ADD THE DIGITS

Purpose: To check multiplication problems of 2 or more digits.

Example: 58x37= 2146

Now "ADD THE DIGITS" of each part to check for correctness.

58 (5+8=13, 1+3=4) 4
x37 (3+7=10, 1+0=1) x1
-----
406 (4+0+6=10, 1+0=1) 1
+1740 (1+7+4+0=12, 1+2=3) +3
-----
2146 (4)

SHORT DIVISION

Purpose: To teach the initial concept of division by one digit without the confusion of the long division form.

____
3) 7 (Have students use this form)

Student Asks: How many 3's are in 7? (Answer: 2)

__2_
3) 7

Student Asks: How many are left over? (Answer: 1)

__2_r1
3) 7

To Check: (3x2) + 1 = 7

Example:

_______
3) 7 2 (Have students space the numbers)

Student Asks: How many 3's are in 7? (Answer 2)

_2___
3) 7 2

How many are "left over"? (Answer 1)

__2___
3) 7 2
1

(Place the 1 between, near the 2). Explain: The 2 is now 12. (Relates in form to carrying.)

Student Asks: How many 3's are in 12? (Answer: 4). How may are left over? (Answer: 0)

_2_4_
3) 7 2

To Check: 3 x 24 = 72

Difficult example:

_________
4) 6 3 7 5

Student Asks: How many 4's in 6? (1)

_1______
4) 6 3 7 5

How many left over (2)

_1______
4) 6 3 7 5
2

How many 4's in 23 (5) How many left over? (3)

_1_5____
4) 6 3 7 5
2 3

How many 4's in 37? (9) How many left over? (1)

_1_5_9___
4) 6 3 7 5
2 3 1

How many 4's in 15? (3) How many left over? (3)

_1_5_9_3_r3
4) 6 3 7 5
2 3 1

The problem is now complete.
To check: (4 x 1593) + 3 = 6375

Read more: http://technicalstudies.youngester.com/2009/08/mathematics-shortcuts.html