Subtraction

Subtraction is introduced in 1st grade as taking away from a group, with facts to 20 emphasized. Second grade brings two- and three-digit subtraction with regrouping (borrowing), and 3rd grade extends to larger numbers. A central goal across these years is fluency with the basic subtraction facts — the inverse of the addition facts — so students can recall, not compute, things like 14 - 8.

Subtraction has two meanings that students need to recognize: take-away (you had 10 cookies, ate 4, how many left) and difference or comparison (Sara has 10 stickers, Ben has 4, how many more does Sara have). Word problems use both, and kids who only know one struggle to identify when to subtract. Fluent subtraction underpins multi-digit operations, money problems, elapsed time, and eventually negative numbers in 6th grade.

Regrouping is where most subtraction struggles live. A student who can do 65 - 23 but freezes on 62 - 25 doesn't have a subtraction problem; they have a place-value problem dressed up as one. Slow down and use base-ten blocks. Physically trade one ten for ten ones in front of them. Do it dozens of times until they can predict what they'll need to trade before they touch the blocks.

What helps:

• Teaching subtraction as the inverse of addition — if 7 + 5 = 12, then 12 - 5 = 7
• Number-line work for the difference interpretation
• Counting up strategies (38 to 75 by jumps) as a mental-math backup
• Word problems that mix both meanings of subtraction so students learn to recognize each

Check understanding by asking your student to make up a word problem for 42 - 19. If they can only come up with take-away scenarios, work on the comparison interpretation. If they can't make one up at all, the symbols haven't connected to meaning yet.