Best way to teach carrying?

[StaceyinLA]

What program does the best job of explaining carrying? My grandson is just really not grasping the concept, and I want something that will really focus on that. He’s doing Rod & Staff math, which my daughter likes using, but it’s just not doing the trick with this. 

Anything I can add that would help? Just a specific little something that would cement the concept? Or would you be using a completely different math?

We were thinking of moving him to TT starting with level 3, so he could just use it all the way up, but he definitely needs to get this mastered. He acts like I’m speaking to him in a foreign language when I explain it.

Edited June 13, 2019 by StaceyinLA

[HomeAgain]

Anything that you can only have groups of 9.  Decimal Street was such a nice way of thinking about it that I made it to fit base-ten blocks as well.  I made stacking number cards to go as well, so that the units cards were 1/3 of the length of hundreds cards, tens cards 2/3 the length...

[HomeAgain]

And if you don't have blocks, print graph paper on 3 colors of card stock.  Cut out the right sized shapes.

[forty-two]

Working through lots of carrying problems with base-10 blocks (I used Cuisenaire rods for 1s and 10s, with large 'jewels' for 100s).

With both girls, I needed to pause our main math program to do more work on regrouping (carrying and borrowing).  I made up problems and we worked through them with our improvised base-10 blocks.  I'd have them do a step with the blocks and then do the exact same step with the standard algorithm (it felt like 'recording' the block result on paper), making sure they saw the connection between what we did with the blocks and what we did on paper.

Here's the basic steps: 1) make each number in blocks, 2) combine the ones blocks and find the total, 3) exchange groups of 10 ones for 1 ten, 4) write down the ones total in the ones place and write the number of carried tens over the tens place.  5) Do the same with the tens: combine the tens blocks (including the carried tens) and find the total, exchange groups of 10 tens for 1 hundred, and write down the tens total in the tens place and write the number of carried hundreds over the hundreds place. 6) Do it again for the hundreds.

I would work problems together, blocks+writing, with me prompting each step.  Then once the kids started getting it, they would work the problems themselves with both blocks and writing, recording each step as they went.  I let them use the blocks as long as they wanted, and they eventually dropped them once they were solid.

[sweet2ndchance]

My son (6.5yo) really likes this video but I will say that carrying and borrowing is/was an idea he really needed to play with for a long time before he started to comprehend it. He's quite good at math and very intuitive with it for the most part but he needed some "simmer time" with the idea of carrying and borrowing before it started to make sense for him. Playing with the nooms on Dragonbox Big Numbers really helped as well. Playing and experimenting with tens frames seems to help too.

[Rosie_0801]

CSMP mini computers worked for us.

[8filltheheart]

My granddaughter was visiting us for a couple of weeks and I was working with her and recognized she didn't understand borrowing. We used C rods to work through problems. I am still not sure she 100% understands that numbers are base 10, but the rods let OTA much better understanding than she had. 

She struggles with math and always has. (She didn't automatically grasp that 2+3 is the same thing as 3+2. (She is so incredibly different than my kids.)  She really, really needs constant visuals with constant repeated practice. She just doesn't grasp concepts until after weeks of doing something over and over.

[carriede]

Check out Educationunboxed.com for using c-rods or other base ten blocks.

[StaceyinLA]

15 hours ago, square_25 said:

How are you trying to teach him, and what is he not getting?

 

Basically just explaining it, which isn't working. He needs something concrete to "see" I think.

[StaceyinLA]

35 minutes ago, HeighHo said:

SM

mental math should already have been done with add of single digit with regrouping and subtract of single digit from double digit

use discs with 1,10,100 printed on them.  

start with just 1s.  review single digit addition w/o regrouping, then show how to write what was just combined using vertical format

four 1s in a pile combined with 3 1s in a pile is 7 1s in a pile.  4 + 3 = 7  write that vertically also

four 1s in pile combined with 8 1s in a pile....we have 12 1s.  4 + 8 is 12. one ten plus two ones...wait, we have twelves ones.  what do we do?   swap one group of ten 1s for one 10.  show 12 as one 10 and two 1s.  go back and show the vertical algorithm...we can only put one digit in the ones place and that digit must be the number of ones we have.....we must 'carry' the amount of tens we have to the tens column. we have one ten, so we'll write that in the usual place for carrying, then add up and put sum of tens in tens place.

continue on to double digits and triple digits

it is helpful to use a different color marker for each place while explaining

discs are used because some children are new to rods and cubes and the visual number on the disc reminds them it represents a ten..with rods and cubes they would have to recount. others do not have the short term memory to do it all.

 

I think this is part of his issue. The mental math thing seems to be lost on him. I swear he can do 8+5 on one line of his workbook and when he sees it on the next, it's like he never saw it before. It's like he doesn't remember the strategies from one day to the next either. 

I think he needs to basically be drilling his facts and also have some concrete stuff to make it all stick better.

I've told dd I'm gonna work with him over the summer, so I just wanted some suggestions to get him doing better with this, and feeling more confident.

I'll be teaching them (him and his sister) two days/week starting this fall also, so I'm wanting some good suggestions that will work for them both (she's only 16 months younger, and will likely pick up concepts pretty readily as well).

I have CR, and I'm pretty positive I have base ten blocks as well. I'm gonna check the website mentioned above to be sure I'm teaching the concepts correctly. It's been a LONG time since I've taught math to littles (my baby is almost 24).

Edited June 14, 2019 by StaceyinLA

[Monica_in_Switzerland]

I would do lots and lots and lots of manipulative before ever thinking about "drilling facts".  There is very little point in memorizing by rote something you still don't understand.  

We use base ten and c rods, and often for my current early learner, I draw a juggler on the white board.  He has 8 balls tossed up with one hand, and 5 balls tossed up with the other.  She knows she needs to draw a circle around all 8 and an additional 2 (We spent lots of time on "What makes ten?" games) to make a group of ten, then she can see there are 3 additional ones hanging out as well, so the juggler has 13 balls.  She's the only kid I've drawn jugglers for, go figure.  😛  

We are doing this right now, actually, and she is my slowest to really click with the concept.  So we do a few examples with manipulatives or the juggler, then I write a new problem and ask her to mentally picture how many balls she needs to move from one number to the other to get a group of ten.  Then how many would still be left in the ones pile?  And so on.  Today, she did a total of about 20 problems on the white board, and all of them were adding with 9.  9+1, 9+2, etc.  In order, then out of order.  She knew she needed to shift one ball in order to get her group of ten, and taking away one is something she can do mentally, so that let her get every problem correct.  Tomorrow, we'll try 8s and maybe 8s and 9s mixed together.  

This particular child just needs a lot more hand-holding than the two older.  I would much rather take the time NOW with the mental concept, rather than rush it to get to a carrying algorithm that becomes a sort of "magic trick" she may be able to do, but can't understand.  

We use manipulatives through Singapore Math 2b (the grade the child is in is irrelevant, I just mean that level of math) on a daily basis, then switch to "as needed" from then on.  

 

You might also consider the "Math Facts that Stick" book offered by WTM Press, it uses a 10 frame to help cement the base ten system, and that's another great method.  

 

[StaceyinLA]

He is 7 (2nd grade, but kinda late bday so more halfway through second) and his sister is 6 (some K some first - late bday).

He started strong with math, but I think R&S is just so dry and basic that he hasn't had as much exposure to different strategies and things. Dd has had a really stressful year (separated from her husband/their dad) and I think she has struggled to just keep her head above water with school. That's one reason I'm helping her over the summer, and then once "school" starts up again.

It seems he really just needs concepts solidified for sure. Yall have mentioned so many good things that I don't even remember doing with my kids when they were little. I was so much more from that old school drill, drill, drill - probably why most of my kids hated math.

He hasn't even seemed to really grasp counting up and other strategies. I don't want to make it sound like he's got any learning issues; I just don't think it's been presented well, and he's not super fond of math (which could also be because it hasn't been presented well).

Is there something I could watch that would show me how to teach these concepts to him, or maybe a math program that has that more built-in along with some good instruction?

The games are a definite. We play a lot of games, and he LOVES yahtzee and other games that do require math skills. We'll kick that up a notch for sure.

[EKS]

Math U See, RightStart, or Singapore.

Edited June 15, 2019 by EKS

[Sarah0000]

For targeted stuff without switching your main curriculum take a look at Education Unboxed. Also make sure in a real life or pretend play scenario he can mentally figure how much of something at least within five, preferably without counting, and how many of something if the parts of the whole changes for any quantity. For instance if setting the table for five (have an action figure picnic for fun) but there's only three muffins, how many get left out? If there are 17 cookies total and you give 11 to person A, 6 to person B who gives 1 of those to person C, and nobody has eaten any, how many cookies are there now? Ask questions like that, working up to keeping all the items in the basket while he answers the question. Assuming he has no problems with that kind of thing, I'd do:

1. Math for All Seasons and other Greg Tang picture books from the library for developing mental math and visual grouping,

2. All the King's Tens from the library plus building two digit numbers with rods or any handy manipulative on a printable place value chart,

3. Kate Snow's Addition Facts That Stick, also the subtraction one if you still think it's necessary after the addition or do gradual addition and subtraction problems using a ten frame or abacus,

4. Then Greg Tang's free printable addition and subtraction worksheets that walk through breaking down numbers to make a ten in more of a standard worksheet format. Use manipulatives with a double ten frame and a place value chart if it still looks necessary,

5. Then reread All the King's Tens and build three digit numbers with manipulatives in a place value chart. Do +1, +10, +100 questions with the chart and move on to other numbers and subtraction,

6. Read Big Numbers from the library to show place values getting bigger. Do simple oral problems starting with ones then moving up through the places. Shout "5+3=__" and he shouts "8!" Then do "5 tens+ 3 tens=__" but shout the 5 and 3 and whisper the tens part to emphasize that the problem is the same arithmetic as the one he just did. Guide him to say "8 tens." Repeat for hundreds and gradually move to no shouting or whispering and saying the usual number name 80 and 800 in addition to then instead of 8 tens and 8 hundreds.

[Monica_in_Switzerland]

Videos:  Watch EVERYTHING over at Education Unboxed.  All videos are great, and if he hasn't used C-rods consistently, going back through even basic math will feel "new" to him, and maybe take away any thought he might have that it's "baby math".  The younger child can absolutely participate, spring for the Small Groups bucket of c rods!    

Set him up for success.  Once he has the values of the rods down (this might take a week, and during that time you can be playing lots of rod games), encourage him that he doesn't have to select the right rod on the first try.  So if you place a 3 rod and a 4 rod together, he can test the 6, and the 8 before finding that 7 is correct... and that's perfectly ok!!!  You should not "check" his work until he tells you he is ready.  At this stage, be sure to point out explicitly, and let him test, that it doesn't matter if you put the 3, then the 4 or the 4, then the 3, their total length is still the same as the 7 rod.  You don't need to tell him this is the commutative property of addition, but he needs to UNDERSTAND that this property exists.  So ask him lots of questions about it.  Multiple times per class, for multiple weeks:  "You're right, the 4 rod plus the 2 rod equals the 6 rod!  What happens if I put the 2 rod, then the 4 rod?"  Let it become so well understood that he rolls his eyes when you ask the question!  Then, you'll know he's got it.  

Next, fact families.  (There are videos for all of this on educationunboxed.com).  Show him that one rod "picture" can generate 4 math equations.  Refer to the total (ex. 6) as the whole, and the parts (ex. 4 and 2) as the parts.  Make sure he understands that with addition order doesn't matter, but for subtraction, we start with the whole and subtract one part to find the missing part.  Keep working on this idea until he can write out the 4 equations of the fact family for any rod picture with a total less than 10.  In the mean time, as you work on rod puzzles (finding a total for finding a missing part), he will be intuitively learning his facts to ten.  As you see he is automatically reaching for the correct rod on the first try for smaller problems, start introducing strategies for large numbers (still total under 10).  If he knows his doubles (and if not, teach them explicitly), then he can figure out that 4+5 is just a bit bigger than 4+4, so "What might you guess is the answer?".  Teach counting on for adding 1, 2, or 3, and doubles or near doubles strategies for other additions (still ten or under!!!).  Addition War, or Jelly Beans are great games to just get a lot of additions in one sitting, make sure the rods are out and there is no stigma about using them during the games!!!  

Every single day, have kid figure out all the ways to make ten.  Don't move on until this is memorized.  The easiest way to do this is to have the kid set up with c-rods all the combos to make ten, then he can have those out in front of him while you play "Go to the Dump", basically Go Fish but where instead of looking for pairs, you look for ten facts, so 2 and 8 make a pair, 7 and 3, etc.  This should be fun, and if at all possible throw the game so the child can win often.  

 

Only when he has truly gotten his up-to-ten facts should you start looking at regrouping.  

 

 

[8filltheheart]

7 hours ago, Sarah0000 said:

 

2. All the King's Tens from the library plus building two digit numbers with rods or any handy manipulative on a printable place value chart,

Thanks for reminding me about the Sir books. I just ordered All the King's Tens for granddaughter.

[HomeAgain]

For c-rods, these books are amazing.  They're free online and there are demonstration videos on youtube.  My son had finished Right Start D and we still started with book one, "The Study Of Numbers From 1 To 20".  Education Unboxed can be a great help, but if you need something more and want to go back to the original, these are it.  Vertical notation isn't formally taught until book 2, just to make sure kids have a very firm grasp of linear blocks first.

[Monica_in_Switzerland]

1 hour ago, square_25 said:

 

These are all excellent ideas! I like your list. 

However, I'll say that if I forced my daughter to do nothing else until she got her up-to-ten facts down, she would have loathed math. She isn't particularly motivated by arithmetic and she really liked moving ahead with conceptual things. We were working on binary and she still had to think about some of the sums where two of the numbers are under 10. We kept drilling facts along the way (mostly we'd do quick quizzes when walking to her classes), we'd make sure to keep everything concrete and hands on (mostly with visual representations), but we also worked base 10, and regrouping, and fill in the blank problems, and puzzles. 

Which is to say that I wouldn't necessarily be so rigid about the ordering :-). 

 

 

While I agree to follow interest, I think it's safe to say your daughter is exceptional in her mathematical thinking.  🙂  But I do totally agree, if kid wants to flip coins or draw balls from a hat or investigae why a square number is a square, always follow the interest!  

[Monica_in_Switzerland]

To add on to what others are suggesting about continuing on with math while still working on facts:  Singapore, and I assume other math books, have about half of each level dedicated to geometry and measuring.  These chapters are typically VERY easy compared to the computational chapters, and can easily be done out of order so that you are still making progress through material.  This is typically how we do SM 1, 2, and even 3 because it speeds up the books and breaks up the computation a bit.  

[daijobu]

We used Singapore.  I cut out dozens of squares of construction paper and labeled them "1" "10" "100" etc.  Then to represent 347, that would be 3 "100" cards, 4 "10" cards, and 7 "1" cards.   I would group the pieces of paper together in areas labeled "Ones" "Tens" and "Hundreds."  

IIRC, Singapore uses "renaming" instead of "carrying".  So after doing the addition, if you have more than 10 "1" pieces, you can make a fair exchange:  10 "1"s is the same as 1 "10".  Make sure the student understands why this is a fair exchange, and it technically doesn't change the number at all.  So you are renaming 10 "1"s and 1 "10" if that makes sense.  We give it a new name, but the value is the same.  

If you add 347 + 5, when you are combining the paper pieces, you'll end up with a total of 12 "1" pieces.  Exchange 10 of those for 1 "10" piece, and now you have 5 "10" pieces and 2 "1" pieces.  We did this example over and over so they always understood what was going on "under the hood" when you carry the one.  

Same thing with subtraction.  If you need to borrow a ten, what you are really doing is making a fair exchange of 10 "1"s for 1 "10".  HTH.  

[Angie in VA]

Abacus?