Mental Math Strategies

One of my goals for this year is to help the students take apart numbers and put them back together. We will practice mental math strategies throughout the year including two they already use but may not have had a name for: partial sums or products and compensation.

Partial sums and partial products gives a process to adding and multiplying mentally. With partial sums, students add digits together in the same place value spot then add those values together. No need to carry, borrow, etc.

For example: Students can think of 639 + 478 as

600 + 400= 1,000;
30+70 = 100
9+8 = 17
Then easily add to find the sum of 1,117

Partial products works much the same way:
73 x 4 =
70 x 4 = 280 + 3 x 4 = 12

Then add 280 +12 = 292

With compensation students can take from one number and give to another to make a problem easier to solve.
For example: 592 + 416 =

Students think, "I only need 8 to make 600. I'll take it from the 416."
592 + 416 =
+ 8 -8

600 + 408 = 1008