I can't believe I didn't notice.

[MomtoJGJE]

I just noticed today that Jayden absolutely does not understand relationships between numbers with regards to addition and subtraction. I thought that just occasionally she was not thinking or wrote the wrong thing or didn't see the sign right or whatever. But today it was plain as day that she can't see it. Does anyone know a way I can show her this? We've done all the hands on stuff, plus some. The problem is really two fold....

She cannot look at something along the lines of x costs 8 dollars, I have 6 dollars, how many more do I need and see the process. She can tell me the answer, but not the process. She cannot see to write down 8 - 6 = 2. Or even that that's what she needs to do.

The second part of the problem we are having is that she just doesn't see numbers as a whole... like to her 182 is 1 8 2.... so if she looks at a problem like 182-75, she'll say that the answer is 113... she'll say 5-2 is 3, 8-7 is 1, and 1-0 is 1. Instead of 2-5, can't do that borrow, subtract, etc. Actually, it's only been very recently that she hasn't done it from the left to right instead of right to left... which honestly I do it right to left, but because I understand borrowing and carrying I can get the answer right. she does the same thing with addition, but forgets to carry... but since that's not huge, I'm not overly concerned about that... reminding her to work right to left before she does math fixes that every time.

Anyway, does anyone have any suggestions as to how to get her to be able to see the relationships? I think I can help her figure out the seeing a number as a whole thing, but I don't know how to get her to put numbers together...

[Tree House Academy]

Did you happen to just start Singapore 2B today? LOL I ask that because we did too and the same thing dawned on me! My 8 year old knew the answer a lot of the time, but explaining how he got there to me was tough for him. I think we just need to keep plugging along and showing them. Did you see the activity that Carrie planned out in Unit 18, Day 2 with the circles and counters? We used that again today when he got lost on what to do and it seemed to help. The more you do it, the more I think it will "click."

I also gave him counters and told him to see what he needed to do to get to the answer: i.e. the problem 28-____ = 5. I gave him 28 counters and told him to take it down to 5 counters and fill in the missing number. He did that pretty well. Then I gave him 8 + ___ = 16. In that case, I gave him 8 counters and asked him how many he needed to make 16. Then, I gave him 16 and told him to figure out the same problem that way. It took him a few more minutes, but he finally divided the groups up with 8 on one side (and of course, 8 on the other). I am hoping that will get him thinking in the right direction.

Also, in the next few pages, they start in with number bonds again and I think those help them see the relationship better.

As to the other problem you mention, I am not sure what to do there other than to just keep reminding her that she has to subtract from right to left. My son occasionally slips up there too, but he is getting it.

[MomtoJGJE]

No... sadly enough we are finishing 2B Friday I dont' want to move her on until she can at least tell me what she's supposed to be doing. She can do it with counters, but she cannot tell me the process. She can see the three numbers (if you think of the triangle thing that they teach early on in Singapore) but not the process to use to figure out word problems. She can use manipulatives and get the answer, she can get the answer in her head, but she has no idea how she got it or what she did. She GETS the numbers and concepts, just not the process she uses. Singapore has done great for her mental math but it hasn't taught her the process.

And I feel like it's my fault for not catching that this was a true problem until now. Ok, I know it's my fault, but I feel guilty about it. She's starting Preparing and 3B Monday!

[MomtoJGJE]

Oh, and I forgot to say that dh thinks that if I give her basically addition/subtraction worksheets with like 20 problems a few times a week and just keep giving her the same sheet until she gets all of them right (like start with easy 1+4= and then get harder) that it'll work itself out. And it probably will... I just feel like she hasn't gotten this in 2 years of school (because she doesn't get the relationship of the number bonds!) and it's my stinking fault because I thought at first "she can do it with manipulatives, she gets it" and then "she's making silly mistakes" when in reality she just doesn't get it. AHHHH

And what's worse, is that she COMPLETELY gets mult/div/fractions/money/time... everything but addition and subtraction....

[my3sons]

...like to her 182 is 1 8 2.... so if she looks at a problem like 182-75, she'll say that the answer is 113... she'll say 5-2 is 3, 8-7 is 1, and 1-0 is 1. Instead of 2-5, can't do that borrow, subtract, etc.

Each one of my dc have done this at some point too, and so did the dc I taught third grade in ps. Personally, I think that the concept of reading left to right interferes with the concept of working math right to left. For each of our dc, I flipped back to the hands-on activities for help. I redid the hands-on activities with the new math problems until they understood it better. For example...

If your dd comes to a subtraction problem that requires borrowing, I'd work through these hands-on activities as a review...
Unit 7, Day 1
Unit 7, Day 3
Unit 7, Day 4

Subtraction with borrowing is an introductory skill in Level 2A/2B. Dc continue to move toward mastery of this skill in 3A/3B. It took Riley that long to have mastered it, at least, and he does well with math.

Also, I've found just talking through it out loud has helped be a quick review for my dc. For example, if the problem was...
512 - 268 =

I'd talk through it. I'd say 2 take away 8, hmmmm, can I do that? If they say, "Yes, it's 6." I'd say, "Really?!? If I have 2 (and I grab 2 markers), can you take 8 away from me?" Then, they understand it pretty quickly. I usually grab 10 markers then and show how you'd have to borrow from the neighbor. Basically, I just say out loud each step. This seems to work well too!

Oh, and for money, I'd get actual money and go through the problems. That inherently seems to make more sense to my dc! I hope this helps!

In Christ,
Julie

[MomtoJGJE]

That is what we do in those situations.... so that's good to hear. It's also good to hear that mastery isn't expected until 3A/B

But what about just not getting the relationships? Like the problem today was "Kelly has $6.80. The stamp album she wants to buy is $8.50. How much more money does she need to buy the album?" Jayden said "she needs 1.70" I said "good. Write down the problem and do the actual written math." she wrote "6.80 + 1.70 = 8.50"

So I used number bonds, pre-algebra, and showed her how you can't use the answer (we said x or ? could work for what you are wanting to figure out) to figure out the problem. That the answer has to be by itself on one side of the = sign. That she has to use the other numbers given in the problem on one side and figure out how they go together to get then answer to be by itself. By the end of the discussion, she got it.... but it didn't have the feel that she'll be able to do it later. We'll see, she has more word problems tomorrow

I just don't know another way to teach it. She GETS the math, she GETS the concepts, she can do it with manipulatives and any hands on things... but she doesn't know HOW she's supposed to put that on paper.

[twoxcell]

I would use Cuisenaire rods to teach her the first concept and base 10 blocks to cement the place value issue. I'm thinking the best thing to do at this point is to pause your regular math work and work on these two concepts for awhile.

[my3sons]

...Kelly has $6.80. The stamp album she wants to buy is $8.50. How much more money does she need to buy the album?" Jayden said "she needs 1.70" I said "good. Write down the problem and do the actual written math." she wrote "6.80 + 1.70 = 8.50"

Thank you so much for sharing this - it helps me understand what she is doing better. Honestly, this is an example of excellent mental math! She actually thought of the problem as a missing addend problem: $6.80 + ? = $8.50

This is just fine. If she is able to do this, I would not require her to write down the problem and do the actual written math. She is using what she has learned about doing mental math from Singapore and applying it well. She actually used one of the mental strategies she was taught in Singapore. She probably counted up from $6.80 to $8.50. This is a more advanced skill than writing this problem as a subtraction problem and doing the borrowing, and, I bet she found the answer more quickly and efficiently as well. Singapore encourages teaching several different methods for solving problems, and this helps dc choose the method they personally find most efficient. That's exactly what your dd did here, so applause! I'd not make her rework it another way if she found the correct answer using her chosen method. There is no need when she arrived at the correct answer.

However, in the other example you shared, where she worked the subtraction problem from left to right, some review would be helpful. HTH!

In Christ,
Julie

[MomtoJGJE]

Ok... so it's ok as long as they get to the answer to not know how they are supposed to get there? She did add up... if that's actually ok, then I'll apologize for the "extra" discussion today and tell her that it's all right

Based on the answers here I'm going to assume that it'll get there eventually since she does know what the answers are. I am still going to give her some extra practice problems for "homework" a couple of times during the week... We've never worked on math facts ever, and with the problems she does have I think it'll help her.

Thanks everyone for letting me know she's great where she is and that if she can get things with reminders it's ok