How do you get dc proficient in math fact strategies vs. straight memorization?

[snickelfritz]

There's a long story involving not buying the Singapore HIG at first and trying a switch to Math Mammoth, but it's really extraneous to my real question.

 

What strategies do you teach? Can you break it down for me? I'm making a list to keep dd going through a systematic review of the different strategies. She knows them, but isn't at the point of using them proficiently. She reverts to fingers.

--doubles and near-doubles

--1's and 2's are counting up

--9's are 1 less than adding 10

--making 10. And then do most people really just build off of this for bigger numbers? ie... for 7+4, to see that as 7+3+1 or 10+1

--What am I missing?

 

And then, how do you drill subtraction? If we get addition down cold, will the subtraction start to come a little easier? I'm using the Right Start games and flashcards. We're keeping on going in Singapore 2, but I'm spending time each day working on the facts. I just need to get a plan written down, instead of just randomly working on things.

[Snowfall]

The two fives strategy: If you're adding 2 numbers less than 10 but more than 5, first make ten with the 2 fives in the numbers, then add whatever's left over. For instance: 7+6=10+2+1 or 7+5=10+2. DD prefers to do the near doubles, the nines strategy, or her own elevens strategy (which is that if it's one more than whatever equals ten, it's eleven, as in 7+4=11 because 7+3=10). She really only uses the two fives for 7+5, 8+5, and 8+6, come to think of it. lol

[MaMa2005]

I can't help with the strategies, but one thing that has helped DS become proficient with math facts is a daily 5 minute drill on paper. Without fail we do an addition, subtraction, multiplication, division and a mixed facts sheet each week. DS is racing against himself and I have noticed a marked improvement. DS has also commented on how much easier math is to do now that he just 'knows the answers'. Here is a great site that generates 5 minute drills - http://themathworksheetsite.com/

[JulieD]

I like how RightStart works with larger numbers right away where using a strategy is clearly easier than counting and memorizing is virtually impossible. So 27+48 requires a strategy. I didn't quite understand that at first, but now I see it.

 

For subtraction it is important for them to see it as the reverse of addition. Then they can think for 13-7 what plus 7 equals 13. For the facts greater than 10 my son prefers to subtract the number from 10 and add the ones. So he thinks 13-7=10-7+3=6. My daughter prefers to subtract down to 10 first and then subtract the rest. 13-7=13-3-4=6. Obviously addition facts need to be mastered first to use either of those strategies.

 

For the RS games for subtraction, it is good to start with difference war where the smaller card is always subtracted from the larger card. This practices facts within ten.

 

When the kids get good at that, move on to subtraction war to practice subtraction within 18. In subtraction war the order the cards are laid down matters, so it is best to sit across from your child and do your subtraction backwards. Put your first card 6 on your right, then lay the 8 to the left of it. In subtraction war if the first card is lower than the second card you can borrow a ten. So the problem is 16-8=8. But if the first card is 8 and the second one 6, then the problem is 8-6=2. The child should put the cards down from left to right.

 

I like playing war because it's easy to model the strategies for your child on your turn. I don't just say 3+8=11. I say, " 2+8=10 so 3+8=11," or "I can give 2 to the 8 to make 10 and there's still 1 left so that's 11."

 

Since my kids aren't good at memorization, the biggest problem I have is getting them to realize they've come to the point where they have memorized the answer.

 

Do you have an abacus? It is easier to visualize problems greater than 10 with the abacus than with fingers. Fingers can be fine manipulatives, but we only have ten of them. Also, using the abacus is like using a pacifier, but using fingers is like sucking a thumb. It's much easier to ditch the abacus later.

 

Sorry these thoughts are random. I'm not feeling well, and my brain feels like mush.

 

Julie D.

[kalanamak]

I just need to get a plan written down, instead of just randomly working on things.

 

I beat my head on a plan quite a bit. I repeated myself until hoarse. Kiddo seems to be just working at his own mental pace, and, while I still point of a strategy periodically, he seems to be discovering them on his own in a way he can remember/use, and what I say, and what paths I direct him down, stay fog-shrouded to him.