONFIDENTIAL22 2) Find out the value of 2x2 with the help of the model given below? Number of Rows x Number of squares in each row Square number x

23. CONFIDENTIAL23 3) Find the value of 3 x 5 by the method of Use a Known Fact.

24. CONFIDENTIAL24 4) Find the value of 6 x 4 by the method of Double a Known Fact.

25. CONFIDENTIAL25 Find the products of the following: 5) 3 x 4 = 6) 7 x 2 = 7) 9 x 9 =8) 5 x 5 =

26. CONFIDENTIAL26 Very Good! Let's Review We learnt about the following terms:  Multiple: It is the product of a number and any whole number.  Even numbers: Whole numbers that are divisible by 2 are even numbers.  Odd numbers: Whole numbers that are not divisible by 2 are odd numbers.  Prime numbers: Numbers whose factors are only 1 and the number itself are prime numbers.  Composite numbers: All the non-prime numbers except 0 and 1, are Composite Numbers.

27. CONFIDENTIAL27 We can multiply by the means of Skip Counting also. By Skip Counting we mean that we can find the multiples of any number by hopping equal steps on the number line. 0123456 222 There are other strategies that can be used for multiplication. Find 7 x 3. Use a Known Fact 7 groups of 3 = 7 groups of 2 plus 7 7 x 3 = 7 x 2 + 7 = 14 + 7 = 21  Here the numbers are taking 3 jumps each of 2 steps. Double a Known Fact Find 8 x 6. 8 x 6 = (4 x 6 ) + (4 x 6) = 24 + 24 = 48 8 groups of 6 = 4 groups of 6 + 4 groups of 6

28. CONFIDENTIAL28 We looked into the Multiplication Table and its patterns now: x 0123456789101112 00000000000000 10123456789101112 2024681012141618202224 30369121518212427303336 404812162024283236404448 5051015202530354045505560 6061218243036424854606672 7071421283542495663707784 8081624324048566472808896 90918273645546372819099108 100 2030405060708090100110120 110 2233445566778899110121132 120 24364860728496108120132144 In the table, the pattern of the square numbers are shown within the yellow squares.

29. CONFIDENTIAL29 You have done a nice job. See you in the next session.