Any Maths Genius To Explain why "5+5+5=15 is incorrect"

[blackbike]

If you are asked to find out what 5 times something is using the 'repeated addition' method, it doesn't make sense to write down a sum with only three numbers in it. That sum must have five numbers in it to adhere to the prescribed method.

Had the question asked what is 5 x 1000000, the child would have had a an awful lot of writing to do with his decision to reverse he question, when he could simply have done it quickly and correctly by summing together 5 lots of one million.

[Psamathe]

If you are asked to find out what 5 times something is using the 'repeated addition' method, it doesn't make sense to write down a sum with only three numbers in it. That sum must have five numbers in it to adhere to the prescribed method.

Had the question asked what is 5 x 1000000, the child would have had a an awful lot of writing to do with his decision to reverse he question, when he could simply have done it quickly and correctly by summing together 5 lots of one million.

I interpreted the tone of the question differently. It says you should "Use the repeated addition strategy to solve 5 x 3 = ". I just assumed that saying "strategy" is a more general expression rather that specific. It also says "to solve 5 x 3 =" which to me suggests you should be solving the equation rather than 5 times something. i.e. they are after an answer and the technique you should use to get it - and that is what the student did (s)he got the right answer and used "repeated addition" to get it, which is what the question asked them to do.

Maybe it comes down to how one interprets the language.

Ian

[AlaninWales]

Maybe it comes down to how one interprets the language.

Ian

It does. I read it as 'take the number five and use repeated additions to find what three of them are": Which is exactly what was done. Other readings are possible, but to argue that they are the only right ones simply shows people as narrow-minded.

[Vorpal]

The students will have had this explained to them: what the order of the numbers means, what is additive strategy, etc.

The child who got this wrong should have known that it was 5 threes and not 3 fives. I expect that learning this is part of learning about the commutative properties of multiplication. But of course, they don't tell you that. They also don't show more than two questions, so we don't know if another question asked is 3X5 the same as 5X3, or if students were also asked to do it the other way round.

There are some problems with Common Core, but this isn't one of them. US American parents love to complain about it, though, and if you look around, you can find all kinds of examples of this kind of thing that doesn't demonstrate anything other than a desire to complain about Common Core.

[Psamathe]

The students will have had this explained to them: what the order of the numbers means, what is additive strategy, etc.

The child who got this wrong should have known that it was 5 threes and not 3 fives....

I've never been a teacher so can't comment on the education process, but I do think that penalising a child for getting it right is daft. Maybe his/her parents had been tutoring them, maybe they'd been getting info from many other sources. The answer given did use the repeated addition strategy and did solve 5 x 3 - which is what the question asked. To teach a child that 5+5+5=15 is wrong only to teach them in subsequent years that it is actually right I'd have thought confusing at best. I appreciate education does involve simplification and more details are taught as one progresses, but to penalise for being a bit ahead of the teaching and being right I feel cannot help a child develop.

(But personal opinion as I've no teaching knowledge)

Ian

[blackbike]

The question is perfectly clear to me.

It asks what is five times three.

So to answer it you must consider five lots of something, in this case three. We write that 3+3+3+3+3+3.

If you eat three sweets five times you've eaten 3+3+3+3+3+3 sweets.

If it had asked what is three times five then you need to consider three lots of something, in this case five, and we write that as 5+5+5.

If you eat five sweets three times you've eaten 5+5+5 sweets.

[Vorpal]

The students will have had this explained to them: what the order of the numbers means, what is additive strategy, etc.

The child who got this wrong should have known that it was 5 threes and not 3 fives....

I've never been a teacher so can't comment on the education process, but I do think that penalising a child for getting it right is daft. Maybe his/her parents had been tutoring them, maybe they'd been getting info from many other sources. The answer given did use the repeated addition strategy and did solve 5 x 3 - which is what the question asked. To teach a child that 5+5+5=15 is wrong only to teach them in subsequent years that it is actually right I'd have thought confusing at best. I appreciate education does involve simplification and more details are taught as one progresses, but to penalise for being a bit ahead of the teaching and being right I feel cannot help a child develop.

(But personal opinion as I've no teaching knowledge)

Ian

5+5+5=15 isn't wrong. And the lesson about commutative proprties of multiplication should be with or immediate after learning how to do multplication by addition. But 5+5+5=15 was not the correct answer to the question. The commutative property says that 5X3 = 3X5 but they are not necessarily the same thing. It doesn't matter when you are only talking about numbers, but it may when you begin talking about practical applications. Are five bikes with two wheels each the same as two bikes with five wheels each?

IMO, it's much less confusing to teach it this way than the way I learned, which was to memorize the times tables (or be punished fro not doing it) without any reason given for doing so other than we needed it to progress.

[TonyR]

Maybe it comes down to how one interprets the language.

Ian

It does. I read it as 'take the number five and use repeated additions to find what three of them are": Which is exactly what was done. Other readings are possible, but to argue that they are the only right ones simply shows people as narrow-minded.

Its not narrow minded. Maths is precise. 2 + 3 x 4 being 14 not 20 is being correct, not narrow minded. If the student had written instead

5 x 3 = 3 x 5 = 5 + 5 + 5

I am pretty sure they would have got full marks.

[Psamathe]

Maybe it comes down to how one interprets the language.

Ian

It does. I read it as 'take the number five and use repeated additions to find what three of them are": Which is exactly what was done. Other readings are possible, but to argue that they are the only right ones simply shows people as narrow-minded.

Its not narrow minded. Maths is precise. 2 + 3 x 4 being 14 not 20 is being correct, not narrow minded. If the student had written instead

5 x 3 = 3 x 5 = 5 + 5 + 5

I am pretty sure they would have got full marks.

Would agree (that 5 x 3 = 3 x 5 = 5 + 5 + 5) should have got full marks. But you can miss (obvious) steps out in solving an equation so 5 x 3 = 5+5+5 = 15 would have been equally correct (they did not say "Show all steps" which is the sort of thing I remember from my school days exams).

(But this is a really minor issue we are discussing - but it's wet and miserable and I can't/won't get out for a ride today ...)

Ian

[Psamathe]

The students will have had this explained to them: what the order of the numbers means, what is additive strategy, etc.

The child who got this wrong should have known that it was 5 threes and not 3 fives....

I've never been a teacher so can't comment on the education process, but I do think that penalising a child for getting it right is daft. Maybe his/her parents had been tutoring them, maybe they'd been getting info from many other sources. The answer given did use the repeated addition strategy and did solve 5 x 3 - which is what the question asked. To teach a child that 5+5+5=15 is wrong only to teach them in subsequent years that it is actually right I'd have thought confusing at best. I appreciate education does involve simplification and more details are taught as one progresses, but to penalise for being a bit ahead of the teaching and being right I feel cannot help a child develop.

(But personal opinion as I've no teaching knowledge)

Ian

5+5+5=15 isn't wrong. And the lesson about commutative proprties of multiplication should be with or immediate after learning how to do multplication by addition. But 5+5+5=15 was not the correct answer to the question. The commutative property says that 5X3 = 3X5 but they are not necessarily the same thing. It doesn't matter when you are only talking about numbers, but it may when you begin talking about practical applications. Are five bikes with two wheels each the same as two bikes with five wheels each?

IMO, it's much less confusing to teach it this way than the way I learned, which was to memorize the times tables (or be punished fro not doing it) without any reason given for doing so other than we needed it to progress.

(As I said above, today it's wet and windy and I can't or wont be going out for a ride - which I should be doing rather than writing about minor things like this).

I agree about not being the same if you are talking about 5 bicycles and their wheels. But that is introducing additional constraints to the question that were not there. The student was just asked to solve 5 x 3 using repeated addition - which to my mind they did. Maybe they did it using something they had not yet been taught, but the question did not say "using repeated addition as you were taught in class". We sometimes used to get questions phrased in physical world terms e.g. "6 people ... how many shoes" where there would be physical constraints, but the question was just about solving a mathematical expression.

It certainly used to be the case when I was younger that some struggling kids with parents that could afford it had extra tuition, so it was quite possible that one person could be aware of things that were slightly beyond what was being taught in class - and I feel it is wrong to penalise a child for that.

Ian

[Tangled Metal]

Correct me if I'm wrong here but in the English language there is a convention the recipient of an action goes b second. What I mean by this is X does the action to Y when X is before the verb and Y is after. NounA verb Nounb in that order means A carried out the action given by.the verb on B.

Five times three is just the same. 5 lots of 3. The answer may be 15 but the way to get there is different.

These are the rules of maths and English language I think. We need rules to standardize things to prevent confusion. I guarantee in maths there will be some really complex theory where this basic rule is critical for the solution. So basically it's not important this is right but it could be so better to be a jobsworth now and get it into the child.

[TonyR]

Would agree (that 5 x 3 = 3 x 5 = 5 + 5 + 5) should have got full marks. But you can miss (obvious) steps out in solving an equation so 5 x 3 = 5+5+5 = 15 would have been equally correct (they did not say "Show all steps" which is the sort of thing I remember from my school days exams).

Yes but they need to show enough steps in an exam to show that they understand what they are doing. Simply writing 5 x 3 = 5 + 5 + 5 does not do that as you can't tell whether they have missed out a step in their working or misunderstood the principles.

[TonyR]

(But this is a really minor issue we are discussing

Hey, this is the Tea Shop, what do you expect?

[Psamathe]

(But this is a really minor issue we are discussing

Hey, this is the Tea Shop, what do you expect?

Just wanted to make it clear that, as I posting a lot to this thread, I'm not developing any high blood pressure over it.

But QR skewers ... just let me ... oh dear.

Ian

[661-Pete]

I think we've all by-passed a whole lot of formal maths, here. Let me set that right.
Starting with a somewhat simpler sum (skipping the first 300 or so pages):

(from Principia Mathematica)