The document describes several methods for adding and subtracting multi-digit numbers: The partial-sums method involves adding numbers column-by-column from left to right, recording partial sums, and then adding the partial sums. The column-addition method adds each column separately in any order, carrying numbers to the next column as needed. The partial-difference method performs subtraction column-by-column from left to right, subtracting the smaller number from the larger number in each column and recording partial differences.

1. Adding and
Subtr acting

2. Partial-Sums Method:
 Algorithm: is used to name
_________________________ procedures for
__________________a mathematical problem.
*Addition is performed form left to right, column by
column
*The sum for each column is recorded on a separate line.
*The partial sums are added either at each step or at the
end.
348 + 177 = ?
3
4
8
+ 1
7
7
400 + 110 + 15
525

3. Partial-Sums Method:
Algorithm: is used to name
_________________________ procedures for
__________________a mathematical problem.
*Addition is performed form left to right, column by
column
*The sum for each column is recorded on a separate line.
*The partial sums are added either at each step or at the
end.
4.65 + 3.25 = ?
4.
6
5
+3.
2
5
7 + 0.8+ 0.1
7.9

4. The Column-Addition
Method
*Each column of numbers is added separately, and in any
order.
*If adding results in a single digit in each column, the sum
has been found.
*If the sum in any column is a 2-digit number, it is
renamed and part of it is added to the sum in the
column on its left.
***This adjustment serves the same purpose as "Carrying" in the traditional
algorithm.
359 + 298 = ?
3
+2
5
9
9
8
Explain the difference once a decimal is added into the
problem. What do you have to be sure of?

5.
The Trade-First Method
 *Problems are written in vertical form.
 *If each digit of the minuend (the larger number) is
greater than or equal to the digit directly below it, the
problem is very easy to solve.
 *If any digit of the minuend is less than the digit directly
below it, then the minuend is adjusted before any
subtraction is done.
 *The minuend is adjusted by "trading."










463 - 275 = ?
6
-2
32.9 - 15.6 = ?
4
5
7
3
2.
9
-1
5.
6
5
3 16
2 7
2 12. 9
1 5. 6
5
5

6. The Partial-Difference
Method
The subtraction is performed from left to right.
*The smaller number in each column is always subtracted
from the larger number.
*If the bottom number is less than the top number, then the
result will be added to obtain the final answer.
*If the bottom number is greater than the top number, then
the result will be subtracted to obtain the final answer.
*
4261- 2637 = ?
4
2
-2
6
6
3
1
7
4000 – 2000 =
200 – 600 = (-400)
60 – 30 =
1-7 = (-6)
2000
-400
1600
+30
1630
-6
1624

7. The Partial-Difference
Method
Let’s try Partial-Sums with Decimals
7
-3
6.
9.
3
8
8
1
70 – 30 =
6 – 9 = (-3)
0.3 – 0.8 = (-0.5)
0.08 – 0.01 = 0.07
40.00
-3
37.00
-0.5
36.50
+0.07
36.57
What do you think will be the difficulties with decimals
using this strategy? What are the benefits?

8. Adding/Subtracting and Place
Value
When we subtract, we take values away from the
larger quantity. Sometimes we need to borrow a ten
from the larger place value to cover what is being
taken away.
324
-56
I cannot take 6 away from 4, but I can take 6 away
from 14. I will borrow a ten from the tens column
and add it to the ones column.
This does not change the value of the number, but it
changes the name of the quantities in the column.

9. Adding/Subtracting and
Place Value
324
-56
3 hundreds 2 tens 4 ones = 314
3 hundreds 1 ten 14 ones =314
324
31 14
-56
-5 6

10. Adding/Subtracting and
Place Value
324 -56
What if we looked at the problem
another way.
Can you take 6 away from 24?
24 – 6 = 18
Because of your subtraction, 324 now
becomes 318. The new problem is
318 – 50.

11. Adding/Subtracting and
Place Value
318-50
Think about what makes sense here.
What can you subtract 50 from
easily?
300-50=250
Now just combine the differences of the
two easier problems you completed.
250 + 18 = 268

12. What About Decimals?
 How do these strategies apply to
decimals?
 What are the possible problems you will
have with these methods?

13. Time to Practice
 Get with a partner you work well with.
 Partners will coach each other through
these strategies.
 It is important that you understand how to
use each of these strategies before you
decide if they work for you or not.
 Complete both sides of the page.
 Check in with the teacher when you are
finished.