Multiplication/Skip Counting

[John'smom]

So we are at the end of 2A with my dd. Math has always been a weakness for her. I think she is doing better since we have switched to Singapore (and supplement with MM as she needs more review). Now that they've introduced the multiplication/division it has sent her into a tailspin. She cried and said she didn't know why they were making division when she hasn't learned all the multiplication. Anyway, we only have about one more week in 2A and the multi/div is nowhere mastered, I mean the understanding of it. So I'm going to work with her one some games and some MM sheets concerning it all. Yes, I always do the hands on HOD plans with her and repeatedly. Plus she plays the Rainbow Rock computer games.

My question has to do with skip counting she has the 2's and 3's memorized of the skip count patterns. I really don't see how it is that helpful for her in a sense. I mean unless she uses her fingers or tally marks on a paper to know how many times she has skip counted it doesn't help. So is that what you do with your dc, allow them to skip count using their fingers to know how many times they have skip counted. I'm kind of reluctant to encourage this as math is her weak area and I don't want to create a crutch that she can never get rid of. She has 2 aunts (one on each side) that still count on their fingers today, say they hate Math, etc.

So my question is, how do you implement the skip counting? Any other advice or ideas is welcomed too.

[raceNzanesmom]

I would work on her facts before moving on. Divison is so much easier when you know your multiplication facts.

My ds learns skip counting first, we use songs, patterns, online games, manipulatives, videos, anything that will help. Then we do actual multiplication problems with that number. We don't move on until he has that number mostly memorized.

[Mommamo]

I never really stressed math facts with C, and she's nearly done with 4A now and has her facts just fine. She memorized with skip counting too. Now, she still uses skip counting when dividing, but that is really the only time it shows up.

[Carrie]

John's mom,

We do let our sons use their fingers for skip counting, as it is needed to help them keep track of how many times they have counted. The real benefit of skip counting shows itself more and more the further kiddos progress down the math path. It is a truly helpful skill as kiddos begin doing long division with remainders, work on finding least common multiples and greatest common factors, and seek to reach common denominators when adding and subtracting fractions.

Using one's fingers to skip count is not the same as counting on one's fingers to add and subtract. This is because in skip counting the fingers are just a method for tracking the number of multiples of a given number counted to reach a product, rather than the fingers actually standing for the numbers themselves. Skip counting is a much higher level skill which goes beyond typical manipulatives. Plus, if your child can skip count for multiplication, she should also be able to use that same skip counting method to find the answers for division problems. This is because of the fact families. For example, here is a fact family for '2', '8', and '16':
2 x 8 = 16
8 x 2 = 16
16 divided by 8 = 2
16 divided by 2 = 8

So, if your child knows how to skip count by '2', she should be able to use that method to solve any of the problems above. In the first two equations, she would skip count eight 2's. In the next two equations, she would skip count by 2's to reach 16, which is also eight 2's.

Usually, as kiddos progress through Singapore math they internalize most of the math facts on their own. This allows you to wait to drill any facts until there are only a few troubling facts left to drill.

It is also good to note that the 'A' book of each level of Singapore is always quite a bit of work, because Singapore does not do what other math programs do in starting out with review. Instead, the 'A' book just jumps in where the previous level left off. This means that you may have to slow down to catch your breath a bit at the beginning of the 'A' book, especially if you are new to Singapore math. Singapore does have a great ebb and flow, however, so if you keep on moving through the book your will see that just as you feel you cannot take much more, it switches to something much easier with a whole different set of needed skills.

Blessings,
Carrie

[John'smom]

Carrie,
Thanks so much for the reply. We are finishing up 2A now and yes we are new to Singapore, but did 1B through the summer. I have seen the very same thing as you mentioned with Singapore having an ebb and flow. I already looked ahead to 3A and saw they give a little break for the multi/divi concepts. So dd used her fingers to skip count today and did wonderful. The negative, later on she tried (the first time ever) to use them to do a subtraction problem (she is doing the review at the end of 2A). I know she is super visual and that is one of the reasons Singapore works so well for her. We had a talk about NEVER using our fingers for addition and subtraction and only for keeping track of how many times she skip counts. I tried to get across what a bad habit it would be to start doing that.

I am so pleased though at her work on this review in the other areas of Singapore. One myth I wish that would be dispelled is that Singapore is for mathy kids. My dd is so not mathy and it has been a HUGE help to her for which I am thankful.

[Carrie]

Edwena,

Thanks so much for your reply! One thing you could consider is letting your daughter use her fingers for subtracting for now, because if she's a visual learner it may really help her for a time. Since she is 8, it isn't out of the question for her to still be using her fingers, as we still used manipulatives in third grade for kiddos who needed them. We actually even used manipulatives into 4th grade with very visual kiddos. The goal is to eventually transfer away from this method.

So, I think it is reasonable to allow her to use her fingers as needed through 3rd - 4th grade. At that point, if she hasn't transitioned away from this method for adding/subtracting, then it is time to get out the flashcards and just get her facts down pat.

I used to be a teacher who thought that addition/subtraction facts should be memorized by 1st/2nd grade and multiplication facts had to be memorized in 3rd grade. The more years I taught, I realized that memorization does not equate to understanding, and understanding what you are memorizing really helps! So now, I don't rush my kiddos, and I have been pleasantly surprised to see how much they internalize simply due to need. This makes my job easier overall! If you do wish to work on facts, then summer is a great time to work on memorization of facts. Good old flashcards are still my favorite method, working on the 0's first, then the 1's, and so on. I usually only make sure kiddos memorize their addition facts, as the addition facts transfer to subtraction. The same is true for multiplication facts, as the multiplication facts transfer to division.

Blessings,
Carrie

[Sharon]

One thing that worked for my dd to make the connection between multiplication and division fact families was triangle math fact cards.
We would build with manipulatives the multipication fact and then show the divison fact that went down each side of the triangle card to show the relation to division. DD kept a little math notebook that she would write the fact family in and sometimes she would draw pics to go with the fact family. Then we just used the triangle cards for drilling multiplication and division facts together.

[John'smom]

Carrie,
I appreciate your being honest with your opinion. Can you tell counting on fingers scares me? Even if I don't go that route, your second post really was a help to me. Maybe dd is normal. She is so different from ds when it comes to math. To be honest at times I think she has some kind of math disability. So if you're seen kiddos that still need manipulatives at this age maybe she isn't abnormal.

I would be drilling facts now except that I know she HATES it. It isn't because she's lazy, but I know it makes her feel frustrated that she hasn't got ____ (fill in the blank) memorized yet. I can see the stress on her physically when using flash cards.

She has a good deal memorized (most actually). The funny thing is the ones she seems to struggle with contain 8's and 9's. There are times that she can say 8+6=14 and other times it is like it has vanished out of her head. She freezes up and then can't remember to make tens. I don't know how many times I've said make tens, make tens, make tens.

Do you think this is normal? To me it isn't but I've not seen all the children you have.

We will keep plugging away and I have to remember to take it by the week rather than dwelling on how the day went. I know backwards from what we're usually told. If I dwell on how she's doing one day, I could lose my mind, but if I dwell on how far she's come since starting Singapore this last summer, then I would rejoice.

[my3sons]

I don't think your dd sounds off the norm at all! Unless my dc were too. Our older dc were both late to know their facts, both addition/subtraction and multiplication/division. The wonderful thing now though is they never miss them. They truly KNOW them. It is more number sense than memorization, which is why using objects or counting on fingers is fine. It signifies a number's worth. I don't know how many times our dc used a number line, fingers, or manipulatives to count up. I taught them to start with the bigger number and count up from there. Eventually, they just gave it up on their own. They could visualize it without the objects or fingers, and they just knew the answers. At the end of 3B, Riley knows all his facts well. I don't think he would have really known them any more solidly any more quickly if I'd drilled and drilled him because I tried that route with Wyatt, and he still really knew them 100% by the end of 3B. I think the point of skip counting is that they are just saying it over and over again. That repetition helps them with number sense, seeing how it goes up 'x' amount each time they count, as opposed to cold turkey memorizing flashcards that often times have little number sense associated with them. However, if at the end of 3B, you find there are some facts dc don't know, this is a good time to get flashcards and work on just those tricky ones.

Here are a few links that fit with this topic that may be helpful...
viewtopic.php?f=6&t=3777

Informal tips we use with our kids for memorizing facts...
viewtopic.php?f=6&t=12850&p=92565

In Christ,
Julie

[Mommamo]

Do you have an iphone/ipad/nook/etc? I have a nook tablet for me, but we use it a lot during school time, and my kids practice their basic math facts on it using two apps: Whack-a-math-fact (like whack-a mole, but they have to hit the right answer) and Math blaster (a space game where you have to shoot the right answer). My oldest is in 4A and is pretty solid on her math facts, but this is helping my little ones learn theirs. So you might look at games like that instead of flash cards if you are really wanting her to practice her facts.

[mom23]

If you decide to use flash cards, consider using a very gentle approach. Don't try to drill the whole stack every day. You might even start with only 2 or 3 cards the first day-like 1x1 and 1/1 and you could add the 1x0 also. The next day add in the next logical fact family 1x2; 2x1 and 2/1 or 2/2. When she's very comfortable with those (after a few weeks of seeing them daily) file them in a spot to use once a week (Label your dividers M-F). When your using more difficult problems only add new cards once a week and drill just a few every day, as well as a stack of very comfortable cards that she sees once a week.

I do completely agree with what the others are saying about understanding the way math works being way more important than memorizing facts, but I'm also a believer that knowing the facts really helps make math easier. I don't see anything wrong with drilling very easy facts while you're teaching her the concept of how multiplication and division work. Once you get to the later/harder problems she'll hopefully have gotten familiar with what multiplication is used for and what it means. For a child who is not particularly math minded, though, I've seen it really add to the frustration that everytime they see 8+6 they have to stop and count the answer. It makes math take 4 times longer than it needs to and every simple problem really boggs them down. Facts have helped our kids.