Math: if a kid isn't "getting" something

[chilliepepper]

I have both of my guys, grades 3 and 4, working on Beast Academy 3. For my 4th grader, it's about right---challenging enough but not hopelessly difficult. The same is mostly true for my 3rd grader, but occasionally we run into something that he just doesn't "get." For example, there were some aspects of the distributive property in 3B that got very difficult for him---we muddled through the exercises, but he needed a lot of guidance and explanation from me and even after that, I don't think he mastered the concept. But we got through, and moved on.

 

For division, likewise...we have completed the first section of long division practice in 3C, p. 48-49, but I really don't think he understands why we put the various numbers where they go in a long division problem. For example he wants to put the remainder up in the quotient area and add it to the quotient in the same way that the material tells you to add each multiple of the divisor. I tried to explain to him why that would give us an incorrect result, but his eyes were glazing over. He didn't get it.

 

Granted, there are still quite a few pages in the Division chapter, so maybe this will be revisited as we go along...BA is pretty good about approaching concepts from multiple angles so that if you don't understand it one way, another approach is presented that might work better.

 

I'm just wondering, though...should we camp out longer on this part of long division, with me making up new exercises? Maybe reread the section in the guide and stay where we are until he gets it? Or, should we move on and trust that it will be revisited later and maybe he'll get it then?

 

I do wish there was BA for grade 2---it probably would have been better for him this year. It also leaves me wondering if continuing with BA 4 next year will be best for him...or should we take a break from it, doing an easier 4th grade curriculum (suggestions? I own Saxon 5/4) next year and then coming back to Beast 4 when he's in 5th grade. It's just that my guys really do enjoy the style of Beast, so going back to something more traditional/conventional might be received poorly. Math Mammoth, for example, practically killed both of my sons---as much as I wanted them to love it. I wish we could repeat BA 3 next year without him knowing we were repeating it.

 

So I guess that's 2 questions. One short term (camp out on the current concept with additional exercises, or move on), and one long term (what to do next year, graduate to Beast 4 or do a less challenging 4th grade curriculum). Thanks!

[deerforest]

Well, I might be the wrong person to ask because I've never just used a single math curriculum. We loved BA, and we used it as our primary curriculum, but we often outpaced it or sometimes needed additional reinforcement. So, I used anything I could find, other curricula, videos, games, manipulatives, living math books, etc., to help supplement, reinforce or deepen understanding. 

 

Those two topics can be tough for some kids to get so I don't think it means that you should switch curriculum, and those concepts will come up again--rest assured! I know division is back in 4B, and although I can't recall if they explicitly teach distributive property again, they definitely use it in the problem sets later on too.

 

My first stop (ever since she created the site) has always been to check out educationunboxed.com and I'm certain that she covers both division and the distributive property.

 

(DD is a strong math student though not as gifted as many kids in this area. She's completing pre-algebra in 6th. Just sharing so you have a point of reference as we have used this crazy approach to math throughout her learning.)

[OlgaLA]

My son is in the division section of BA3C right now. He also didn't quite get it after the 2 pages BA spent on long division. I went to the math fact cafe site and printed a few sheets of long division problems. We went through a few, with explanations in all possible ways I could come up with, then he also watched some videos on Khan academy (I suspect that part was entirely to watch that and then quietly continue with programming videos, but that is another story :) ). I think he gets it now, so we moved on with BA. I am planning to give him a few long division problems every few days until I am sure he is solid with it.

[Miss Tick]

Beast Academy is not going to come back with a "quick review" at any point, like many math programs do. I think you are right not to lose track of topics that you don't think he has really got.

 

You have a few options, though. You could supplement as you have, with similar problems, download "Pizzazz Book A Middle School Math" which has a short section on each of those topics, or get more serious supplement including detailed instruction from Math Mammoth. In any case, you can keep going with BA working on different sections.

 

Next year is so far away! Plus, learning is so non-linear. My ds alternates between an abridged MEP and BA, dd uses MM. Tere are so may choices, many of which will go on sale in July or August (although MEP is always free).

[blue plaid]

In general, when my kids aren't getting something after many attempts/angles are presented, I change topics entirely for a bit and come back to it later.  I think my inclination for division and the distributive property would be to revisit it later this school year if at all possible rather than just waiting to see it again in 4th since those are such foundational concepts, but YMMV.  

 

We've jumped around a bit with math but I feel like this year we are settling in to a BA/Math Mammoth combo.  I will say that my 5th grader (who did some of BA in 3rd and 4th grade) who is doing BA 4C and 4D now (along with MM5) seems to be having a smoother go with BA than when doing it strictly on level.  My 4th grader is finishing 4B now (along with MM4) so probably  for him at least 4D may drag into 5th grade as well.  I really love BA and the way it presents concepts and definitely want my kids to be exposed to it, often as a first exposure to certain topics (long division for example!)  But for us I really feel that BA alone is not enough; my kids just need a little more review/straight forward math for the concepts to stick.  My kids are good at math, but they are not crazy good (i.e. after one exposure they won't remember things for all time.)  So I guess for your second question, I would recommend considering throwing another curriculum in the mix, which could give you more flexibility (or at least make you feel more flexible!) for the timing of BA.  Just a thought!

[wendyroo]

I think the beauty of BA (and Singapore and MM) is that it is conceptual, so I don't move on from a topic if DS doesn't really understand it, even if he can chug through the algorithm by rote.  Sometimes we will leave a topic and work in MM for a while before coming back, but other times I set aside all curricula and just have DS grapple with the topic for a few days.

 

The other day I was dying rice for the sensory tub.  I had 15 lbs of rice and I wanted to dye it 6 colors.  DS has certainly not reached a point that he has an algorithm for long division with decimals, but I like introducing concepts before anyone tells him how to do them.  I put out a big piece of roll paper and a bunch of gel pens and wrote in big text at the top "15 pounds of rice divided into 6 bowls.  How many pounds in each bowl?"  Then I walked away.  Fifteen minutes later I brought out the scale "so we can see if the math works".

 

Half an hour later the paper was covered with shapes and numbers and arrows and DS had the right answer.  More importantly, he had experienced first hand how long division actually works.  I like to use real life problems such as this to lead into covering topics...sometimes topics that we won't officially cover for a long time.  A few weeks ago DS puzzled out how much tax he would have to pay if he bought a $13 lego set.  Another day we took four of his brother's train cars and DS figured out in how many different orders he could hook them up.

 

If it were me, I wouldn't primarily worry about if your son can plug and chug long division problems, but I would not move on until he could thoroughly explain how he would evenly split 952 books onto 8 bookshelves...without using the algorithm.

 

Wendy

[zarabellesmom]

Having worked through all the BA there is so far (though that doesn't make me an expert by any means), I agree that I wouldn't move on without understanding how to do long division. Beast continues to use it over and over and over again as you continue on. As for the distributive property, meh. (Not that I don't think the distributive property is important because it obviously is, but they don't use it again in Beast for awhile--5A--and when they do, they refer you back to the original coverage for a review.) By the time you get around to the distributive property again, he may be more receptive. I don't think there's any way around the division. I'd just hang out there until he gets it. Or, maybe step away from Beast for awhile and do some other math review like clocks, money...I don't know...just something totally different for a week to let his brain rest and then give it another shot.

[pamela722]

I've not used BA but have had similar issues. My children are in grades 2 and 6 and whenever either of them has hit a roadblock, I go back to the beginning of the topic and start over with it. However, I keep it very light. I might print off a worksheet that covers the topic and only have them do the top row and then try and find a fun way to incorporate the learning. That would be the lesson and then move on to the next subject. I will do this a few days and then see if we can go back to our math book. 

 

I just went through this with my dd. She just wasn't understanding word problems and the key concepts of them along with basic counting on in 1's, 5's, 10's, 100's. She could count on from what she learned while at school but struggled with number patterns over 100. So I found sheets with varying word problems and would have her complete just a few of them and then fill in a 100's chart working on one the areas she needs help in. It actually took nearly 2 months to get her past the issues but now she is full steam ahead and 100% happy. We may be behind by 2 in her workbook but we are really miles ahead in learning math and will do this whenever they need help. I'm all for going backwards when needed. 

[chilliepepper]

Ok, here's a little update: on advice from several contributors here, we spent some time today going over the concept. We worked through several made-up examples together, and though I think he now understands the PROCESS better, he still gets stuck on WHY we put numbers where we put them and WHY we subtract things at the bottom, etc.---despite my repeated explanations. I think I will also look it up in Math Mammoth (which incidentally, IIRC, doesn't really present long division until 4th grade, or if it does come up in 3rd it's at a very basic level) and give him some problems from that, and check out some of the links folks have suggested above. So thanks!

 

After that, I believe we will move on. I know division WILL get revisited, so whenever it comes around I can try again to add layers of understanding.

[BooksandBoys]

Ok, here's a little update: on advice from several contributors here, we spent some time today going over the concept. We worked through several made-up examples together, and though I think he now understands the PROCESS better, he still gets stuck on WHY we put numbers where we put them and WHY we subtract things at the bottom, etc.---despite my repeated explanations. I think I will also look it up in Math Mammoth (which incidentally, IIRC, doesn't really present long division until 4th grade, or if it does come up in 3rd it's at a very basic level) and give him some problems from that, and check out some of the links folks have suggested above. So thanks!

 

After that, I believe we will move on. I know division WILL get revisited, so whenever it comes around I can try again to add layers of understanding.

Here's an example of how the conversation would go when I teach the algorithm of long division (algorithm taught after child understood conceptual division, and with a kid who has a firm grasp of place value, otherwise, we back up and do those):

 

Ok, we have 825 gummy bears in a big bowl, and we want to make bags of 5 gummy bears. So, 825/5.

 

We start with the hundreds place. Can we make 100 bags of 5 gummies each of we have 825 gummies? How many gummies would we need to make 100 bags? 5*100, so 500. Do we have enough?

 

Yes?

 

Ok, so we need to write down how many hundreds of bags we made (1) in the hundreds place.

 

Now...do you remember how many bags we just made? 100? And how many gummies we used up to make those 100 bags? 500? Awesome. So, now, how many gummies do we have left in our bowl? 825-500. And we write that down here...then subtract...we have 325 gummies left. We have to write it down, otherwise, we might forget we took the gummies out of the bowl and try to use them again!

 

Now for the tens place. Can we make 10 bags of 5 gummies each? How many gummies would we use up? 50. But we have 325 left. How many sets of 10 bags can we make out of 325 gummies? 5 gummies in 10 bags times 6 tens equals 300 gummies and 60 bags.

 

So, we write how many tens of bags we made...6, then, remember, we have to subtract the number of gummies that we took out if the bowl to put in the bags. 6 tens of bags is 60 bags times 5 gummies equals 300. 325-300=25,

 

25 gummies left. This is the ones place. How many single bags of 5 gummies can we make with 25 gummies?.

 

5. We used up 5*5=25 gummies, and now our bowl is empty.

 

So, how many bags did we make? 165,

 

 

Then, repeat as naseum with different numbers until it clicks. I find it helps kids to picture the bowl of gummies getting emptier and the bags being created (we'be done this with manipulatives when teaching it conceptually, so I rarely use manipulatives with the algorithm...just the story...but I do l break them out if necessary.).

 

My own kid liked to imagine passels of puppies instead of bags of gummies, but he's an odd one.

[BooksandBoys]

As for sticking with something or moving on, I tend to do a combination of the two. I slow WAY down with the hard concept (long division), doing only 1-2 problems a day, while allowing them (I'm a math tutor too, so not just my kid here) to move forward with another, easier, concept (like time, money, or measurement). Singapore, Miquon, Math Mammoth and others lend themselves well to this. I only have BA 3A, so I can't speak to how all that would work with BA, but I think you could make it happen.

[chilliepepper]

Here's an example of how the conversation would go when I teach the algorithm of long division (algorithm taught after child understood conceptual division, and with a kid who has a firm grasp of place value, otherwise, we back up and do those):

 

Ok, we have 825 gummy bears in a big bowl, and we want to make bags of 5 gummy bears. So, 825/5.

 

...

 

Yeah, that's pretty much what I did. He got so he would say that he understood, but if I asked him to explain WHY we were subtracting the number of kids that we just put onto the school buses or the number of beads we just put on the necklaces for friends at his birthday party or the number of books we just put onto the bookshelves, he would say "I just can't explain it" even though he just listened to me explain it complete with illustrations. I'll keep trying with different examples---I like your example with dummies in a bowl, because we haven't yet did an example where we had to take things OUT of one thing to put them into another. Maybe that will help it click. :)

 

(FWIW, BA's initial presentation of long division doesn't go into place value. It just has you guess the quotient, and as long as it doesn't cause you to go over the dividend when you multiply it by the divisor, you just keep adding to the quotient, multiplying what you just added by the divisor, and subtracting the result from the dividend until you are left with a remainder that is smaller than the divisor. I tend to favor the place value method, but for now I'm just going along with the way BA is presenting it. I haven't read ahead to see if/when it moves on to the place value method.)