I haven't been student teaching for very long, but it's been long enough to watch my co-op teaching the students (2nd graders) how to do two-digit addition. I learned about the little squares (ones) which get regrouped when you have 10 of them so that you end up putting one ten-piece in the tens column to take their place. It hasn't been too confusing to understand, but it's been very confusing to imagine how to teach it myself.

My co-op will soon be finished with addition. Then it's on to two-digit subtraction, and it will be my turn to teach! I'm very nervous about this because I don't want to instill the wrong things in the minds of these young children, with regards to the regrouping process (which I really don't understand how it works backwards). I will have a book to follow, although my co-op doesn't like to offer too much help because she wants to see what I can do on my own.

This is really easy for her because she's been teaching it for 28 years! I, on the other hand, have never taught it. I would much rather teach geometry, measuring, time, money, numerical patterns, bar graphs... virtually anything except subtraction. Does anybody have any advice on how NOT to mess this important concept up for the kids?

[hngsmom]

Does your cooperating teacher have any connecting cubes (multi-link cubes) to use as a manipulative? Its a great way to show kids what the whole regrouping thing means. For example, build 90 (9 groups of ten) and then take away 42. The students will have to "break a ten" to get the 2 ones that they need to remove. Having a concrete example has really helped my students see the whole regrouping process. I also teach them to remember BBBB--bigger bottom (number), better borrow (from the tens). Its so hard to put this into words--if you could come to my classroom, it would be so much simpler! Good Luck!

[Bonnie gr. 2]

If you have more than one kind of connecting cube available, unifix or multilink, use the unifix. They only go together one way, wo there are fewer ways to play with them while the lesson is going on. I have done this with cubes, places value blocks, and craft sticks. The thing with the sticks is that they can take apart the groups of tens. The sticks come in bocxes of 1,000. I put 99 in a zipper plastic bag.

Which thing works best depends on the class. If they really got the addition, they tend to do better with the subtraction.

[Tounces]

Subtraction with the Base 10 blocks works like this:

Subtraction without Regrouping

1. 55 - 32. Child lays out 55. Take away 2 units and write the number of the remaining units (3) in the ones column.
2. Take away 3 of the tens and writing the number of remaining tens (2) in the tens column.
3. Continue. Later add problems not requiring regrouping into the 100s place.

Subtraction with Regrouping

1. 34 - 18. Child lays out 34. Try to take away 8 ones. There aren't enough. Where can you get more? Take one of the tens and exchange it for 10 units (you could cut it into ten units, but exchanging does the same thing). Now take away 8 ones and write the remainder, then take away one ten from the 2 tens that are left. The answer is 16.
2. Do lots of these without pencil and paper when introducing. Make sure the child really understands the concept and can explain it. Continue to the 100s place.
3. Transfer to paper and pencil by showing each step first with the manipulatives and then with the representation on paper. Use manipulatives to check problems done with pencil and paper and return to review if problems surface.

[mrsb203]

I would do some review of the subtraction math facts. If they are still using their fingers or don't have the facts memorized this really slows the whole process down.
There was a subtraction poem I found on here that I used for the first time this year that was very benificial:
More on top no need to stop.
More on the floor go next door and get ten more.
Numbers the same, zero's the game.
I made a big poster with these on it plus a sample problem next to it.
As the kids did problems on the board they had to tell me which rule they were using. I also told them when they regrouped from the tens that that you couldn't just take something and not leave a note. That helped them remember to show the regrouping on paper. Even after they understand the concept, they forget to show the regouping and make a mistake when they subtract the tens.
I make sure I go very slowly and methodically cueing them step by step.
These two concepts (two digit addition and subtraction) are the hardest that they will learn all year. Good luck

[imacacher]

This thread makes me so thankful that we're using Investigations.

All 22 of my kiddos can solve these problems, with, or without regrouping. They don't use the traditional vertical method, and yes, it takes them slightly longer, but they are all able to do it.

We've done story problem after story problem, and I am completely blown away with what they are able to do!

If your kiddos have to master the vertical method, then this won't help, but my kiddos use any strategy they want, some use the manipulatives (tens rods, cubes, counters, etc.), but the majority use their hundred chart, and they are more accurate than my class last year (before Investigations). I also know that they truly understand what they are doing, and eventually, they will pick up on the "traditional method."

Addition is another story--99% of my students solve ALL problems by writing them horizontally. First, they add the tens, then the ones, then add them together. They are amazingly accurate, and with addition they are QUICK. To them, this strategy makes more sense, I think because it was a strategy that THEY developed, and I didn't have to force the traditional method.

Good luck--two digit was tough last year!

[mrsb203]

Ok, more info please. Anything that works that good I have to investigate!

[imacacher]

Investigations is a math program by TERC. http://investigations.terc.edu/

Our district bought this program, along with Scott Foresman, to provide a "balance".

This year, we've had the option of using both programs as we've seen fit. I used Scott Foresman to teach the first two and a half chapters (addition, subtraction, and place value). I switched to Investigations only for the last three and a half (money, mental math strategies with two digit addition and subtraction, and then two digit addition and subtraction).

Investigations really focuses on the constructivist views of teaching. The activities are all hands on, and student centered. The use of manipulatives is KEY, and they are used daily.

From what I've heard, Investigations is similiar to Everyday Math, but Investigations doesn't use the spiraling approach, as much.

To teach two digit addition and subtraction, I read them a story problem "There were 22 students on the bus. 14 more students got on. How many students are in all?" That was it...they got their manipulatives, solved the problem, and then needed to explain HOW they solved it.

Another key component is the discussion/share time. This was very, very time consuming at the beginning. Each student gets a chance to share how he/she solved the problem, and we keep a chart of strategies that work.

Strategies that the students use for addition: counting two groups of cubes/counters, put them together, and then count how many in all, using the 100 chart to take "hops"--some automatically take jumps of "10" first, and then the ones, others count each square, the most commonly used strategy now is for the students to write 22+14, and then add the tens (2+1=3, so thats 30), then the ones (2+4=6) then add together, 30+6=36.

They use similar strategies for subtraction. I introduced the traditional vertical algorithms last week, and this is a strategy that the students can use to check. However, they aren't as accurate, and they aren't nearly as quick with this method.

Because students are REQUIRED to write and explain how they solved each problem on a daily basis, we are hoping to see a big improvement in the free response portion of the PSSAs.

Out of my 22 kiddos, I would say that 5 of them would be at risk if it wasn't for this program. Everyone of my students can solve the problems...I'm amazed.

Investigations is time consuming. We taught math for only 35 minutes/day last year (plus calendar math). This year, math is 70 minutes/day plus calendar. The time is definately worth it for me, and we can't wait to see how the test scores correlate!

I have a great rhyme for teaching subtraction, I tried it with my 2nd grade class and they loved it!
more on the top
no need to stop

more on the floor (regrouping)
go next door

numbers the same
zero's the game

Hope this helps! Keri