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Hi everyone,

Just wondering if anyone out there can help me get my head wrapped around the mental math stuff that shows up in 2B, specifically subtracting 3 digit numbers/borrowing (although SM doesn't do borrowing as I learned it in school). I think that is where we are stuck. My DS 8.5 did Review 3 today and got most of the answers wrong on the top of page 84 in the WB. I tried to help him with a few and I got stuck too! Now, granted, I am NOT a math person and I don't think it is really his strength either, but it was frustrating me as well as him.

For example, how would you mentally figure out $4.25-$1.45 w/o borrowing on paper? I thought we had it figured out, but then the answer was wrong. I think we are getting really confused about mental math now that it is including carrying/borrowing and 3-digit numbers, although he seems to do better with addition than subtraction. Can anyone help us? Should I buy the teacher book to help me wrap my head around this concept? We already have the textbook, but I don't think it is helping us much.

Thanks in advance, everyone!

Hi Jessica! We're doing 2A/2B right now, can you tell me what page number you are on? I think I could advise better then. Thanks!
In Christ,
Julie

Sure, it's Review 3, starting on pg. 83 in the WB -- the problems that were difficult for him are at the top of page 84, especially b, d, and f. I think I figured out f, but b & d are eluding me! Thanks, Julie!

I know I have said this is another post, but I find the teacher's guide very helpful. It shows you how to teach the concepts. I was doing Singapore before we found HOD and so I have always purchased the teacher's guide. This is my personal prefernce. Hope that helps.

I'm sure Julie will help you with the specific exercises there. I don't have our level 2 books out anymore. I will tell you how I would go about the problem you suggested. I think this is the way it would be done in Singapore. To find the difference of $4.25-$1.45, I would first figure out what I would have to add to 1.45 to get it to an even dollar amount, so in this case .55, which would bring me up to 2.00. Then I would add the dollars I need to go from 2.00 to 4.00, which would be 2.00. So far, I have added .55 to get to 2.00 then 2 more dollars to bring me up to a total of 4.00. Now I have to get to 4.25 so I add .25. So the difference between 4.25-1.45 is .55+2.00+.25 which is 2.80. Did that make sense? I hope I didn't confuse you more, but that's the way I would do a problem like that.

$4.25- $1.45

your only regrouping the hundreds/ten the 5' cancel each other out

4.20 -1.40 take the 2 tens away from the 4 tens
4.00 -1.20 now its easy because its a ten combo.. split the 4 into two 2 hundreds
20-12 = 8
$2.80

but that is just how I would do it.

If you look back on pages 47 & 48 in the textbook maybe that will give you a better idea of how they suggest doing the mental math. As I understand it from the textbook visuals, they do the easier ones mentally as shown on the bottom of p.48 in the textbook and the more complex ones on paper the long way as shown at the top of the same page in the textbook.

My dd did #5-D on wkbk pg 84 on separate paper in the way as show in #6 in the textbook p.48 and b as well ( the long way with scratch paper and borrowing and carrying.) All the rest of that page she did mentally. I let her do any problem the long way if she can't get it through the mental math route.

HTH

Edie

Hopefully the advice you've gotten will help you through it. We had to abandon the Singapore ship because it was sinking fast! I couldn't sit through any more tears (mine and my daughters)

we just finished this review last week. Edie was right, you do it the long way on scratch paper. not all the problems were meant to be done mentally on the review. they learned borrowing earlier in 2a and 2b.

ps sorry for no caps. i'm holding the baby and typing!

Thanks so much, everyone! All of your replies helped a lot!

Patty, what you said,

pjdobro wrote:I'm sure Julie will help you with the specific exercises there. I don't have our level 2 books out anymore. I will tell you how I would go about the problem you suggested. I think this is the way it would be done in Singapore. To find the difference of $4.25-$1.45, I would first figure out what I would have to add to 1.45 to get it to an even dollar amount, so in this case .55, which would bring me up to 2.00. Then I would add the dollars I need to go from 2.00 to 4.00, which would be 2.00. So far, I have added .55 to get to 2.00 then 2 more dollars to bring me up to a total of 4.00. Now I have to get to 4.25 so I add .25. So the difference between 4.25-1.45 is .55+2.00+.25 which is 2.80. Did that make sense? I hope I didn't confuse you more, but that's the way I would do a problem like that.

helped me soooo much! I explained it to him this way this morning and he seemed to "get" it a little more! DH is going to go over some more problems with him tonight and make sure he has it down, but this helped me envision what to do -- thanks!

I'm so glad it helped and didn't confuse you more! I'm glad that you and your ds are feeling a little more comfortable with the mental math. It's actually a really handy tool to have. I actually use this sort of thinking all the time in real life.

I'm so sorry I am just getting back to you, Jessica, but you had some great responses already! Pjdobro explained it just like I would have. That is what we do as well. The hands-on math lesson from Unit 27, Day 4 teaches that strategy of counting up to mentally find the answer and takes it one step further. Here is that problem and the hands-on lesson for it, and the taking it one step further part is bolded...

*If you have $3.30 - $0.99 = ____, you can think to yourself, $0.99 is $0.01 away from $1. I can think of $3.30 as $2.30 + $1.00. I can easily subtract $0.99 from the $1.00 part to get 1 cent left. Then, that leaves me with the $2.30 and the 1 cent left, which is $2.31.

So, by thinking of the biggest number $3.30 as being the same as $2.30 + $1, makes it easy to subtract the buck and then add the penny. Doing multiple problems like that on the marker board with your ds if he's having a tough time with it would be a good idea. That is a tougher concept, but learning that strategy sure makes it easier to do once the strategy is in place. So, for instance, here are a few problems to get your ds practicing it...

$4.20 - $0.99 = ___
Think of $4.20 as $3.20 + $1
Take way the $1 and get $3.20
Add the penny since you really needed to take away 99 cents, and the answer is $3.21


$5.50 - $.98 = ____
Think of $5.50 as $4.50 and $1
Take away the $1 and get $4.50
Add the two pennies since you really needed to take away 98 cents, and the answer is $4.52


$10 - $2.95 = ____
Think of $10 as $7 and $3
Take away the $3 and get $7
Add the nickel since you really needed to take away 95 cents, and the answer is $7.05

Now, if this is all kind of confusing, some dc do better to begin with just counting up. So, for the previous problem, you'd count up from $2.95 to $3 first, remembering that took you 5 cents. Then, count up from $3 to $10, which took $7. So, together that's $7.05.

Likewise, this works in adding.

$3.85 + $2.05 = ____
Think of it as $3.85 + $2 = $5.85
Since we were really needing to add 5 cents more, the answer is $5.90

$4.55 + $0.99 = ______
Think of it as $4.55 + $1 = $5.55
Since we added one more cent than we should have by adding $1 instead of 99 cents, take away 1 cent and the answer is $5.54.

This kind of playing with numbers can be used in this problem too:
369 + 631
Take the 1 from the 631 and add it to the '69' part of 369 to get '70'. Add the '70' and '30' to get '100'. Now just add 300 + 600 + 100
Essentially, that's what we'd be doing on our good old scratch paper, but thinking of it this way makes it possible to do it quickly and mentally. I used problems from the Review you mentioned to try to help explain this.

I will say that when we started this in Singapore, I didn't get it and neither did my ds at first, BUT, then with doing it awhile, HE got it and I was still limping along with it. It is like I am learning mental math right along with him. I so looooooooong to reach for scratch paper and just do it the old way, and likewise, I was tempted to just show him how to do it on paper instead and tell him to forget that other way of doing it. I have learned the hard way that it is better NOT to give into temptations to show "my old way" of doing it to him. It confuses him more than anything. My oldest ds in 4B now uses this strategy ALL OF THE TIME on his own. I am just getting how to do it myself. I've been trying to make myself use the Singapore way of doing things, and I am needing less and less scratch paper. That being said, if your ds wants to use scratch paper or hands-on objects for awhile, I'd let him, but then I'd reteach the HOD hands-on lessons and the Singapore strategies they match with until he understands it better. It is important to know that eventually Singapore mixes problems that this strategy works with along with problems that do probably just need to be written out the long way - BUT, by then our d can spot the difference and use mental math as much as possible. In fact, my ds has this strange way of carrying and borrowing that doesn't require him to write out the entire problem lined up perfectly at all. I won't explain that here - not sure I can, but let me say my ds learned his facts later than most dc doing other math programs, but that was so worth it as the mental process was learned along with the facts which benefited him more in the long run. HTH!

In Christ,
Julie