Dear Parents/Guardians,
By the end of second grade, students will be expected to know how to use the math algorithm called, “Partial
Differences” to add 2-digit and 3-digit numbers. Below is a “cheat sheet” to help you know how to help your kiddo
at home. The partial differences algorithm is a stepping stone to learning the traditional algorithm that you
probably learned as a child.
2-Digit Equations
7 7
- 5 6
2 0
+
1
2 1
This method starts from left to right, in the same manner as we teach
children to read. As we move from left to right, each place value is
acknowledged by its real value – the 7 in the tens place of the first number
is 70, not 7. The numbers in the tens place are subtracted and placed
under the bar. Students then subtract the numbers in the ones place and
place that under the difference of the tens place numbers. The total
amount of ones is then added to the total amount of tens. The final
difference is placed under the second bar. ** Students subtract the ones
from the tens if they have a negative number. Students are encouraged
to use mental math skills to compute the final answer.
Step 1: Subtract the tens.
70 -50 = 20
Step 2: Subtract ones.
7-6=1
Step 3: Add the tens to the ones.
Step 1: Subtract the tens.
5 6
- 1 2
4 0
+
4
4 4
20 + 1 = 21
50 -10 = 40
Step 2: Subtract ones.
6 - 2=4
Step 3: Add the tens to the ones.
40 + 4 = 44
2-Digit Equations when a negative number occurs
Step 1: Subtract the tens.
7
- 5
2
1
4
7
0
3
7
70 – 50 = 20
Step 2: Subtract ones.
4–7=3
Step 3: Subtract the ones from the tens.
20 – 3 = 17
Step 1: Subtract the tens.
7 7
- 5 8
2 0
1
1 9
70 - 50=20
Step 2: Subtract ones.
7 - 8= -1
Step 3: Subtract the ones
from the tens.
20 – 1 = 19