We can’t assume students understand without probing deeper through questioning. For example: Say we are subtracting 81 - 27. The student might announce that they need to trade a ten to get more ones. They show the work by crossing out the 8 tens, leaving 7 tens, and adding 10 more ones to the original 1 one, giving 11 ones. No subtraction has taken place yet--just the regrouping. Then I ask them the question, "Do you still have 81?" Hmmm.. how many students will say “no”?
Recount with them -- then pose a problem – how many ways can you show me 35. They should show you 3 tens and 5 ones… but what other way can you show me 35?
Here is a matching game to play in groups once you have addressed this misconception.
by Donna Boucher