2 digit horizontal addition Singapore Math question

[intotheirhearts]

What is the purpose of doing 2 digit math equations horizontally instead of vertically? The 1B book teaches it horizontally and says vertical will be introduced in 2A. My son is struggling to get the hang of it horizontally but I'm pretty sure he'd be able to handle it vertically. I think the teacher guide does say you can teach it vertically if you want but that it will be introduced in the next book. I don't want to switch to teaching it vertically if it is going to make my son miss something important or not develop a particular skill.

(By the way, we are using the Home Instructor's Guide for Singapore Math. It has personally helped me teach it better.)

[StephanieU]

I think horizontal is done because it is more mental arithmetic than computations. But really, it doesn't matter at this age. We are using Horizons, and they actually teach vertical first and then horizontal because when you get to carrying, it is easier to do that vertically.

[blessedmama]

We do math vertically. In our house we call it "stack math." I don't know why we started calling it that but we did and it stuck. So...we do it vertically.

[intotheirhearts]

So with doing it vertically, have they still established the mental portion of math well that perhaps the horizontal addition is suppose to help support?

[StephanieU]

Singapore (and other curriculums that are more hands-on) try to have kids figure out some of the conceptual ideas behind how we do standard arithmetic algorithms. By having them written horizontally, they can't just add down the columns. They have to understand more of the conceptual ideas first. It promotes them breaking apart numbers and figuring out what carrying actually is.

[cjbaby]

We rewrite the problems vertically. It is so much easier as you move into borrowing and carrying over.

[my3sons]

There is a purpose to every little bit of the way Singapore math does things (and I believe in this particular scenario, StephanieU summed it up - no pun intended - quite succinctly in her last response). I have learned through the years to teach it the way it is taught in the textbooks - it is extremely successful. I used to interject my little 'helps' and 'tricks' when teaching Singapore early on. I stopped as I was confusing my ds. We've completed all of Primary through 6B, DM 7A, and then just went right into Foerster's Algebra I, with total success. HOORAY! I'd just encourage you to teach it as it is written - if it's across do it across and then if you want do it vertical - but for sure do it the way it's written - and enjoy the rewards! HTH!

In Christ,
Julie

[intotheirhearts]

Thanks Julie & Stephanie for your posts! I guess we are going to be camping out here for a while on 2 digit addition. Or is it okay to move on and it will be revisited later?? I'm also not sure how to reconcile the fact that HOD says they don't NEED to know their math facts yet but Singapore says the kids should hopefully know their math facts yet (or know how to quickly calculate them). So we are still working on math facts. And we are needing to continue working on the 2 digit addition horizontally. We are SO close to being done with 1B. We started 1A at the beginning of LAST school year and moved fast so we were ahead for a lot of the year and then it went slower and now we still haven't finished the 1A/1B series. I have had some spots along the way that I have been stuck in teaching, so I got the home instructors guide. That helps a lot for me! But now it's my son that is a little stuck on the 2 digit addition horizontally. I guess we need to spend some extra time on it. But how much extra time? How much more time before we just move on? And what about math facts??

[MomtoJGJE]

I've learned to not spend extra time on something. We go through it, correct answers, and move on. They get it. It's amazing.

We typically don't do math facts. This year I'm having my two oldest (the second simply because they like to do things like this together... I might even add in DD3) write down their multiplication facts once a week, just to make it faster for them. They know how to multiply, they get the concept, but it's not just rote yet. Which makes their math, especially the oldest, take extra time.

But as far as concepts and the actual Singapore stuff... I used to try to teach it until my oldest got it. Which was frustrating for both of us.... she'd get it, then it would go to something else, then it would be like teaching it all over again when we got back to it. I decided in the middle of the year last year to just go through it and not worry about it. And just like before, when we were both frustrated, it eventually just clicks... except we aren't nearly as frustrated, and math doesn't take nearly as long.

[queenireneof3]

Julie and Lora Beth...

I am wondering about this too. We are working through 1A right now and we stopped the singapore math text to learn and practice the addition fact families via Math U See before proceeding with the singapore 1A text into subtraction. I am not sure if he needs to have those facts memorized before moving on or not? Should we not stop and learn the addition fact families before moving on to the subtraction in the Singapore book? I looked at the scope and sequence on the Singapore website and it seems like, other than book 2A, we won't be working on addition, so I wasn't sure if i was supposed to supplement memorizing the facts. He does great with the SIngapore questions so far. He gets it and does not struggle with answering their questions.

Would love your or anyone's two cents about this.

Sara

[StephanieU]

Honestly, I think memorization is best done in ways like Lora Beth described. Spending days on memorizing facts doesn't always make them stick in the long run. And instead you are in a way wasting time, taking away time they could be advancing in math. Most standards don't have memorization of facts until 2nd or 3rd grade for this reason I think.
When I took Calculus in high school, our teacher let us use a table of basic formulas. Then in college, my professor didn't allow them and I panicked for a second. Then I realized I already know most of them, and I could figure out the ones I didn't know with a little trial and error. It proved to me spending hours doing flash cards for math facts wasn't necessary.

[my3sons]

In Singapore Math, dc learn facts by continually working through math problems that require them to figure out the facts to arrive at the answers. For example, my dc started naturally counting by 2's, 3's, 4's, 5's, and 10's just by working through the daily problems in Singapore. They sometimes used their fingers, tapped their pencils while counting, or looked at the ceiling pondering a way to find the answer. While looking at the ceiling , they would be saying things like, 'let's see, for 9 x 7 that's like 10 sevens, ahhh 70, less a 7, so that's 63.' Or for addition they'd say things like, 'let's see, for 5 +7, that's just 5 and 5 (10) and 2 more... ahhh, 12.' This is the 'practice' of the facts, that usually naturally leads to the memorization of them, as they just know in their mind 5 + 7 is the same as 5 + 5 + 2, which is 12... and finally, just 5 + 7 is 12. So, by slowing down or stopping the daily math lessons Singapore has planned, dc are actually slowing down or stopping their 'practice' as it was intended in Singapore as they are no longer systematically working through the daily work. With our dc, fact memorization came later in Singapore Math, but when it did come, it came with nearly 100% accuracy, and it came with an accompanying understanding of the "why" of the computation.

So, my advice would be to continue moving through the daily lessons together, making sure to do the hands-on math lessons HOD has planned, making sure to have in hand a markerboard and dry erase marker to work problems together, making sure to do every single part of the Textbook's lessons together (including all side notes/word bubbles/pictures etc.), and continue to be available to help as dc work through their workbook sections. If they get stuck, use the same mental reasoning taught in Singapore or the same hands-on HOD activity taught in the lessons for that skill to help dc work through whatever they are stuck on. They should do well with it, and fact memorization should eventually come.

Exceptions to moving ahead with daily lessons would be...
if dc have come into Singapore at an upper level and do not have in place the previous 'mental reasoning' skills the younger levels of Singapore would have taught
if dc if dc have not been doing the hands-on math activities consistently that HOD has planned for levels Kindergarten through 2B and are struggling
if dc are not showing basic number sense (i.e. What is one more? What is one less? Is 5 more than 2?) that should be intact prior to learning facts

In these scenarios, it is crucial...
...dc take the free Singapore Placement test to determine the proper level to begin with in Singapore. It cannot be assumed dc should simply do their grade level (according to age) within Singapore Math. Singapore Math is advanced, so it is common for dc to do younger levels of math than their current grade level. A good rule of thumb - complete Primary 6B by the end of Grade 8. If dc do this successfully, meaning they did well with it and understood it well, they can probably go directly into Algebra 1 next, or certainly a short pre-Algebra course.
... dc need to get whichever HOD guide has the hands-on activities to match their placement and do those hands-on activities as planned
... older dc may need additional help with fact memorization, such as skip counting tapes or flashcards, as they may be past the younger levels of Singapore but due to not having completed the previous younger levels of Singapore they may not have 'inherently' learned their facts

HTH!
In Christ,
Julie

[queenireneof3]

Wow! Thanks for the replies. We both enjoy Singapore better than MUS anyway, so it will be nice to go back and just work though continually like Julie suggested. Julie, we are using the Beyond guide for the hands on activities for 1A, so we do not have the textbook. Did you go thru the textbook, HOD hands on lessons and workbook? Is the workbook with the HOD activities enough?

Thank you again!

[intotheirhearts]

Well...I decided to go ahead and go back to some of the double digit horizontal math again. I wanted to make sure I had thoroughly taught it well with the Singapore methods and hands on activities and math manipulatives. I did that on Wednesday. And then Thursday he worked through several problems on his own with just paper and pencil, no math manipulatives. And he could just look at the math problem and work it out without writing a bunch of stuff on the paper (like arrows and stuff). I was impressed! What he was struggling with 2 weeks ago he totally gets now! He does do a slightly different strategy then is taught in the home instructor's guide but he knows their strategies too. What he's doing is working and he is understanding the concepts so that was exciting!

Queen Irene - It is my understanding that as long as you do the hands on activities in HOD then you do not need the home instructor's guide at this level. I ended up buying the home instructor's guide though and am SO glad I did. For me, it is very helpful to make sure I am teaching the concept that is suppose to be taught and to make sure I am not interjecting my own concept that will actually be taught later down the road.

[MomtoJGJE]

We don't use anything other than the HOD hands on and the workbook until 3A (I think that's when it starts, haha) when HOD doesn't have hands on any more... Then we use the text book.

Honestly, I don't remember drilling addition and subtraction in school. I remember drilling multiplication, but not division (because we already knew our multiplication). DH REALLY wants the kids to have multiplication down pat.... for what practical reason other than speed and ease I do not know. So that is the only reason we are doing any practice outside of Singapore work at all. I can totally see how KNOWING multiplication tables makes it faster and easier... therefore they would score higher on testing

But like Julie said... with Singapore, the facts might be memorized later than average in public school, but I can guarantee you they GET IT better. They know WHY 1+1=2 instead of just the fact. So even though they might not be able to just say 7+5=12 without breaking it apart and really thinking/counting/using manipulatives until they are older, they can do basic algebra/pre-algebra in 3rd grade because they know WHY it works the way it does.