Initiating Multiplication With Units-Longs-Flats and more

4  2

4  2 4 8

4  7

4  7 4 8 12 16 20 24 28

10  3

10  3 10 20 30

5  10

5  10 10 20 30 40 50

10  10

10  10 100

Commutative

5  3 vs 3  5

5  3 3  5

Associative

7  3  4

Number of plates: 7 Number of blocks in each plate: 3 Number of squares in each block: 4

How many squares in all plates? How many squares in each plate? 7  (3  4) 3  4 No. of plates  no. of squares in each plate How many squares in all plates? How many blocks in all plates? 7  3 (7  3)  4 No. of blocks  no. of squares in each block

2  60

Number of plates: 2 Number of blocks in each plate: 6 Number of squares in each block: 10 2  60 = 2  6  10

How many squares in all plates? 2  (6  10) 6  10 (2  6)  10 2  6 How many squares in each plate? How many blocks in all plates?

30  9

30  9 = (3  10)  9 = (10  3)  9 by commutativity = 10  (3  9) by associativity = 10  27 = 270

Distributive

4  (2 + 5)

4  2 + 4  (2 + 5) 4  5

4  (10 + 7)

4  10 + 4  7 4  (10 + 7)

52  3

 tens units 5 2 52  3 3 place longs-units and arrow cards according to the given numbers 5 0 2 3

 5 tens 2 units 3 52  3 15 6 Note the longs-units and make the numbers with arrow cards tens units 6 15 tens units 5 0 2 3 1 0 0 5 0 6

 5 tens 2 units 3 15 6 52  3 5 0 2 3 1 0 0 5 0 6  5 tens 2 units 3 color the small lattice according to the big one 15 6

 5 tens 2 units 3 52  3 15 6 5 0 2 3 1 0 0 5 0 6  5 tens 2 units 3 draw the diagonals in small lattice 1 5 6

5 0 2  5 tens 2 units 3 3 1 0 0 5 0 6 1 5 6 1 hundred 5 tens 1 0 0 5 0 6 6 units = sum it up 6 50 100 + 156

39  8

 tens units 3 9 39  8 8 place longs-units and arrow cards according to the given numbers 3 0 9 8

 3 tens 9 units 8 39  8 Note the longs-units and make the numbers with arrow cards 24 72 tens units 72 units 24 tens 3 0 9 8 2 0 0 4 0 7 0 2

 3 tens 9 units 8 24 72 39  8 3 0 9 8 2 0 0 4 0 7 0 2  3 tens 9 units 8 color the small lattice according to the big one 24 72

 3 tens 9 units 8 39  8 24 72 3 0 9 8 2 0 0 4 0 7 0 2  3 tens 9 units 8 draw the diagonals in small lattice 2 4 7 2

3 0 9  4 tens 9 units 8 8 2 0 0 4 0 7 0 2 2 4 7 2 1 0 0 2 hundreds 11 tens 2 units 2 0 0 4 0 sum it up 2 7 0 110 200 + 1 0 0 3 0 0 1 0 3 0 0 1 0 2 312 =

4  26

place longs-units and arrow cards according to the given numbers  units tens 4 2 6 4  26 4 2 0 6

Note the longs-units and make the numbers with arrow cards  4 units 2 tens 6 8 tens 24 8 tens 4  26 units 4 2 0 8 0 24 units 6 2 0 4

 4 units 2 tens 8 6 24 4  26 4 2 0 8 0  4 units 2 tens 6 6 2 0 4 color the small lattice 8 24

 4 units 2 tens 6 4  26 8 4 24 2 0 8 0  4 units 2 tens 6 6 2 0 4 diagonals 8 2 4

4  4 units 2 tens 6 2 0 8 8 0 2 4 6 2 0 4 8 0 10 tens 4 units sum it up 2 0 4 100 + 1 0 0 1 0 0 4 104 =

38  24

 tens units hundreds 3 8 2 4 38  24 place longs-units according to the given numbers

38  24  3 8 2 4 6 16 12 32 6 16 32 12 tens units hundreds hundreds Note the flats-longs-units

 3 tens 8 units 2 6 hundreds 16 4 12 32  3 tens 8 units 2 hundreds 4 38  24 6 16 12 32 arrow cards color the small lattice 3 0 8 2 0 6 0 0 1 0 0 6 0 4 1 0 0 2 0 3 0 2

 3 tens 8 units 2 hundreds 4  3 tens 8 units 2 4 38  24 6 16 6 1 6 12 32 diagonals 1 2 3 2 3 0 8 2 0 6 0 0 1 0 0 6 0 4 1 0 0 2 0 3 0 2

3 0 8  3 tens 8 units 2 4 2 0 6 0 0 1 0 0 6 0 6 1 6 1 2 3 2 4 1 0 0 2 0 3 0 2 1 0 0 1 0 0 2 0 8 hundreds 11 tens 2 units 2 6 0 0 3 0 sum it up 110 1 0 0 6 0 800 + 912 1 0 0 9 0 0 1 0 9 0 0 1 0 2 =

74  39