Doodlebug Posted January 1, 2015 Share Posted January 1, 2015 Monday is around the corner, and I need to find a new way of coming at solving for the unknown variable in subtraction problems. DS can not remember if he should subtract, or add together the known variables to solve for x. For instance... 514 - N = 432 X - 82 = 432 Saxon expects a student to draw upon fact family patterns, which DS did well with (smaller numbers) to solve for the unknown. But DS just stares into space on these and the fact family stuff isn't cutting it. Is there another technique for teaching this? (I did try equation style solving with DS before break, but don't think that was helpful). Thanks! Quote Link to comment Share on other sites More sharing options...
Barb_ Posted January 2, 2015 Share Posted January 2, 2015 Two parts make a whole. So part + part = whole. In subtraction, you always begin with the whole and remove a part to get the other part. If you know the whole and one of the parts like in your first example, you simply remove the part you know from the whole to get the missing part, regardless of where it falls in the equation. In your second example, the whole is missing, so you put the part you know together with the other part you know to get the whole that is missing at the beginning of the equation. Quote Link to comment Share on other sites More sharing options...
Daria Posted January 2, 2015 Share Posted January 2, 2015 I agree with Barb that talking about "parts" and "wholes" or "totals" is helpful. One thing I do a lot is to use a graphic like a number bond, and moving back and forth between number bonds and equations. Kids learn to look at a problem and see it as one with a missing part (in which case you subtract) or one with a missing total (in which case you add). I find this is helpful in solving word problems too. I'll have kids act out a word problem (e.g. Bill went to the bakery with $12.92 cents. He paid for a cookie. Now he has $11.54. How much did the cookie cost?) I'll have them act it out with "invisible money" and then ask "At what point in the story did someone have all the money? Bill had all the money in the beginning, before he spent any. So, that's the total. Do we know how much he had? Yes, we do, so this must be a subtraction problem. Quote Link to comment Share on other sites More sharing options...
Sunshine State Sue Posted January 2, 2015 Share Posted January 2, 2015 I always tell the student that the goal is to get the unknown on one side of the equal sign and everything else on the other side of the equal sign. What steps can you take to do that? Quote Link to comment Share on other sites More sharing options...
bethben Posted January 2, 2015 Share Posted January 2, 2015 I usually make the problem a lot easier such as N-5=8 or something like that. I teach them how to solve the easy problem and then go onto the harder one. Quote Link to comment Share on other sites More sharing options...
LaCEmom Posted January 2, 2015 Share Posted January 2, 2015 Two parts make a whole. So part + part = whole. In subtraction, you always begin with the whole and remove a part to get the other part. If you know the whole and one of the parts like in your first example, you simply remove the part you know from the whole to get the missing part, regardless of where it falls in the equation. In your second example, the whole is missing, so you put the part you know together with the other part you know to get the whole that is missing at the beginning of the equation. This! With a 3rd grader I'd make sure that he actually understands the logic behind the operations. If he does, he should be able to talk his way through the problem without actually "remembering" anything. Quote Link to comment Share on other sites More sharing options...
EKS Posted January 2, 2015 Share Posted January 2, 2015 I used manipulatives (linking cubes, I think they're called) for the bigger numbers, not for the three digit nimbers, but the two digit ones that they start out with. So for 57-N=23, I'd give my son 57 cubes (5 sticks of 10 and a stick of 7) and I'd say: how many do you have to take away from 57 to get 23? And he'd do it in some laborious way and finally get an answer. Then I would have him do it again and eventually he would see that that the answer was 57-23. This took maybe an hour one day. Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted January 2, 2015 Share Posted January 2, 2015 I usually make the problem a lot easier such as N-5=8 or something like that. I teach them how to solve the easy problem and then go onto the harder one. This is what I do. And you can also show this with counters so he/she can see why/how it works. Quote Link to comment Share on other sites More sharing options...
Plink Posted January 2, 2015 Share Posted January 2, 2015 For us, the key was to mark up the problem. Circle or highlight the total (not the =, but the total number of things you are considering, the biggest number). The other two numbers are the parts. Next, build or draw the problem. Look at what you know, and see if you can re-arrange the problem in a way that makes more sense, then solve for the unknown. Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted January 2, 2015 Author Share Posted January 2, 2015 Two parts make a whole. So part + part = whole. In subtraction, you always begin with the whole and remove a part to get the other part. If you know the whole and one of the parts like in your first example, you simply remove the part you know from the whole to get the missing part, regardless of where it falls in the equation. In your second example, the whole is missing, so you put the part you know together with the other part you know to get the whole that is missing at the beginning of the equation. This is exactly what I was looking for!!! Thank you. I think part of the problem is the language used in Saxon. A lot of "some, some went away" not to be confused with "sums." Only it IS confusing. ;) Just out of curiosity, is there a curriculum from which you pulled this? In my spare time, I'm looking into math curriculums that might be a better fit for DS at this stage. My multiquote isn't working, so I'll try to do this... Daria said: I agree with Barb that talking about "parts" and "wholes" or "totals" is helpful. One thing I do a lot is to use a graphic like a number bond, and moving back and forth between number bonds and equations. Kids learn to look at a problem and see it as one with a missing part (in which case you subtract) or one with a missing total (in which case you add). ​I find this is helpful in solving word problems too. I'll have kids act out a word problem (e.g. Bill went to the bakery with $12.92 cents. He paid for a cookie. Now he has $11.54. How much did the cookie cost?) I'll have them act it out with "invisible money" and then ask "At what point in the story did someone have all the money? Bill had all the money in the beginning, before he spent any. So, that's the total. Do we know how much he had? Yes, we do, so this must be a subtraction problem. Not surprisingly, we are struggling with the word problems, too. That's why I want to go back and cover the basic operation... something isn't clicking. I think you're right that it will help him in word problems. The number bond is insteresting... Saxon uses a tower diagram, which I find confusing when paired up with all the "some" language. (some, some went away, some left over -- or difference). EKS said: I used manipulatives (linking cubes, I think they're called) for the bigger numbers, not for the three digit nimbers, but the two digit ones that they start out with. So for 57-N=23, I'd give my son 57 cubes (5 sticks of 10 and a stick of 7) and I'd say: how many do you have to take away from 57 to get 23? And he'd do it in some laborious way and finally get an answer. Then I would have him do it again and eventually he would see that that the answer was 57-23. This took maybe an hour one day. I had this thought, but sold all my rods last summer. I could kick myself. I thought about using money, but that would add another layer of conceptual thinking that would be confusing. If my new approach doesn't do it, I will be in the market for more rods. Plink said: For us, the key was to mark up the problem. Circle or highlight the total (not the =, but the total number of things you are considering, the biggest number). The other two numbers are the parts. Next, build or draw the problem. Look at what you know, and see if you can re-arrange the problem in a way that makes more sense, then solve for the unknown. I think you have another piece to my puzzle. Color coding things is helpful to DS. If I can mark up the problem, color coding whole, part 1, and part 2, I can see that working well for him. Thanks so much! Quote Link to comment Share on other sites More sharing options...
SparklyUnicorn Posted January 2, 2015 Share Posted January 2, 2015 I find that sometimes I have to repeat concepts 1000 times before they sink in. It's like one day they have it, and next day poof it's gone. If you just keep nibbling at it, he'll eventually remember. Quote Link to comment Share on other sites More sharing options...
Daria Posted January 2, 2015 Share Posted January 2, 2015 The number bonds come from Singapore Math. I haven't taught it, so that's not a recommendation, but a lot of people like it, so it might be worth exploring. Quote Link to comment Share on other sites More sharing options...
Barb_ Posted January 2, 2015 Share Posted January 2, 2015 The strength of Singapore Math is conceptual understanding and the language used to talk about math. I believe Math Mammoth teaches the skills in a similar way but I haven't used it and cannot comment. Quote Link to comment Share on other sites More sharing options...
Kiara.I Posted January 2, 2015 Share Posted January 2, 2015 Rightstart uses number bonds too, but calls them "Part-Whole Circles." I really, really, REALLY love Righstart. In case you actually go looking for different curriculum. ;) If you want to use rods but don't have any, try getting a huge pack of popsicle sticks at the dollar store. You can use elastic bands to make them into bundles of 10, if you want, so that you are working with numbers of "ones" in the ones column and numbers of "bundles" in the tens column...that kind of thing. Hundreds would be harder. ;) Rightstart uses Base 10 picture cards that are very helpful for place value and addition/subtraction. You could probably make something like them yourself on cardstock... Not surprisingly, we are struggling with the word problems, too. That's why I want to go back and cover the basic operation... something isn't clicking. I think you're right that it will help him in word problems. The number bond is insteresting... Saxon uses a tower diagram, which I find confusing when paired up with all the "some" language. (some, some went away, some left over -- or difference). I had this thought, but sold all my rods last summer. I could kick myself. I thought about using money, but that would add another layer of conceptual thinking that would be confusing. If my new approach doesn't do it, I will be in the market for more rods. Quote Link to comment Share on other sites More sharing options...
Doodlebug Posted January 6, 2015 Author Share Posted January 6, 2015 I just wanted to come back and say thank you for the excellent advice. I think identifying the whole in subtraction and addition problems was the key. We worked using the bond diagram in colors for whole or parts. From there, we circled whole/parts in their corresponding colors and plugged them in to the diagram. DS said this was SO much easier. Here's a pic of the three problems he did on his own today... Sorry so messy, but he did it! YAY! Quote Link to comment Share on other sites More sharing options...
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