Skip Counting

[happynurse]

How far does a child need to be able to skip count in 2nd/3rd grade? This may seem like a dumb question, but as someone who never learned to skip count a day in her life, I'm learning this along side my 7 year old son. :) The skip counting songs we've memorized take us up to 39 with the 3s, and 40 with 4s. (He's got 2s, 5s, 10s, & 100s, etc. down pat.) I'm curious if I should take it a little farther? FWIW, we're using Horizons Math 2 with success (finally found something that doesn't make him shut down) and he's doing really well with it.  I don't see anywhere in my TM that encourages me to skip count any further than what we're doing. Maybe that'll come later? Is it not necessary? Genuinely curious. Thanks!

[happynurse]

8 minutes ago, CuriousMomof3 said:

How did you learn to tell time on an analog clock or count money without skip counting?
  

 

Good question. I never had a problem skip counting 2s, 5s, 10s, 20s, 100s, etc. But 3s, 4s, 6s, 7s, 8s, 9s? Nope. At least not as far as I can recall. I will say that I thought I was HORRIBLE in math all through school until sometime in late high school. I remember just flat out giving up in 2nd grade because of what we called "Timed Tests" (timed math speed drills). I had the worst anxiety over those tests, because I couldn't do them as quickly as I thought I should have (perfectionist here). And after that I just decided I was bad at math and didn't really put in any effort.  I nearly failed math in 7th grade. 

Fast forward a little bit. I went to college at a large university with good quality teachers. As it turns out, I wasn't bad at math at all. I wasn't necessarily a math whiz, but I certainly had become competent. Clear back in second grade, my anxiety took root and I just believed that I couldn't do math. That is why I don't 'time' my kids on drills. I just remember it as being so traumatic! 

I managed to graduate from a rigorous nursing program at said university, without missing a SINGLE math problem on our nursing school math tests. We had to pass our math tests with 100% or we failed and had to retake it (which we could only do twice). So with time, maturity, and desire I became good at something that I never thought I was good at. (No thanks to my public school experience.) That personal experience is one of the many reasons I homeschool in the first place. :)

[sweet2ndchance]

16 minutes ago, happynurse said:

That is why I don't 'time' my kids on drills.

Same here. I have never and will never give timed math drills. I will say that my mathy kids liked timing themselves and then try to beat their own time but I've never given my kids say 2 minutes to try and finish a certain number of problems. I'm more concerned with accuracy than speed. In my opinion, speed will come with practice and speed should not compromise accuracy. I would rather my cpa or banker be slow and accurate rather than fast but prone to mistakes, kwim? Of course, if they are fast and accurate, I would assume they have a lot of experience and that is great but if I have to choose fast or accurate, I will always choose the latter.

On the topic of skip counting, I think it depends on your goals for skip counting and how you are implementing it. If you are just memorizing a rote series of numbers or songs, I don't see much use in it. We learn to skip count to see the patterns. We look at a number line or hundreds chart and notice the patterns such as how counting by fours is every other number counted by twos and 5s and 10s are the same way. We see that every number counted by twos ends in an even numbers. We look to see what numbers coincide like how if you count by any even number between 0 and 10, they all eventually land together on 120. We look at how skip counting, multiplication and division are related. If you are just memorizing a song or a series of numbers by rote, it could be helpful I guess but if you aren't looking at the patterns and the how and why skip counting works like it does, it's just another piece of memory work, in my opinion. You aren't using the skill of skip counting to its full potential.

My youngest son is actually working on skip counting relationships right now. He's 7 and in first grade this year but he works at a late second grade level in math. We are just starting to take on multiplication so skip counting is a good way to ease into it. He loves seeing how many skip counts it takes to get to X number or whether you can even get to that number by skip counting (i.e. can you skip count by 5s and get to 88?). I haven't made him memorize the skip counts but he can skip count by any number as high as he wants to go because we look at the pattern each different skip count takes and he can extend that pattern out indefinitely. We've gone up into the thousands just skip counting for fun on long car rides. We each take turns counting up by whatever number we choose. So I would say "2", ds would say "4", dh would say "6" I would say "8" ds would say "10"etc and we just keep going to see how high we can go or how long it takes us to get to a certain number like 800 or something like that. It passes the time and works his math and logical thinking skills.

[sweet2ndchance]

1 hour ago, square_25 said:

 

Well, I can't speak for others, but I taught my daughter to tell time after she could multiply, and I just told her the time intervals between numbers were 5 minutes, and she figured out to multiply by 5. 

 

Just saying, I really don't think waiting to teach telling time until after they have learned multiplication is a very common approach. Skip counting by fives isn't hard for most kindergartners and one of the most practical applications for counting by 5s is telling time (with the other being counting coins) but not all kindergartners are ready to wrap their heads around the concept of multiplication in my experience. Some average to advanced kindergartners could probably understand multiplication as repeated addition but almost every kindergartner I've come across could understand skip counting by 5s without problem even if they don't quite understand yet that it is more or less the same thing as repeated addition.

Not all kids, even ones who know how to multiply at any age, could connect the dots and realize that they could multiply the number on the clock by 5 to figure out the minutes. I would say most kids at the very least would need to be lead to that conclusion, if not explicitly told. I've tutored college students who sadly could not have come to the same conclusion your daughter did on their own. Your daughter is very bright and math intuitive just based on what you have posted about her around here. Not all students have that advantage in their back pocket.

[blue plaid]

For one of my kids, knowing how to skip count has seemed to be a big disincentive to memorizing multiplication facts. Ugh.

[sweet2ndchance]

11 minutes ago, square_25 said:

I made sure they simply seemed like generalization of counting (which is something kids understand very well.)

I think the parenthetical is a broad generalization. Not all kids understand simple counting by ones very well when they enter kindergarten or even first grade, even if they can count by rote well beyond 10. I think pretty much all your students have had an advantage of environment, intelligence or both.

I can't remember where I first saw this example but it was talking about math remediation for young kids and it discussed asking a 5yo or so girl who struggled with math concepts to identify which set of circles had more. She had two sets of paper circles about the size of quarters in front of her. The top line had 5 paper circles all lined up touching edge to edge. The bottom line of circles were spaced out with about a 1/2 inch between them so that even though it only had 4 circles, the line of paper circles seemed longer than the top line of circles because of the spacing. The 5yo girl identified the bottom line as having more. When asked why, she said because it was longer than the top row. I have seen many children come to that conclusion or similar conclusions. They may be smart kids but just weren't taught the concept of counting and numbers in a way that made sense to them so they made their own, albeit faulty, conclusions. If you are lucky, it just takes a couple of remediation sessions to get them on the right track. Worst case scenario, you discover after several sessions that the child's math issues run much deeper than a simple misconception and you need to start looking into possible learning disabilities. 

 

34 minutes ago, square_25 said:

I think if you have a very good understanding of what multiplication is (which is repeated addition), it becomes clear that to get the number of minutes is equal to the number the minute hand is pointing to times 5.

Like I said, I had college students (yes plural and many of them education majors *facepalm*) who could not come to that conclusion on their own. They could rattle off several different ways of thinking about multiplication and could do simple to semi-complex (at least middle school level) multiplication problems that "didn't involve any letters" (their words for variables) without problem. But they either would not or could not synthesize that information into a new application such as how does multiplication help you tell time. Is it inflexible thinking? Is it lazyness? Is it a failure of true understanding? Is it stage fright from mathphobia? Well, yes on the surface it appears that it could be any or all those things. But it just goes to show you cannot make any assumptions about what a student can or cannot derive from your instruction.  The answer is not to spoon feed them or treat them as intellectually inferior (think Sheldon Cooper trying to teach first grade math to a bunch of average first graders), you just cannot assume that anything will become clear to all students just because you taught the basic concept that underlies the usage situation. Some kids just do not make conceptual leaps like that even if they are bright kids overall. And there will always be kids that need explicit instruction for every little thing because assuming they will be able to apply anything they have learned outside of what you have explicitly taught is folly.

 

14 minutes ago, CuriousMomof3 said:

I think some kids can hear that a * b is a copies of b, and run with it, and some will need more structure, but the kids who will be able to run with it will be building on other experiences that require them to make multiple groups the same.  To me, good instruction in multiplication starts years before you introduce the multiplication sign and formal vocabulary.  It's things like helping to serve cookies with 2 on each plate, or counting your money in monopoly (both of typical kids were way into monopoly at around age 6, and learned a ton that way) or figuring out how many short bricks you need to finish your lego wall when you ran out of long ones, and skip counting comes up pretty naturally in all those contexts.  So, while I can absolutely see teaching multiplication without using the "skip count on your fingers" strategy, I feel like skip counting experiences are what builds the foundation for it.  

I absolutely agree. Many kids can multiply long before you call it multiplication. But that doesn't mean that they all can. Some kids really do need literally years of exposure to a topic before they can really internalize it. I tried introducing the idea of multiplication to my bright mathy ds about this time last year. He could tell you that if you had 2 cookies on each plate and you had 3 plates then you have 6 cookies. It certainly sounded like he was ready for the next step up from addition. But he wasn't. He didn't get it when I explained about repeated addition being another operation called multiplication we could play around with. So I waited and tried again this year. He now thinks much more abstractly. He doesn't need the cookies and plates anymore to see the relationship. He can say with ease, "well I need 9 things because three 3s is 9" and other such things. He needed a little more time to cook the idea in his head before he was ready to grapple with the idea of multiplication.

I also agree that the wording "a copies of b" is a pretty abstract idea for early elementary kids. Even if you show it to them as plates of cookies or math blocks, there are going to be more than a few kids with the deer in the headlights look. And there is no guarantee whatsoever that any of them can take that idea and synthesis it for use in new situations even if they understood the concept and could apply it during your instruction. Square_25's dd is a very abstract thinker and able to synthesize information effortlessly it seems, which is great for her, but she is no where near the norm for an elementary school child. She is quite lucky that she can be homeschooled because I doubt even gifted programs could keep her challenged and not bored just from some of the examples of her explanations of concepts that have been given.

To be clear, I don't think that skip counting is a vital, "not-to-be-missed" part of early elementary math education. It is a tool that has many possible uses but it is not the ultimate or only way to teach the essential topics of early math education. But I definitely think that for some kids, it can be the key that gives them the "aha!" moment of understanding for some topics which is why so many math programs include skip counting exercises. I absolutely agree with you @square_25 that rote memorization of skip counting number series' does children just about as much good as memorizing their phone number to learn how to subtract. If the skill of skip counting is learned in isolation of other math skills, it is just pointless memorizing that hopes the child can draw the connections themselves correctly. And as I said above, you just cannot count on all children or even adults to make those connections correctly every time.

[Clemsondana]

I taught my kids to count by 2s, 5s, and 10s when they were little.  I don't know that I had a goal in mind - it was mostly another thing to 'sing' as we got ready for bed.  I think it helped when they started multiplication, as did looking at the number grid with the numbers all written out with 10 in each line so that they could see patterns.  I don't know how my older learned to remember multiplication facts - he's the one that seemed to absorb math from the air - but with my younger, it was a combination of skip counting, being able to take numbers apart, and memorizing (flash cards).  She could skip-count the 'easy ones'  - 2, 5, 10, and I think 3 and 4.  She would also break down the numbers so that she could say 3x5 + 6 is 3x6, or 4x10 - 8 is 4x8.  Once she understood it, we used flash cards to get faster (and also the mental math was ore painful for bigger numbers - she understodd, but was more likely to make a mistake, with 6x10 - 12 is 6x8).  

That being said, skip counting is a huge advantage for kids who can't add mentally.  Some of the kids that I volunteer with know their multiplication facts.  Some understand that if you know your 2s, 5s, and 10s (which are easy, although they may skip count to remember them) then you can add or subtract to find the others.  This is time consuming, but it works.  There are others who solve by repeat addition. This is fine, except that for repeat addition they are either counting  (1,2,3,4,5,6) instead of adding 3+3=6.  That's how they add, so that's how they repeat add.  Since they are using their fingers to do the adding, they don't have another set of fingers to keep up with how many they added, so they'll get to 12 or so and then ask how many 3s they've added.  Or they draw the dreaded 7 sets of 3 and then count them all.  An argument could be made that these kids aren't ready to multiply, but then again, the problem isn't the concept, and at any rate the syllabus waits for no student. For these kids, singing the skip-count song would be a tremendous improvement.  

Among the kids I do math with, there seem to be 3 kinds (I'd assume this applies to many things other than math).  There are the kids who absorb it from the air - the 'natural athletes' of math who need a few rules and are off and running.  Then there are the vast majority of kids who need to be taught and do some practice. They'll need varying amounts of instruction and practice and learn with varying levels of ease.  Different students may do better with different approaches, but they will all 'get it' for most concepts in a reasonable amount of time.  Then there are the kids for which I take a 'whatever works' approach.  If we had enough time, and maybe more individualized instruction, maybe they could develop true facility with numbers.  But, with many schools barreling on towards the required skills and later sequence, there isn't time.  There was one boy that I worked with, and eventually after I talked to the new director at the after school program found a math specialist to help him (he was probably 9 by then), who didn't understand 2 digit plus 2 digit addition for 2-3 years.  I would help with whatever homework that he had, knowing that he had no comprehension at all as he did subtraction and multiplication.  He had sort of given up and was just guessing.  I'd grab him any time I was there and he was free and we'd just do addition.  Eventually he started to understand it.  It probably could have happened earlier if we'd just been able to focus on adding.  But, the schools are not going to dedicate 2 years for adding, then 2 for subtracting, etc, if that's what a kid needs, even if that's what would be best.  This kid understands the concepts of multiplying and repeat addition, but I can't imagine how long he might need to understand assembling and disassembling numbers.  Memorizing times tables and skip counting (he's done both) are what has worked.  Honestly, with this sweet kiddo, who used to throw tantrums of frustration over math, when I see him smile because he can tell me how to do a math problem and all I have to check for is careless mistakes, I want to weep with joy.  Behind with less than ideal techniques is better for him than completely stuck.  

[Shoes+Ships+SealingWax]

16 hours ago, blue plaid said:

For one of my kids, knowing how to skip count has seemed to be a big disincentive to memorizing multiplication facts. Ugh.

Beast Academy does an awesome job with this issue. At the end of a chapter on skip-counting it presents several scenarios in which having to count that way is obnoxious... then presents multiplication as a much simpler short-cut 😉 Lol

[Sarah0000]

Neither of my kids skip count. They also don't like to sing, especially on command. While looking at an analog clock at five and six years old they just make tens such as nine 5's is 8/2 tens plus one 5. They visually match up the tens. Since we start basic multiplication with small numbers and tens at four years old it hasn't been a problem to ditch skip counting. Admittedly, my oldest is a math whiz but my middle doesn't seem to be.