Oh boy.

[Rivka]

Alex has been working through the multiplication and division sections of MEP 2b, including some problems that involve division with a remainder.

 

Today I gave her eight pattern blocks and asked her to divide them into groups of three. She moved the blocks into place, looked at the resulting configuration, and told me, "It's two and two-thirds."

 

Um. Yes, it is, but are you really supposed to intuit that in second grade math?

 

She was mad as anything when I told her that for the purposes of the lesson, she was supposed to answer "two, remainder two." Now I'm second-guessing myself and wondering if I should have just gone ahead and let her work all the problems in mixed numbers.

 

In the same lesson, she cried and resisted attempting something new because "I'm bad at math!" :001_huh:

[Jean in Newcastle]

Yes, I would have let her work them in mixed numbers. But I would point out that on some multiple choice tests she might see the same answer written as "two, remainder two".

[ebunny]

Today I gave her eight pattern blocks and asked her to divide them into groups of three. She moved the blocks into place, looked at the resulting configuration, and told me, "It's two and two-thirds."

That's amazing!

 

Yes, I would have let her work them in mixed numbers. But I would point out that on some multiple choice tests she might see the same answer written as "two, remainder two".

:iagree:

[acurtis75]

Fwiw we use mus and just started division with remainders. The first lesson covered just listing the remainder but then the next lesson used fractions for the remainder. Mus doesn't thoroughly cover fractions until the next level (we're on delta and epsilon covers fractions) but it introduced the concept with division. I just asked her to do the problem the way that particular lesson focused on but then said, "what's another way we could write/say the answer." it seemed to work well. The teacher's notes also emphasized that 2/3 really means 2 divided by 3.

[regentrude]

Yes, I would have let her work them in mixed numbers. But I would point out that on some multiple choice tests she might see the same answer written as "two, remainder two".

 

:iagree:

It is extremely frustrating for a strong math student if a teacher or curriculum tells him that he is not allowed/supposed to work the problem correctly because "we have not covered that".

(Another typical situation like this would be a student using negative numbers instead of saying a subtraction problem like 6-8 has no solution as the teacher would like to hear.)

[Iucounu]

Doing division with manipulatives is a good idea for building a basic foundation of understanding for just this reason. One can instantly grasp exactly what a remainder is, which can be lost in the shuffle when a child just manipulates symbols on paper during long division.

[Dana]

She was mad as anything when I told her that for the purposes of the lesson, she was supposed to answer "two, remainder two." Now I'm second-guessing myself and wondering if I should have just gone ahead and let her work all the problems in mixed numbers.

 

 

I'll show my son stuff that comes up much much later in math and if he can handle it, I'll let him do it.

 

I really strongly dislike (hate, abhor) the texts that have students write the answer to a division problem as the quotient with a remainder. It can cause problems later on (polynomial division).

 

It also is nasty because you learn addition, subtraction, and multiplication as operations where you do something with two numbers, you get a single number as answer, but all of a sudden, when dividing, you get two numbers as an answer, not just one. That's not true. You get one number as an answer - it just often isn't in the same set of numbers (rational instead of integer).

 

I do make my son use the remainder notation for a few problems, so he's exposed to it (especially due to standardized tests) but I prefer him to write answers as mixed numbers. Miquon does an excellent job of introducing division like this.

[Carpe]

Am I the only one that thinks dividing with remainders is not only a valuable interim step, but also a useful skill in and of itself? :001_huh:

 

What if the question had been: "A mother wants to buy as many balloons for her three kids as possible, but each child must have the same amount. The balloon seller has eight balloons. How many balloons will each child receive?"

 

That would be 8 / 3 = 2 R2

There is no such thing as 2/3rds of a balloon, once you try to divide it, you no longer have a balloon. There are other indivisible items as well.

 

Or: "There are eight employees that need to work in three even groups. What is the fewest number of temporary employees that need to be hired for this project?"

 

With that question the remainder is the only important part.

[Iucounu]

Am I the only one that thinks dividing with remainders is not only a valuable interim step, but also a useful skill in and of itself?

No, you're definitely right. Another sort of obvious problem where remainders are important is where the remainder describes discrete objects that should be counted separately: "After putting ten hamburgers into each wildebeeste, how many will be left over?"

[regentrude]

Am I the only one that thinks dividing with remainders is not only a valuable interim step, but also a useful skill in and of itself? :001_huh:

 

What if the question had been: "A mother wants to buy as many balloons for her three kids as possible, but each child must have the same amount. The balloon seller has eight balloons. How many balloons will each child receive?"

 

That would be 8 / 3 = 2 R2

There is no such thing as 2/3rds of a balloon, once you try to divide it, you no longer have a balloon. There are other indivisible items as well.

 

Or: "There are eight employees that need to work in three even groups. What is the fewest number of temporary employees that need to be hired for this project?"

 

With that question the remainder is the only important part.

 

Agreed - but I would suspect that a smart child who intuitively can grasp the concept of fractions would have no problem seeing the number of balloons and the left over ones, so remainder is not really a difficult concept that must be practiced.

[Nan in Mass]

Mine did this. I just told them there were several ways of writing the answer to a division problem: decimals, fractions, and as a remainder. I made sure mine could convert from one to the other. I used money to explain decimals. I also pointed out that time, with its minutes and hours worked rather like decimals, too, but with base 60 (and 12 and 24 and 7 and 28/29/30/31 and 365/366 lol). I just had them work the conversions for the things that made sense and for the things they understood.

Nan

[Rivka]

Am I the only one that thinks dividing with remainders is not only a valuable interim step, but also a useful skill in and of itself? :001_huh:

 

No, you're not the only one at all. Interestingly, Alex had no quarrel with dividing with remainders in the context of story problems - packing items into boxes, hens dividing up a pile of eggs, etc. In those contexts she understood that you can't have 2/3 of an egg, and that it was important to know how many items wouldn't fit in a box. It was just when it was presented as pure math that she felt upset.

 

Today during math I set up the problem again, told her that I had made a mistake in asking her not to do it that way, validated that she had come up with a great way of solving the problem, and said she could choose which way to do it from now on. She seemed really relieved.

[Carpe]

No, you're definitely right. Another sort of obvious problem where remainders are important is where the remainder describes discrete objects that should be counted separately: "After putting ten hamburgers into each wildebeest, how many will be left over?"

Agreed - but I would suspect that a smart child who intuitively can grasp the concept of fractions would have no problem seeing the number of balloons and the left over ones, so remainder is not really a difficult concept that must be practiced.

No, you're not the only one at all. Interestingly, Alex had no quarrel with dividing with remainders in the context of story problems - packing items into boxes, hens dividing up a pile of eggs, etc. In those contexts she understood that you can't have 2/3 of an egg, and that it was important to know how many items wouldn't fit in a box.

Things were seeming very anti remainder for a bit there. I'm glad I'm not alone.

 

 

It was just when it was presented as pure math that she felt upset.

 

Today during math I set up the problem again, told her that I had made a mistake in asking her not to do it that way, validated that she had come up with a great way of solving the problem, and said she could choose which way to do it from now on. She seemed really relieved.

 

That's very interesting. I'm happy to hear that you both are feeling better about it.

[EthiopianFood]

Today during math I set up the problem again, told her that I had made a mistake in asking her not to do it that way, validated that she had come up with a great way of solving the problem, and said she could choose which way to do it from now on. She seemed really relieved.

 

Oh, good! I am still distinctly remember how irritated I was when they taught us using remainders one year, only to have them reteach division the next year using long division. I really didn't appreciate that they told us we were learning how to do something, when it wasn't even the right way in the first place! I know this is sort of over the top, but this is one of the little examples of why I don't want my kids to have to deal with the public school system. :tongue_smilie:

[go_go_gadget]

Yes, if they have been using measuring cups or spoons, or divvying up pizza family style, this concept is obvious for an unclassified 7 yr old.

 

Enjoy. You can compact and move on.

 

This. And while I agree that the concept of the remainder is an important one, it's more intuitive and for most students, likely doesn't need to be practiced much. I would not, however, just gloss over the fact that there's more than one way to state the answer (there usually is in math, and sometimes one is more appropriate than another).

[nitascool]

... I would not, however, just gloss over the fact that there's more than one way to state the answer (there usually is in math, and sometimes one is more appropriate than another).

 

This is a concept that comes up often in our home, in math, in life. I have two very inflexible older boys (and a mostly inflexible husband) who think that their way of doing something is always the "right" way, and any other way is the "wrong" way.

 

We have actually had to practice doing things "wrong" ways so that they can see that their way is not the only way. Even dh is learning to do math the "wrong" way with MUS. And so many times I've hear... oh, that is so much easier then my way.

[marcyg]

It sounds like she would like to skip remainders and jump to fractions. We had a similar situation and decided to fast forward to fractions for a few weeks and then go back to remainders. We used Keys to Fractions which is four, 25 page comsumable booklets. They did a phenomenal job presenting the material and ds loved it! In fact, we started using the various "Keys" books as unit studies between Singapore books. We are finished with Singapore and at 10 years old - we decided to do Pre-Algebra in a more relaxed fashion so about a month ago we started the Keys to Algebra and he has already finished book 2 out of 10. The Keys books truly boosted his self-confidence and enjoyment of math.

[zaichiki]

Agreed - but I would suspect that a smart child who intuitively can grasp the concept of fractions would have no problem seeing the number of balloons and the left over ones, so remainder is not really a difficult concept that must be practiced.

:iagree:

I've ALWAYS *hated* "remainders." Why not just teach division the proper way from the start? It's not like it's difficult to remember the differences between whole things and things you can divide. I hated being limited to dividing with remainders so much that I refused to divide at all for a whole year in elementary school . (I guess I was a stubborn child. Hee hee.)

[Halcyon]

Mine did this. I just told them there were several ways of writing the answer to a division problem: decimals, fractions, and as a remainder.

 

 

:iagree::iagree:

[Halcyon]

It sounds like she would like to skip remainders and jump to fractions. We had a similar situation and decided to fast forward to fractions for a few weeks and then go back to remainders. We used Keys to Fractions which is four, 25 page comsumable booklets. They did a phenomenal job presenting the material and ds loved it! In fact, we started using the various "Keys" books as unit studies between Singapore books. We are finished with Singapore and at 10 years old - we decided to do Pre-Algebra in a more relaxed fashion so about a month ago we started the Keys to Algebra and he has already finished book 2 out of 10. The Keys books truly boosted his self-confidence and enjoyment of math.

 

 

Interesting. My son might like these :) I forgot about them!

[freerange]

:iagree:

I've ALWAYS *hated* "remainders." Why not just teach division the proper way from the start? It's not like it's difficult to remember the differences between whole things and things you can divide. I hated being limited to dividing with remainders so much that I refused to divide at all for a whole year in elementary school . (I guess I was a stubborn child. Hee hee.)

 

:lol:

[horsellian]

Am I the only one that thinks dividing with remainders is not only a valuable interim step, but also a useful skill in and of itself?

 

No! I'm doing a maths degree at the moment, and this year's module on Group Theory had loads of calculating remainders for modular (or clock) arithmetic.

 

A school example of modular arithmetic would be that in the 12 hr clock, 10 o'clock plus 4 hours isn't 14 o'clock, it's 2 o'clock (i.e. the remainder of 14/12). In this case, fractions, decimals and remainders aren't equivalent!

[Jill]

I just told them there were several ways of writing the answer to a division problem: decimals, fractions, and as a remainder. I made sure mine could convert from one to the other. I used money to explain decimals. I also pointed out that time, with its minutes and hours worked rather like decimals, too, but with base 60 (and 12 and 24 and 7 and 28/29/30/31 and 365/366 lol). I just had them work the conversions for the things that made sense and for the things they understood.

Nan

^ This. There is value in being flexible and knowing which type of answer you need in which situations.