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the difference –Discovery Math
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4myboys,
The cost of RS kept me from trying it for 2 years. I don’t know if this would help in your decision….but RS does offer a 60 return policy.
So don’t purchase it until you are ready to use it….then you have 60 days to give it a try to decide if it will work or not.
RS also has a good resale value so if you do like the program then you can sell your Level C when you are finished and use that towards your purchase of Level D
Another thought……have you looked at the RS Math Games kit…..it comes with an Abacus and teaches many of the strategies that are in the lessons….what is nice is that these games can be used with ALL ages and any curriculum. The games start off very simple and increase in complexity. There are around 70 games alone for addition. The only math concept not covered in the games is decimals.
suzukimom said:
Let me think it through again… lol….
Ok, say 34-7 (it would have been in a column format.) Instead of borrowing the 1 from the 3 in the tens.. I would just go… ok 4-7=-3 and 30-3=27. It works. It makes sense, and to me, it was easier. Conceptually it is also sound.
I’m probably going to embarrass myself with this question
but, would you mind explaining this solution better? 4 minus 7 is “negative 3”. 30 minus “negative 3” would be 33. So where does the normal 3 come from in your solution?I think the main reasoning in this problem is that you already did the subtraction of 7. So you don’t subtract again. Taking the 7 from the 4 and getting -3, you then add that to the remainder of the problem: 30. Thus 27.
I’m no math wiz, but that is what the logical thought seems to me.
yes ruth..you don’t actually subtact -3 (that would be adding 🙂 but you do add the -3 to the “remainder” here…and that would be the same as subtracting 3 from 30 giving 27. don’t try to teach your younger students this method…But if your student starts such wonderful out of the box thinking on own–don’t squish!
this is a example of a child’s clear understanding of the cocepts involved (negative numbers)..and some creative and accurate mental math.
jo
I think you can think of that problem (or say it in your head) in several different ways (or at least one more way)….I thought about it for a bit then tried what I thought Suzukimom was explaining with other numbers and the answers were correct. I didn’t get into all the neg. or remainders about it, though….I didn’t think that indepth about it, I have to admit. I have my own way of thinking or visualizing subtraction problems but my kids have adopted their own way based on how their minds work. Isn’t that funny?? I’ve tried to show them “my” way and they just look at me like I’m crazy. Everyone has their own way (obviously some people think alike, but ykwim) and I’m trying to help my kids find their own way that feels more natural to them. And, my kids are all complete opposites 🙂
This has been a very interesting and helpful thread.
I guess I can understand breaking the 7 down into “4 and 3” – take off the 4 to make 30, then the 3 to make 27. But I’m not really sure why the subtraction gets used up and so you would add back in the -3 instead of subtracting it.
This is why I’m just happy that I can balance my checkbook, compare deals at the grocery store, and do “kitchen fractions”.
rene…people get all tied up with negative and positive numbers. don’t let it get to you…the words add and subtract and the word negative confuse the issue…the negative really means opposite of…and it is way simplier than it at first seems.
maybe one day in the future i will try to explain it simply–a little negative number lesson if you will. if ya’ll remind me.
later, jo
Very good point made by Rene: This is why I’m just happy that I can balance my checkbook, compare deals at the grocery store, and do “kitchen fractions”.
That is the kind of practicle math we want our kids to be able to do. But, math also teaches them basic “problem-solving skills”. How much paint do I need for the walls and ceiling of this room? How many posterboards do I buy to put our school timeline on and how do I mark off the centuries and decades? Which is the better deal at the store for our family’s money? How do we share the pizza equally and split the cost equally? Is my new business making any profit? …Life Problems…Word Problems…Math Problems!
I wanted to try RS without the high cost. We are using the AL Abacus and the Activities Guide and Worksheets along with MUS program. I don’t care that we are behind on the MUS schedule because I am after mastery and understanding. We also bought the kit of Math Games from RS. I find the appropriate RS activities to go with the same MUS lesson. Example: MUS lesson 10 is adding 8. So, I look in the Activity guide for AL Abacus for adding 8 and show it on the abacus, which is very similar to MUS blocks, but it seems to click better with my student by him using the abacus. The manual that comes with the Math Games cards kit also has a game under the sub-title of “adding 8”, so I can play a card game. I can print as many worksheets for practice that I need from the MUS website for +8 until we have mastery. By the way, the “jr.” abacus that comes with the math games kit is so tiny that it is frustrating for my kids. My little girl uses it to “teach” her baby dolls.
rene…people get all tied up with negative and positive numbers. don’t let it get to you…the words add and subtract and the word negative confuse the issue…the negative really means opposite of…and it is way simplier than it at first seems.
Honestly, the negative number did not bother me. I understand positives and negatives for the most part. What I don’t understand is what happened to the negative number in suzukimom’s problem. It seemed to just turn into a positive number when she came up with 30-3.
Was the dash between the 30 and 3 supposed to be “minus” or the word “negative”? Thrity minus three, or thrity negative three? Would “thrity negative three” even be anything mathmatically?
If the 3 stayed a negative, how do you decide whether to add it or subtract it in relation to the 30 in that problem?
Hey Rene…. I was 7 when I came up with it… I just knew it worked and made sense to me.
Really, as someone else said, I was just completing 10’s… I prefered to do my math with the number 10…
I think the problem I gave was 34-7….
I think my through process was more of along the lines of reversing the problem in a way… So I’d reverse the 4-7 to 7-4…. and in my head becase 7 was more than 4 and was what we were subtracting, I knew I had 3 more that I needed to take away still. So really it was more of a “Ok, I have 34, and I’m taking away 7 from it…. so I take away 4… and I am left with 30, and still have 3 more to take away…)
But at the same time, I knew I was working with negative numbers.
Keep in mind, I’m trying to explain a thought process I had 35 years ago, when I was only 7! And yes – this wouldn’t be the way I’d try to explain it to my kids at all!
Other things to keep in mind… I was a MATH child (and also a gifted child.) My dad was a math teacher. I corrected high school math papers from about age 5 (although I didn’t know what I was correcting.) I was in grade 2, could add, subtract, multiply, do simple division (not long division), and knew about squaring numbers. I could do mental math (not to the point that gets you on tv or anything…) and certainly a year or so later, I would go to the store and could work out the total of my purchases (errands) and the change right to the penny before the cash register did. In grade 2 math, I was bored, and had time on my hands. I prefered (probably because of my mental math stuff) to work with the number 10 (and multiples) than other numbers…. the simple trick of rounding up or down a number, and keeping track of the bit that you need to adjust the answer. like adding $0.99 and $0.99, and knowing the answer will be $1.98 because $1+$1-$.01-$.01 (ok, that is $2 – the 2 pennies) is easier than adding the 9’s together and doing all the carrying involved.
I’m not saying this stuff to show off or anything. Just to explain two things. That there are different ways to do math problems…. and also that I can’t necessarily explain my thought processes from that time but that I know it works.
Oh, and I guess the point of the original post was that this was something I “discovered” on my own.
btw – I don’t know if this had anything to do with my math abilities…. but I owned a calculator when I was a child. (This was in the 70’s, when calculators you could get didn’t do anything past the 4 basic functions and cost a fortune…. My dad gave us each one, don’t know where he got it from…) HOWEVER…. I didn’t use the calculator in math class, or generally when I was figuring out a problem. I played with it a lot though, and did a lot of math on it… again, mainly as playing with it. I have no idea if I learned much that way or not… but could certainly check things I was trying. The one thing I do think I learned with the calculator (and asking my dad) is about not being able to divide by 0.
Hey Rene…. I was 7 when I came up with it…
Yes, I understand that. It’s just that, in this thread it was said that there is rarely one way to get the answer with math (which I agree with) and you posted the 34-7 problem, going into a negative to get the answer.
I can understand if this was something a (very bright) child’s mind came up but in reality it doesn’t work. But no one is anwering the question of whether, as an adult and in the real mathmatical world, it really works this way.
Can you actually get to the correct answer in the above problem by coming up with negative 3 first?
I apologize, because I’m not trying to be a pain or beat a dead horse. I’m not a math person. I am honestly wanting to know if the problem can really be done this way and I would like to see how it is done.
from our previous rene:
JO: rene…people get all tied up with negative and positive numbers. don’t let it get to you…the words add and subtract and the word negative confuse the issue…the negative really means opposite of…and it is way simplier than it at first seems.
RENE: Honestly, the negative number did not bother me. I understand positives and negatives for the most part.
RENE: 30 minus “negative 3” would be 33.
JO: yes …you don’t actually subtact -3
ok Rene-here goes
#1 I was not trying to be in any way derogatory about your abilities with negative numbers…people…even math people get tied up all the time with neg and pos numbers…because there is a lot that is understood (invisible but happening!). I could tell you understood…because of your comment 30-(-3) =33. very true…and when suzukimom wrote that i ignored it cause it was a small error in language and i understood exactly what she was saying. she did not subtract -3. but she had an intuitive grasp of pos and neg numbers and used the correct operation at the time.
i am going to break this down a bit and let’s see if I can do this without being right there with you!
in mostly words:
3 is the same as pos 3 which is the same as pos 1 times pos 3 which is the same as neg 1 times neg 1 times pos 3
in symbols note: () means times and so does *
3=+3=+1(+3)=(-1)(-1)(+3)
notice I am using the rules that you don’t have to write the one when multiplied by a number b/c anything multiplied by one is itself and that a neg * a neg = pos or – * – = +
remember also that + * – = + or pos times neg =neg
now in words:
neg 3= neg 1 times pos 3
in symbols
-3=(-1)(+3) but we don’t have to write that one cause it is being multiplied so it could be -3=-(+3)
so the orginal example
34-7=34+(-7)=30+4+(-7) now here we can do in any order because using the order of operations we are allowed to add however we want to…
so 30+4+(-7)=30+ [4+(-7)]=30+[4-7]=30+(-3) now here we have a pos * a neg = neg
30+(-3)= 30-3=27. ta da!
this is why i say show your work!! 🙂 of course i really broke that down do you could see ALL the steps (i hope!). I would not have expected a student in a reg prob to show all of that…but when we study pos and neg # in depth…then they need to –so i can see do they really really understand all the understoods?
how was that rene?
i’m sorry i couldn’t get back to answer sooner.
God Bless,
jo
I didn’t step through Jo’s answer… but though more about it last night….
when doing 34-7 the “normal way”…. you borrow the 10 from the 30 to get you basically 20+14-7 (34 is 20+14) then you subtract the 7 from 14… so you get 20+7, then you add the 20 and the 7 together to get 27.
So I did the same thing basically… I just did 34-7 is the same as 30+4-7 then figure out the 4-7=-3 and put that in so I’d get 30+(-3) which is 30-3 which is 27.
It does work, I just didn’t explain it well when I wrote it originally.
but, would you mind explaining this solution better? 4 minus 7 is “negative 3”. 30 minus “negative 3” would be 33. So where does the normal 3 come from in your solution?
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