Question about math concept for 1st grader (X-2=3)

[pehp]

My son is working through the Miquon Orange book.  Today he did a bunch of review problems (addition, some subtraction, multiplication) and nailed them all.  THEN on the other side of the sheet he got several problems wrong and they were all involving the same thing: solving for x when x minus something equals something.  So for instance, one problem was x-2=3.  His answer to x was 1.  Of course this comes from the fact that he was somehow turning this into 3-2=1.  If I give him 5-x=3 he will get it.  If I give him 5-2=x he will definitely get that.  But somehow it is very hard for him to grasp the concept of solving for x when x is the 'largest' number in this equation.

 

I stopped everything and worked with him a bit.  I hesitate to say "you are trying to find the LARGER" number because he understands at least the concept of negative numbers, and you *can* subtract a large number from a small number if you wind up with a negative! So I am trying to call the first number in the subtraction equation the "whole" number--and we have the parts, we just have to find the whole. I demonstrated how this is basically the reverse function of adding.  He gets it--sort of vaguely.  He seems to kind-of-sort-of-grasp it, but I stopped working on it before math fatigue set in because I try to be sensitive to his needs.

 

(ETA: I also drew a number line and we used that to try to visualize the concept and solve the problems. It maybe helped??)

 

We'll work on it again in the morning.

 

But in the meantime: is there a better way to teach this specific type of problem? 

[ondreeuh]

We approached it with the same language you are using: with subtraction, you start with the total. You take away one part and find the other part.

 

So I would read the question to him: what is the amount you are starting with if you take away 2 and still have 3? Or - what number can be split into a group of 2 and a group of 3?

 

You could put a 2-rod and a 3-rod in your closed hand, take out the 2-rod, then open your hand to show the 3-rod. Putting both parts together shows how many you had at the start.

 

I think the semantics of that type of problem are a bit abstract for 6. Even kids who understand that subtractions is "taking away" may have a lot of trouble with that format. Do what you can to translate it to something more concrete or understandable, but otherwise just put a post-it on that page and come back to it later.

[Gil]

I would do a few of those triangle fact-family type exercises right before we did a few more of those equations.

Buddy struggled with this same concept when we did it a couple of years ago, but then I started giving him a few hand-made fact-family sheets that used the same numbers he would be seeing in his equations. It got a lot easier and after a couple of days, he had it.

 

Like doing number-fact math drills, doing drills that reminded him of the relationship between the numbers really helped him. He knew that 3,2,5 all went together with + and -, so if he saw x-3=2 he would try to find the 'missing piece' of the puzzle.

 

You can also use a "whole-parts" box to arrange the equation visually. Thats what helped Pal, but Pal had a much easier time with equations than Buddy. He got it in one sitting.

 

[silver]

I started by using an unlabeled number line. So for ?-3=5 I would say, "We start at a mystery number, subtract 3," (hop back three), "and we wind up at 5." (label the ending spot as 5) "What number did we start at?"

 

Using rods, you can take three rods that belong to a fact family and lay them out to show the family. Ask him to name some addition and subtractions that those rods in that setup demonstrate. Then lay out a rod fact family with one of the short ones missing and ask for the additions and subtractions. Finally lay some out with the longest rod missing and ask for the additions and subtractions. For doing this, it was easiest for my son if he had some pieces of paper with the numbers, a question mark, and the addition, subtraction, and equal signs. Then he could slide them around the table to figure it out.

 

Another rod example would be to demonstrate straight subtraction with the rods. After doing a few of those ask "what number" (draw your finger across the table to indicate a missing rod) "minus 4" (place down the four right next to where your imaginary rod was drawn) "equals 3" (place the three in line with the four). If that doesn't click, run your finger along the total length of the 4+3 and ask "what number did we start with here?"

 

Those are the different strategies I used with my son when we started covering that type of problem.

[El...]

We're using Miquon too, and those were tough!  Three things that seemed to help my kid were, first, saying "Read it aloud to me," over and over; second, always using the rods (no visualizing); and third, adding an easier level of Singapore on other days to slow her down.  We are finishing Singapore 1A and halfway through the Miquon red book, so every other day she has to think harder.

 

Another thing: the hardest part of teaching math, for me, is NOT helping her.  I have to be silent while she thinks.  At most, I ask leading questions.  She has to figure it out for herself or she does not understand it independently.  It does come together!  I'm so proud of her math work!

[Amy M]

I think that would be pretty hard for my 6 year old. I like how Singapore explains with the circles around the numbers, putting them into a kind of H2O model, with the answer in a circle on one side, and the 2 parts in circles attached to lines coming off of it. So you could show that you have the answer and are looking for a missing part. But I'm still not sure how helpful that is at helping him to realize that he has to go up to find the answer.

[RootAnn]

I have to say that on this one, a non-Miquon approach always got through to my kids. I had a box where I would put whatever the total # of counters was (5). I would tell them I had a mystery number of teddy bears / dinosaurs in there. Then, I would have them take out some (2) of them. They'd put their (2) counters where they could see them, and I'd show them how many were left in the box (3). It was a game to see if they could figure out how many we'd started with -- the "mystery." After playing this with small numbers we'd already used for addition, they could tell me immediately how many we'd started with.

[Tanikit]

I would definitely teach this in a hands on way - like RootAnn's suggestion.

 

He needs to know SOMETHING (x) take away the number(eg 2) will leave you with the number after the equals sign (eg 3). This is partly a vocabulary issue and not a mathematical issue - those figures are ALWAYS abstract and they need to be seen and understood. Make sure he does understand larger and smaller numbers and also that taking away or subtracting means that a big number must get smaller. (At least for now - number lines are better if you want this set up for doing negative integers later).

[nerdybird]

Here is alternative to all of the hands on suggestions. My oldest was and still terrible with anything hands on. Whenever we encountered problems such as:

 

X - 4 = 6

 

I would have him do this:

 

X - 4 = 6

   +4  +4

    X = 10

 

Straightforward, no muss, no fuss. It took me a long time to realize that not every operation needs to be visualized in order for a child to understand it. Also, I think that teaching solving-for-X type problems like this from the get-go simplifies things down the line when it comes time to start teach fractions, ratios, proportions, and multiple step equations. Fewer things to unlearn, less confusion over isolating variables, etc.

 

Plus I find this method much more intuitive. It worked for us, fwiw. It seems to me as if the OP's son might be seeing the problem like this:

 

X - 4 = 6

6 - 4 = 2

X = 2 (wrong answer!)

 

This indicates that he is attempting to use the number line in a logical way. For example, 6 is the largest number on the number line, so he reasons that 6 must come first before the 4 in order to get a positive answer. Technically, this makes sense. However, it produces the wrong answer. The rational approach to the problem is one that takes his understanding of how the number line works into account. Visualizing the addition of 4 + 6 will be easy for him, imo. And it will give him the right answer that he can then plug into the original problem.

 

[Ellie]

Are you doing the one-on-one stuff in the teacher's lab notations with him before giving him the worksheets?

 

For the record, it isn't clear to me why children that young need to know how to solve for X. o_0 Using the rods, they will eventually be able to figure out all the parts of 5 (just as an example), but I would not expect a 6yo to be able to get that so quickly.

[Paige]

I would stress the equals sign being the most important part of the number sentence. So, I'd get two piles of blocks and a line and I'd put a 3 block on one side and then some other choices on the other side. I'd put a 2 block on top of each one (to demonstrate it is being removed) and see which one makes the same as the 3 on the other side when the 2 covers up part of it.

[Piper]

Would it be any use helping him see it as a "backwards" addition problem?  

If the question is x-2=3, try looking at it from the answer, thinking 2+3=x.  C-rods or other manipulatives would help him see that it's not a new problem, but a different way to present a problem that he already knows.

If that sounds odd, just put it down to the fact that I may not be the best math teacher in the world!! :)

[nerdybird]

X-2=3 is not the same thing as 2+3=X.

 

Yes, they are problems from the same fact family but they are not the same problem. Visualizing 2+3 is not the same as visualizing X-2=3.

 

You are skipping a vital step (which is a big leap to make for young minds, imho).

 

X - 2 = 3

   +2  +2  (You are omitting this step, Piper. Or perhaps this is intuitive for you so you simply disregard it while explaining to your children.)

X = 5

 

You must address the "2" in the problem. In this case, the "2" is a negative number, therefore you have to add "2" to zero it out and you also add "2" to the opposite side to keep things balanced.

 

The inverse also applies if the problem were:

 

X + 2 = 3

    - 2  -2 (You take 2 from both sides to keep it balanced, so on and on...)

X = 1

 

My belief is that these sorts of problems are intended to familiarize young children with algebraic concepts. For the most part, they fail to do so because most curriculum want to skirt the issue by teaching the child to solve number mysteries or memorize fact families. Neither of which (imho) is necessary. Just teach algebra if you want to teach algebra and if not, let it alone. There are already rules and methodologies for mathematics. No need to reinvent the wheel.

 

If you really need a visual approach for these sorts of problems, use tally marks or fingers.

 

Ex:

 

X - III = II -- Have them count the tally marks and they will have the answer. The same applies for fingers. These problems are basic addition and subtraction and there is no need to worry about "solving for X" at this stage unless your child is asking about such things or likes to have the most straightforward and logical reasons for things like mine do. ;)

 

[kiana]

Out of curiosity, can he do the problem if it's more concrete? I.e. Jimmy had some cookies. He ate two. Now he has three left. How many did he start with?

[El...]

Two more ideas:

 

First, Miquon has not yet used "x", but rather a shape to fill in.  DD and I read it aloud as, "Something minus 2 equals three" with a big dramatic "something".  That seems to help her focus on the missing piece.

 

Second, sometimes it helps DD to work problems with "one" rods.         

 

I'd love to hear what "clicks" for you guys!  Good luck!

 

[pehp]

This is my first chance to sit down at the computer. These responses are SO helpful!!  

 

My husband, who is an engineer, actually suggested nerdybird's method tonight when we were talking about it. I felt my heart rate increase at the idea of trying to teach this to my son, because I do think it's kind of a tough concept for....6. (Husband and I laughed that we weren't really doing this until....12?)

 

My initial thought was like Piper's--to teach it 'backwards.'  To say  "Look, when you see x-2=3, just add up the parts to get the whole."  He did this today but I am still shaky on whether it was effective in teaching him to figure the equation out, or just a fun trick!

 

Nerdybird this is EXACTLY how he is seeing the problem:

 X - 4 = 6

6 - 4 = 2

X = 2 (wrong answer!)

 

After talking to my husband tonight I sort of thought--well, we're talking about a few problems for a 6 year old on his first go-round through a Miquon math book.  It's a spiral approach......he doesn't have to be acing this concept now, right?  At the same time, I don't want to overlook or skip something that is important. 

 

I just think....maybe it's not so essential. I mean, he'll nail every other alegbraic equation I give him!! It's these *particular* subtraction problems that are troublesome.

 

Ellie, yes! I am using the lab annotations....they are so helpful. 

 

I like RootAnn's approach too--I might try that out as well.  

 

this has made me wonder if I should supplement our Miquon w/ Singapore.  I initially thought we would work through Miquon and then go to Singapore once we're through the Miquon books.  I'm not sure if it would help or hinder us--I haven't looked at what this blending would entail. 

[Snow]

This is my first chance to sit down at the computer. These responses are SO helpful!!

 

My husband, who is an engineer, actually suggested nerdybird's method tonight when we were talking about it. I felt my heart rate increase at the idea of trying to teach this to my son, because I do think it's kind of a tough concept for....6. (Husband and I laughed that we weren't really doing this until....12?)

 

My initial thought was like Piper's--to teach it 'backwards.' To say "Look, when you see x-2=3, just add up the parts to get the whole." He did this today but I am still shaky on whether it was effective in teaching him to figure the equation out, or just a fun trick!

 

Nerdybird this is EXACTLY how he is seeing the problem:

X - 4 = 6

6 - 4 = 2

X = 2 (wrong answer!)

After talking to my husband tonight I sort of thought--well, we're talking about a few problems for a 6 year old on his first go-round through a Miquon math book. It's a spiral approach......he doesn't have to be acing this concept now, right? At the same time, I don't want to overlook or skip something that is important.

I just think....maybe it's not so essential. I mean, he'll nail every other alegbraic equation I give him!! It's these *particular* subtraction problems that are troublesome.

Ellie, yes! I am using the lab annotations....they are so helpful.

I like RootAnn's approach too--I might try that out as well.

this has made me wonder if I should supplement our Miquon w/ Singapore. I initially thought we would work through Miquon and then go to Singapore once we're through the Miquon books. I'm not sure if it would help or hinder us--I haven't looked at what this blending would entail.

I think you're on the right track here. Explain it, work it a few days and in a few different ways and then move on. The program is planting seeds and it will come around again. We used Miquon almost exclusively last year and I've started using Singapore more this year. Well, it's a nice program. I intend to use it as a supplement going forward, but it's no Miquon which I'm just in love with. And I think we will be going back to just Miquon soon. I don't know why, but ds is just so much more receptive to it.

 

Have you seen the educationunboxed.com videos? Awesome. And a life saver.

[pehp]

Yes! I actually was up late last night hunting around to see if there were any education unboxed videos which would suddenly send a great flash of illuminating light to me.  I watched three (I think?) videos on introducing algebraic concepts and those helped reinforce that at least I think I'm sort of doing this right. 

 

 

[nerdybird]

My husband, who is an engineer, actually suggested nerdybird's method tonight when we were talking about it. I felt my heart rate increase at the idea of trying to teach this to my son, because I do think it's kind of a tough concept for....6. (Husband and I laughed that we weren't really doing this until....12?)

 

My initial thought was like Piper's--to teach it 'backwards.'  To say  "Look, when you see x-2=3, just add up the parts to get the whole."  He did this today but I am still shaky on whether it was effective in teaching him to figure the equation out, or just a fun trick!

 

Nerdybird this is EXACTLY how he is seeing the problem:

 X - 4 = 6

6 - 4 = 2

X = 2 (wrong answer!)

 

After talking to my husband tonight I sort of thought--well, we're talking about a few problems for a 6 year old on his first go-round through a Miquon math book.  It's a spiral approach......he doesn't have to be acing this concept now, right?  At the same time, I don't want to overlook or skip something that is important. 

 

I just think....maybe it's not so essential. I mean, he'll nail every other alegbraic equation I give him!! It's these *particular* subtraction problems that are troublesome.

 

 

Don't fear the algebra! It's.....

 

 

*************

Silliness aside, what's so bad about balancing an equation? It's essentially the same thing as adding the parts to get the whole. You are just teaching him to do the operation to both sides. I believe that teaching a child to repeat the operation on both sides is a good thing that eliminates confusion later on. Addition problems may trip him later and that's when this sort of thing comes in handy.

 

Ex.

 

X + 2 = 8

    - 2   -2

X = 6

 

You can't just tell your kid to add the parts to get the whole here. There has to be an underlying reason, a methodology for obtaining the answer. Sure, you can always skip the balancing step and just say "subtract 2 from 8" or something to that effect, but that sort of explanation does not really explain the reason WHY you must subtract 2 from 8.

 

I'm not an engineer. I merely enjoy mathematics and believe that a firm understanding of mathematics is a vital and often overlooked area of our educations.

 

I have never used Miquon. Too many manipulatives for my tastes and I know that it would overwhelm my kiddos. We use the abacus, the soroban, wrap ups and number cards/charts and that's about it. I focus on mental math with mine a lot too and they are basically human shaped calculators at this point, lol.

 

Good luck on your quest to introduce math to your son. I hope that you can find the right combination of curriculum to help him discover the joy of mathematics. :)

 

 

[Snow]

Silliness aside, what's so bad about balancing an equation? It's essentially the same thing as adding the parts to get the whole. You are just teaching him to do the operation to both sides. I believe that teaching a child to repeat the operation on both sides is a good thing that eliminates confusion later on. Addition problems may trip him later and that's when this sort of thing comes in handy.

 

Ex.

 

X + 2 = 8

- 2 -2

X = 6

 

 

I think this is the way I will teach when we get a little further ahead conceptually. Speaking only about my ds, I'm often having to slow him down and force him to really think about what he's doing. He just wants the answer, he doesn't want to think (lol). And if I just give him a procedure to follow, yes he will get the right answer easily, but it will be without realizing the concept of parts vs whole. So for us it's about *understanding what the problem is really asking*, not focusing on the easiest way to find the answer.

[pehp]

I like the idea of teaching balancing the equation--because that is definitely how I learned to do algebra & how I learned to solve for the unknown.  And I loooooved algebra.  I think the thing that intimidates me is teaching this to a 6 year old.  (MY 6 year old?)  Perhaps it would click and I'm underestimating his ability to look at this type of equation and understand how we're coming to the answer.  I might try it this week and see what his response is.  

 

We balance equations w/ the rods, but not on paper, if that makes sense.  I play a game with him using the rods where you have 2 different rods on each side of the = sign and we have to figure out how to make them the same.

[nerdybird]

I suppose I have a different understanding of mathematics than some. The way I teach it is probably different as well.

 

Why is it important to hammer the concepts of parts and wholes into kids' brains? Where did the concepts come from anyway? It's almost as if someone somewhere was in denial about children having functional brains. Like this person couldn't possibly believe that a small child would be able deduce that you stole a chicken nugget from their plate, or understand the concept of needing the last piece to finish their puzzle. This is fairly intuitive stuff. Anybody who has ever decided to swipe the last of piece of your kid's cookie has found out the hard way that they understand the concept of parts and wholes on a basic level.

 

It is the splitting of a whole (1) into smaller parts (1/4, 1/2, 1/10, etc) that confuses most kids NOT the concept of having 6 ponies after your little brother swiped 4 of them .

 

I view math as being methodological and procedural. It is a lot like language, imo. Except for math demands that you learn the grammar, the rules, before you can form the syntax and express yourself in the language. Holding a mathematical conversation is something that requires serious study. Most of us don't go beyond learning to form basic arguments (proofs) in the language of mathematics.

 

I think that children are capable of understanding the rules and procedures of mathematics in most cases. We're not talking about quadratic functions here. Just simple solving for X/unknowns.

 

For me and mine, using manipulatives to solve these kinds of problems has never really proved to be fruitful. They either get it or they don't and the easiest way for them to get it is to stick to the numbers. Or I can drill them until they just "know" the answers. I prefer the former, but sometimes we will do the latter. It just depends on how things are going on that particular day or how well they are processing the concepts.

 

It is getting late. Brain station is powering down, lol. I love math discussions.... :D

[Snow]

I think that children are capable of understanding the rules and procedures of mathematics in most cases. We're not talking about quadratic functions here. Just simple solving for X/unknowns.

 

I think we just read the op's post differently. I thought she was looking for tips on how she should explain the problem, how to help her kid understand it conceptually because in this case, it wasn't just a simple solving for unknown, he wasn't getting it.

 

But really, I'm just a whatever works kind of person. I agree, there's a time for touchy feely and a time for drill. And I'm certainly not math savvy enough to have developed my own philosophy about teaching it...maybe that's my problem!

[nerdybird]

Eh, originally that is what the OP was talking about, "how I should I teach my son this concept?".

 

I disagree with the notion of splitting hairs and conceptualizing mathematics in general. That is me though, technically minded me. ;)

 

There are two main reasons for my attitude/philosophy towards math.

 

1. I have 2 children who are very technical, math-minded types. Like myself, basically. There was never a real need (and hasn't been so far) for me to do the whole "touchy-feely, let's count rods and blocks and visualize this problem 10 different ways!" thing. My oldest stresses out horribly whenever I try to do those types of activities with him. So I have given up that ghost.
2. I like math and I like teaching it. It is also very important to DH and I that our kids like and understand math.

There is room for many approaches when it comes to teaching grammar and logic level maths. None is perfect and most are highly imperfect, hence the need for supplementation and discussions like this one. ;)

[Snow]

There is room for many approaches when it comes to teaching grammar and logic level maths. None is perfect and most are highly imperfect, hence the need for supplementation and discussions like this one. ;)

.

 

Well said.

[RootAnn]

Many of the math programs out there will get to teaching this type of problem this way:

 

I would have him do this:

 

X - 4 = 6

   +4  +4

    X = 10

 

Straightforward, no muss, no fuss. It took me a long time to realize that not every operation needs to be visualized in order for a child to understand it. Also, I think that teaching solving-for-X type problems like this from the get-go simplifies things down the line when it comes time to start teach fractions, ratios, proportions, and multiple step equations. Fewer things to unlearn, less confusion over isolating variables, etc.

 

But introducing the concreteness of what you are doing with actual objects (or the idea of objects - like the horses in your later example) gets them to understand the concept behind the process without being scared of the process. "Algebra" intimidates many average people. But those kids who have been introduced to the concept of 'solving for an unknown' with something as fun & not-scary as a game of "guess how many I started with" (or my kids' favorite - how many did Mom steal? for problems like 10-x=4) are NOT intimidated by algebra when it finally shows up as an unknown like x or p or n or s. 

 

I think you're on the right track here. Explain it, work it a few days and in a few different ways and then move on. The program is planting seeds and it will come around again. 

:iagree: If it doesn't sink in, don't worry about it. Just move on. You'll both see it again. No sweat.

 

If you haven't already, think about introducing him to Dragonbox. (My 4 & 6 yr olds love Dragonbox 5+.) 

 

And I am an engineer.  :hat:

[Walking-Iris]

I'm not sure if anyone has mentioned this yet...but Miquon Orange should always be used with c-rods. Nothing about Miquon at that level is asking children to do it mentally.

 

I have put my oldest through the entire Miquon program and am on my second go with it. 

 

First thing...make sure your child isn't simply confusing the signs. If my ds answered with a 1 I would assume he was thinking 1+2=3. So make sure he understands what the page is asking him to do...better yet read it to him and do every problem with him at this age.

 

Then you would have your rods out.

 

So for your example of x-2=3 you would first try to have lots of practice building a 5 house. Place down the yellow 5 rod with the red 2 and green 3 under and practice building that fact family for a bit. show that 2 and 3 make 5, reverse it and see that 3 and 2 make 5 and so on. Help him see that in any "house" there are 3 numbers and two addition and two subtraction problems. Maybe play a game where you take three numbers 7 3 and 10 for example and have fun building that fact family with the rods and writing the equations on paper.

 

Also make sure you are using the rods correctly. We place them end to end when adding and under when subtracting. 

 

So if my 1st grader had a problem like that, I would ask him to build it with the rods. He would likely place a 2 and a 3 end to end and see it makes 5. Because those are the numbers he can see on the page.Then he'd write 5 in the box and follow up with taking the red rod away to check. Commutative property in concrete.

 

The idea of "getting it wrong" is not in the Miquon philosophy. The point really of Miquon is to explore and discover, with those rods, the concept behind it. I wouldn't really attempt to overwhelm a 1st grader with a lot of math terminology. Simply practice with those types of problems and the rods and it will happen. 

 

A child shouldn't be doing any page in the Orange book without the hands on. So a 1st grader isn't really solving for an unknown (even though that's what it is)  they are simply building with rods and seeing what is missing. 

 

Also I like to do something else along with Miquon. We're doing MathMammoth. Miquon time is what it says it is "Math Lab time." We talk and work the pages together and follow up with other games.

 

I wouldn't be too worried about a 1st grader not getting this. It comes around again. And again. Simply teach it. Work some examples together. And move on. It's more important I feel that math isn't an anxiety provoking experience at this age. 

[...................]

Well I am definitely a Miquon fan and I believe they really designed an amazing math program.  THat said, maybe it's developmental.  My daughter was and is able to do all those conceptual problems, since first grade.  She just gets it.  

 

My son, on the other hand, (who has a high IQ and is very smart and a logical thinker too....programming on a level that he would get paid 40 grand for, if he were a young adult) ...He did not and could never, no matter how much I explained it, really just easily grasp any of those type of problems.  Until Now!  Now, he is 12 and suddenly he just grasps them.  I'm rather relieved, for I had been very concerned.

 

So...for now, with your son, I would just keep letting him use the cubes to figure it out, or pictures, and guide him through.  Not every child has that conceptual ability at such a young age.

[...................]

OH and my dd loves dragon box.  She is doing the top levels now, for fun.  It definitely is pretty amazing and fun.

[avilma]

I also have a dd6. We are using MEP which has a lot of exercises like that. A few months ago my daughter would solve the problem by substituting different numbers for X until she got the correct result. Today, after having had so much practice, she would just know the answer since it is a number fact that she knows by heart. What we are doing today is exercises of the type x - 37 = 25. Of course it would be too boring to do this using the substitution method.  What I do is I show her the equation x - 2 = 3. She then figures out that the answer (5) is just 3 + 2 and then by analogy solves the equation with larger numbers.

 

So she is able to deduce the rule when she sees a simpler example but isn't able to remember the rule. Once I read a paper by a Russian researcher that stated that children under 10 aren't really able to get algebra. I don't know about 10 but my 6 year old certainly doesn't get it. I am OK with that. I still keep presenting the exercises to her though since at least they are good arithmetic practice and also when she is ready to click with algebra the algebra will be on hand to click. The most important thing is to keep the math lessons light and fun so if she hasn't figured out something in about 30 seconds I either give a helpful hint or give her the answer.

[KSinNS]

My 5 almost 6 gets confused on those types of problems, too. It helps if I rewrite it with a blank instead of a letter. Or we'll play with coins or something. But like the gang above said, don't sweat it. Lots of time to figure it out. Truthfully, I do believe the main point of those questions is to get the idea that x means a blank. 

 

Another trick might be to get him to do the problem back, so when he says x=2 get him to build 2-4 and find out he gets minus 2 (or runs out of blocks-but I think you mentioned that he understood negative numbers), so he knows it doesn't work. 

[pehp]

Yes, we use the rods with every page!! He can do a lot of mental math and I will allow him to do that if we're just reviewing something that is completely obvious (I would not force him to use the rods to solve 10-7 because he's at the point where he figures it out in his head) but they are out and used daily!

 

I will check out DragonBox--thank you!

[pehp]

Yes, we use the rods with every page!! He can do a lot of mental math and I will allow him to do that if we're just reviewing something that is completely obvious (I would not force him to use the rods to solve 10-7 because he's at the point where he figures it out in his head) but they are out and used daily!

 

I will check out DragonBox--thank you!

[Rachel]

My son is working through the Miquon Orange book.  Today he did a bunch of review problems (addition, some subtraction, multiplication) and nailed them all.  THEN on the other side of the sheet he got several problems wrong and they were all involving the same thing: solving for x when x minus something equals something.  So for instance, one problem was x-2=3.  His answer to x was 1.  Of course this comes from the fact that he was somehow turning this into 3-2=1.  If I give him 5-x=3 he will get it.  If I give him 5-2=x he will definitely get that.  But somehow it is very hard for him to grasp the concept of solving for x when x is the 'largest' number in this equation.

 

I stopped everything and worked with him a bit.  I hesitate to say "you are trying to find the LARGER" number because he understands at least the concept of negative numbers, and you *can* subtract a large number from a small number if you wind up with a negative! So I am trying to call the first number in the subtraction equation the "whole" number--and we have the parts, we just have to find the whole. I demonstrated how this is basically the reverse function of adding.  He gets it--sort of vaguely.  He seems to kind-of-sort-of-grasp it, but I stopped working on it before math fatigue set in because I try to be sensitive to his needs.

 

(ETA: I also drew a number line and we used that to try to visualize the concept and solve the problems. It maybe helped??)

 

We'll work on it again in the morning.

 

But in the meantime: is there a better way to teach this specific type of problem? 

I didn't get a chance to read through all the responses so someone may have already suggested this.

 

Education Unboxed has a game "what's in the box?"  You basically set up a problem with one of the rods in a box.  The child has to figure out which is missing.  Playing that game might help him see what he is doing visually.

 

http://www.educationunboxed.com/whats_in_the_box_1.html; http://www.educationunboxed.com/whats_in_the_box_2.html

[nerdybird]

I have played these types of games with mine. I call it the "Problem of the Day". I use a cottage cheese container and I put a certain amount of treats (Teddy Grahams or pretzels usually) in it. On the lid, I write the problem and leave the kids to figure out two things:

 

A) How many treats are inside?

B) How will they split them evenly?

 

They have used lots of different methods to figure it out over the past year or so I have been doing this. DS1 will do the equations like I showed above and then he will divide them by 2 or 3 and be like "I'm done!"

 

Ex.

X - 74 = 150

   +74    +74

X = 224

 

224 = 112 <<< That's how many he and his sister would each get. Sometimes I tell them to share with their brother and /3.

  2  

 

DD is more creative with her approaches. She can do the equation method, but only up about 20. Numbers larger than that overwhelm her right now. So she has done everything from write the numbers and circle or cross them out, to spending several minutes playing with her abacus, to guessitimating.

 

One of her methods is to do this:

    70

      4

    74

+150 = 224

 

Basically, she is using place value to solve the problem. Once she gets the first half of the problem, she will ponder the division carefully. We haven't done a lot of division drills, so it takes her awhile most of the time. She would divide each number by 2 like this to get the answer:

 

2  2  4

2  2  2

1  1  2 <<<Correct answer.

 

*********

That is a more complex sort of problem though. For the original problem, I would still say that balancing the equation is the most straightforward way to teach it. However, if you have gone over the concept multiple times, used manipulatives and it still isn't clicking, move on. If he can do problems like 5 - X = 2 and 5 - 2 = 3, he is competent and progressing as he should through 1st-2nd grade mathematics, imho.

 

:)

.

[Amy M]

If you haven't already, think about introducing him to Dragonbox. (My 4 & 6 yr olds love Dragonbox 5+.) 

 

Do you know if Dragonbox ever goes on sale?

[RootAnn]

I've never seen it any cheaper than what it is now (although I think one of the versions was cheaper at the very beginning). But, I don't pay attention to app prices usually because I had to wait until they had the Windows version out. It was worth the price in my house as I have five kids to go through it. (I haven't gotten the 12+ version. I'm only speaking of the 5+ version.) 

[CaffeineDiary]

X-2=3 is not the same thing as 2+3=X.

 

Yes, they are problems from the same fact family but they are not the same problem. Visualizing 2+3 is not the same as visualizing X-2=3.

 

 

I respectfully disagree.

 

 

If your intent is to teach step-by-step algebra procedures, then nerdybird might be right.  However, from an number theoretical statement, grasping the idea that x-2=3 and 2+3=x are the exact same statement is an incredibly important insight.  Once you realize that any subtraction problem can be rewritten as an addition problem, you understand subtraction in a very fundamental way.  I personally think that's more important than the algebra aspects of this problem.

[ondreeuh]

I completely agree with peterb. Understanding addition and subtraction as dealing with parts and wholes is incredibly important. It's a foundational concept and you cannot skip it.

 

If you go straight to teaching a child to balance an equation algebraically, you are reducing it to a series of steps. Your child may make a mistake and not be able to tell that the answer doesn't make sense because they don't understand what they are doing. A child who solves x-2=3 and accidentally subtracts 2 from each side will get an answer of x=1. Just looking at the problem and seeing the numbers 1, 2, and 3 looks fine, because they are all part of a fact family. But a child who understands that subtraction means you are taking a part away from a whole will see that it doesn't make any sense to start with 1 and subtract 2 and then get a bigger number. They will see that if you put the two parts back together, you will come up with your total.

 

This issue exemplifies the complaints people have about rote, procedural math programs, and the frustration with teachers who don't teach for conceptual understanding. Math is not just a series of tricks to learn, it is about relationships and patterns.

 

Good math programs teach algorithms and shortcuts long after the concept is understood. Rushing things will leave holes and cause future problems. Ask one of the MANY parents on this forum who has had to back up and remediate after realizing that their child really doesn't have a firm foundation and can't move forward.

[nerdybird]

I respectfully disagree.

 

 

If your intent is to teach step-by-step algebra procedures, then nerdybird might be right.  However, from an number theoretical statement, grasping the idea that x-2=3 and 2+3=x are the exact same statement is an incredibly important insight.  Once you realize that any subtraction problem can be rewritten as an addition problem, you understand subtraction in a very fundamental way.  I personally think that's more important than the algebra aspects of this problem.

 

Perhaps this is a matter of teaching styles.

 

The idea that x-2=3 and 2+3=x are the same statement is correct. In both cases, we are talking about parts of a whole or parts from a whole, etc.

 

However, they do not address the same concepts, imho.

 

5-2=3 is a subtraction problem. 2+3=5 is an addition problem. Subtraction and addition are two different concepts.

Can subtraction problems be rewritten as addition problems?

 

Yes. Ex. 5 + -2 = 3 is the same thing as 5-2=3.

 

I do not teach this concept in this way. I prefer to teach in a more formal "let's find out!" sort of way using algebraic methods when possible.  My oldest is a very logical, methodological person. He does not visualize things and so attempting to explain concepts  led to a lot of this: :banghead:  our first year of hsing.

 

My other children are more receptive to conceptual learning. I use Singapore with DD and she does very well with it. However, Singapore's approach is different in that they emphasize depth over breadth unlike many curriculum. I like this approach for teaching math. We also do a lot of drill.

 

However, the essence of the problem does not change. If we are talking about fact families, then yes, x-2=3 and 2+3=x are members of the same fact family. I don't see the need to teach fact families in such a way, so I don't. Different strokes for different folks, it seems.

[kiana]

You know, I see a lot of students who have learned that at some point, you can +2 on both parts of an equation, but they don't really understand why you can do that. They've learned an algorithm, but don't understand the underlying mathematics well enough to understand when it will work and when it will not.

 

The same students often struggle with word problems such as "If $40,000 is invested, with some at 7% and some at 12%, and the interest for one year is $3,550, how much is invested at each rate?", and one of the biggest things they struggle with is setting up the problem. They can understand that we can assign 'x' to be the amount invested at 12%, but they can't figure out that if 'x' is invested at 12%, then '$40,000 - x' must be the amount invested at 7%. There is no relation between addition and subtraction for them. The only way that they can reach that step is to let 'y' be the amount invested at 7%, and observe that x + y = $40,000. Then they can solve for 'y'.

 

I would be reluctant to skip straight to the algebraic solution algorithm.

[pehp]

I just popped back on here and saw new responses. I am enjoying reading the input from other math-teachers and math-lovers.  (I loved algebra but my husband is the real mathematician in our family--I cannot wear that title!)  It's so helpful and interesting to read everyone's insights.  

 

(FWIW, we seemed to have conquered this beast for now using the parts/whole concept and by considering that we are looking for the whole, which is the sum of its parts.  To me this makes conceptual sense--I did a lot of mental math like this in my head as a child to 'check' all my problems at school--and more importantly it is what seems to have clicked the best w/ my son.  And we are moovvvvving on in the orange book!!! :))

[RootAnn]

This issue exemplifies the complaints people have about rote, procedural math programs, and the frustration with teachers who don't teach for conceptual understanding. Math is not just a series of tricks to learn, it is about relationships and patterns.

 

Good math programs teach algorithms and shortcuts long after the concept is understood. Rushing things will leave holes and cause future problems. Ask one of the MANY parents on this forum who has had to back up and remediate after realizing that their child really doesn't have a firm foundation and can't move forward.

 

Just liking this once doesn't seem like enough. *like* *like*  :iagree:  *like*  (And I have some who don't handle the conceptual side well, either. That doesn't change the truth of these statements.)

 

(FWIW, we seemed to have conquered this beast for now using the parts/whole concept and by considering that we are looking for the whole, which is the sum of its parts.  To me this makes conceptual sense--I did a lot of mental math like this in my head as a child to 'check' all my problems at school--and more importantly it is what seems to have clicked the best w/ my son.  And we are moovvvvving on in the orange book!!! :))

 

:hurray:  :party:  :thumbup1:  :cheers2: