Fourth and Fifth Grade Strategies* – Addition and Subtraction
Strategies the students will be using will vary depending on the size of the number. The focus is on grouping
numbers and not counting by ones.
*By the end of 4
th
grade the students should have at least two efficient ways to solve multi-digit problems
mentally or with some recording for addition and subtraction.
Examples of mental strategies and ways to record or keep track:
Knowing the combinations to 10 is
important for the following strategies. It is also important that they know how to get to 100 and 1000**.
Students will develop different strategies for different problems. Students do not use borrowing and carrying;
instead they look at the whole number and work with place value.
Addition:
256 + 687
Adding left to right
(expanded notation)
256 + 687
200 + 600 = 800
50 + 80 = 130
6 + 7 = 13
800 + 130 + 13 = 943
This algorithm is related to the traditional “carrying” algorithm, which is also a form of adding by place, except
that traditionally we were taught to start with the ones rather than the largest place.
Starting with ones of the numbers, then adding on the other number in parts, often (but not always) starting
with the largest place.
256 + 687
256 + 600 = 856
856 + 80 = 936
936 + 7 = 943
Round one or more of the addends to numbers that are easier to work with, then compensate.
256 + 687
256 + 700 = 956
956 – 13 = 943
Transform the entire problem to an equivalent problem that is easier to solve.
256 + 687
256 + 687 = (256 – 13) + (687 + 13)
243 + 700 = 943
Subtraction:
465 – 129
Subtract one number in parts from the other.
465 – 100 = 365 OR 465 – 125 = 340
365 – 20 = 345
340 – 4 = 336
345 – 5 = 340
340 – 4 = 336
Change one number, then compensate for the change.
465 – 130 = 335
OR
460 – 129 = 331
335 + 1 = 336
331 + 5 = 336
Add up from the number being subtracted.
129 + 1 = 130
OR
129 + 300 = 429
130 + 300 = 430
429 + 1 = 430
430 + 35 = 465
430 + 35 = 465
1 + 300 + 35 = 336
300 + 1 + 35 = 336
Transform the entire problem to an equivalent problem that is easier to solve.
465 – 129 = 466 – 130 (adding 1 to both numbers)
466 – 130 = 336
Subtract each column and record each difference, whether it is positive or negative.
400 – 100 = 300
60 – 20 = 40
5 – 9 = -4
300 + 40 – 4 = 336
**Students should be able to break 100 into
90 + 10
and 1000 into
900 + 90 + 10
. This helps them compute to the nearest
100 and 1000 quickly and efficiently knowing the ones should add to 10 and the tens should add to 90. For example 47 to
100 needs a 50 and a 3. Then the child would add on the amount above the hundred. Playing the Close to 100 and Close to
1000 games are key to developing this skill.
Fourth and Fifth Grade Computation Expectations:
Efficient strategies for combinations to 100 and 1000; students should
have at least two efficient strategies for solving multi-digit addition
and subtraction problems.