multiplication vs. division

[OneStepAtATime]

Just curious if anyone here might have a clue why my DS10 does much better with division than multiplication or subtraction but DD14 is the exact opposite?  No real biggee since they are both progressing  but I was surprised at how quickly DS10 grasps and moves through when it is a division problem vs. multiplication or even subtraction.  He actually struggles with subtraction a bit.  He grasps the concept completely.  He just is slow on the computation for subtraction.  But with division he just whips through.  DD14 is finally doing well with multiplication, addition and subtraction but is slow with division.  I expected that, actually.  I just didn't expect the other.

[Heathermomster]

For division facts, DS grasped them quickly after getting the multiplication facts.  For long division, DS used partial products for a very long time prior to transferring to the traditional long division.  

 

For subtraction, DS is most accurate using the mental bridging techniques explained in RB's materials.  

 

DS performs a ton of 2 digit multiplication in his head or he resorts to lattice multiplication.  

 

I can't explain why DS does what he does.  We are currently covering algebraic axioms and properties in algebra using Foerster's.  The work is more like logic and he gets that.  

[kbutton]

Does he do a lot of factoring? If so, maybe he just sort of pictures a 24 broken down into it's factors, but putting them back together to multiply is slower for him.

 

Division seems more complicated than subtraction (more steps in the algorithm maybe), but in a way, it's less messy. You aren't exchanging tens for ones and such, you're just making equal chunks and saying what's left over.

[OneStepAtATime]

Does he do a lot of factoring? If so, maybe he just sort of pictures a 24 broken down into it's factors, but putting them back together to multiply is slower for him.

 

Division seems more complicated than subtraction (more steps in the algorithm maybe), but in a way, it's less messy. You aren't exchanging tens for ones and such, you're just making equal chunks and saying what's left over.

Division was always way harder for me than subtraction.  I don't know about the factoring being influential for DS but maybe.  He whips through division in nothing flat.  Subtraction takes a lot longer.  For instance, we do speed drills but we don't do it by how many you complete in a certain period of time.  They just run through the drill and record how much time it took them and we record the time on a graph to show improvement over an extended period of time.  The kids have liked this so far or I wouldn't even do it, honestly.  But if DS has division problems he whips through them in about 3 minutes (dysgraphia keeps him from ever finishing in the originally expected 1 minutes which is why we don't require finishing in a certain amount of time).  If it is subtraction it takes usually twice that amount of time.

[Heathermomster]

For division facts, we used flash cards.  That was surprisng really, because DS was flash card phobic but he didn't mind them.

[OneStepAtATime]

Yes we started the flash cards when DD started with CLE and while both kids had always hated flash cards, now they enjoy our drills with the flash cards (besides the drills on paper) and DD14 insists that they do them together so if DS10 is elsewhere she runs to go get him.  Each takes a turn.  And DS just whips through the division flash cards.  He is definitely slower on subtraction.  DD is finally doing pretty well with multiplication, addition, subtraction.  Division is slower but she is in a LOT better place than she was even last year so I am not complaining.  :)