Need Advice on Math word problem (subtraction/bar model)

[beishan]

I was reviewing subtraction chapter with my 2nd grader last night and found he had trouble comprehend question like below:

 

John has 15 stickers and Mary has 29 stickers. How many more stickers do they need to make 71 stickers in all.

 

The way school taught them is using bar model. First you draw a bar for 15 and 29, and then come up with total number 44 by adding 15 and 29. He has no issue with this part. Second bar will show 44 and ? as parts and 71 as total. He had a little bit issue placing the number on this part but was finally able to do so after some practicing. However, when I asked him to write the number sentence to get the answer, he could only come up with 44+?=71. And he gave me the answer 27 directly. I know he is using "adding up method" to find out "?" answer. How do I get him understand to use 71-44? I try to use blocks and clay dough to demostrate the bar model, but he still has hard time fully understand it. He understands subtraction concept but just got stuck when it came to this kind of word problem with bar model.

 

We tried similar word problem from Singapore CWP 1 with small numbers (numbers all within 10) before. He can tell me the answer right away without thinking. I think he is able to use adding up method much quicker in his head when numbers are small. However, when number becomes bigger, he got stuck because it takes time to use adding up method in his head and he has trouble to switch the way he thinks to subtraction. How I can help him to understand this kind of word problem?

 

Thanks in advance

[letsplaymath]

Adding up is a legitimate and age-appropriate way to solve subtraction problems. Please don't make your son feel bad about using it. Nothing good will come of fighting his natural intuition about numbers!

 

When he gets stuck on a larger problem, give him plenty of time to think and maybe a white board with colored markers to use as "scratch paper." My kids get mad at me (for good reason!) if I break their chain of thought while they are figuring out a problem. After you have waited as long as you can bear, ask him if he wants a hint. If he says yes, THEN is when you can point out the link between adding up and subtraction---not as if subtraction is how he has to do it, but as "This is how I like to think about this sort of problem."

 

 

[happypamama]

Honestly, I'm 36, and I am a good math student, and I still sometimes use the add-it-up method rather than direct subtraction. I think letsplaymath gave you good advice. :)

[73349]

Has he done the little triangles for fact families? Like

 

    10

  /     \

6       4

 

That's a way of indicating that ten is made of four plus six (or six plus four), or ten minus six is four, or ten minus four is six.

 

So he would then be able to represent this problem as

_____________+ __________ = ______________________________

     44                            ?                                   71

 

OR

 

     71

   /     \

  44    ?

and realize he has to do 71-44 to find the answer.

[lorisuewho]

My boys would have added up. I never thought of correcting this in any way. Maybe when they get into larger numbers if they don't intuitively know how to switch it up we will have to discuss it more.

[beishan]

Thanks for all the advice. My son does the 10 number bond very well and also has good grip of place value. He has better sense on addition than subtraction at current stage. I am ok to have him using adding up to calculate the problem since it is age appropriate. I will try to be patient and hope he can get better understanding with more practices on number manipulation.

[Monica_in_Switzerland]

You can have him practicing writing out a fact family for the equation.  So, 44 + x = 71, x +44 =71, 71- 44 = x, 71 - x = 44.  Make sure he knows that these are all essentially the same "thing" (number bond).  If he gets that, then it doesn't really matter how he solves it mentally.  I solve much faster using the adding method than mental subtraction, but for a difficult problem, I would subtract using stacking.  I remind my kid constantly that in math, there are always a few paths to get to the answer! 

 

In my mind, I would do 44 ------> 71.... hmmm... add 6 to make the math easier, now 50 ----> 71 is another 21... so the answer is 21+6 ... 27.  I would use this method regardless of which permutation of the "fact family" the problem is.

 

This is a method illustrates in SM2.... not sure what level you are in. 

[beishan]

You can have him practicing writing out a fact family for the equation.  So, 44 + x = 71, x +44 =71, 71- 44 = x, 71 - x = 44.  Make sure he knows that these are all essentially the same "thing" (number bond).  If he gets that, then it doesn't really matter how he solves it mentally.  I solve much faster using the adding method than mental subtraction, but for a difficult problem, I would subtract using stacking.  I remind my kid constantly that in math, there are always a few paths to get to the answer! 

 

In my mind, I would do 44 ------> 71.... hmmm... add 6 to make the math easier, now 50 ----> 71 is another 21... so the answer is 21+6 ... 27.  I would use this method regardless of which permutation of the "fact family" the problem is.

 

This is a method illustrates in SM2.... not sure what level you are in. 

 

 

Yes, he understands fact family equation in smaller numbers. The problem is actually from GO MATH they use in school. At home, we are at end of SM 2A. GO MATH uses the same way to solve the problem as SM but it's progressing at much slower pace.

 

I will try to practice the fact equation with bigger number with him.

 

Thanks

[Tanikit]

I agree with beishan - start with much simpler numbers and see if he understands what they are asking - word problems are almost never about the maths - they are about the language. Bigger numbers just make it harder to understand the language as the children get lost in these huge numbers they have to deal with. Use numbers that he should be able to get the answer in his head if it were straight forward math and then work on the language and what it means then substitute the bigger numbers.

 

So can he do: John has 2 stickers and Mary has 3 stickers. How many more stickers do they need to make 7 stickers in all.

If he can, then he can definitely do it with the bigger numbers when you ask him what sign he used in the above sums - how did he get his answer, so do the same for the bigger numbers.

 

 

 

[beishan]

Tanikit

 

He has not issue with smaller number. The way he thinks is 2+3+x=5+x=7. He is very familiar with addition fact within 20 so he can come up this answer like nothing. Same way he thinks for bigger number(15+29+x=44+x=71). He will try to add 30 to 44 and finds it will be over 71. Then he will try adding 20 and finds he needs another 7 to make it 71. That's how he come up the answer 27. I just cannot get him to jump to 71-44=27 which is the way I will use to come up 27.

 

Sometimes I think it's not he has issue with this word problem, but he does not fully understand how to use bar model which is fairly new thing to him.

[Tanikit]

Hi sorry - I tried to revise that post after posting and lost my internet connection for a while. I think you have to use manipulatives to explain why subtraction and adding on are pretty much the same concept. Talk about taking away from vs adding to and use either C-rods or those blocks that fit together. When my DD wants to add on I let her, but still expect her to tell me how else she could do the sum - and make her put the unknown after the equals sign - that way she must switch to subtraction. But again it takes some time and plenty of play and practice.

 

As for the bar models - these also take time. I make my DD draw pictures first or play with manipulatives then show her how to do the bar model that works the same as her picture and show her what the difference between the two are - so a block with a number in it can be the same as her group of blocks or a particular C-rod. C-rods actually work very well for bar models as that is exactly what they are. The bar model is really a slightly more abstract way of showing what is really happening in the problem - he should show it in a way that makes sense to him first and then learn how this can be translated into a bar model.

[beishan]

Thanks. Is c-rods this? http://www.amazon.com/Learning-Resources-Cuisenaire-Rods-Introductory/dp/B000F8T9HW

Or maybe I can use some lego bricks?

[KSinNS]

I agree with making sure he can do it with small numbers first, but if he still struggles with big numbers, I'd just grab a pack of sticky notes and use those as the manipulatives to figure it out. Give him 71 sticky notes and then get him to work it out from there (teddy bears for John and Mary). And then you can lay out the ways to write the "math sentence".

[Tanikit]

Yes, those are C-rods (cuisenaire rods). It is possible to use lego bricks too - especially if you use ones that are all of the same size (the 2x2 ones are probably the best) - there are some added advantages to C-rods, but for this particular problem any block that is of a standard size would be fine.