English translation: (multiplying) by a single digit with carry
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10:16 Mar 16, 2011
Spanish to English translations [PRO] Science - Mathematics & Statistics
Spanish term or phrase:llevando por un factor
Hello. This is from a list of the types of mathematical exercises to be done my primary school pupils:
Explanation: From the list of activities, it looks as though this is the next step after learning the multiplication tables (ie, multiplying a single-digit number by another single-digit number). It seems logical that the next step would be to multiply a multi-digit number by a single-digit number, which involves carrying the tens to the next position to the left. After that, they would go on to multiplying a multi-digit number by another multi-digit number, but that looks like it doesn't happen in this year/grade.
(BTW, does anybody know how to stop an apostrophe getting a backslash pre-appended to it?)
My suggestion is that it means multiplying a *multi-digit* number by a single-digit number. This teaches the concept of carrying the tens, and prepares the students for multiplying a multi-digit number by a multi-digit number, since you take the digits of the multi-digit multiplier one by one. That's why I suggested "multiplying *BY* a single digit", not "multiplying single-digit numbers"
For what it's worth, I actually know some math teachers who teach single digit multiplication as carrying: 9 x 9 is 81, write down the 1 in the ones column, carry the 8, 8 plus 0 is 8, write down the 8 in the tens column. That said, I agree: since most people memorize their multiplication tables up to 10 or 12, whether or not there is (or people view there to be) carrying in single-digit multiplication can be debated.
Single digit multiplication with only 2 factors does not require 'with carrying'.
As for 'carry-over multiplication that's what I vaguely remember it being called at my school - but that was before the internet was around and of course it may just be my particular teacher's terminology
Given the grade level, my guess is that it's single-digit multiplication with carrying (or perhaps double-digit multiplication with carrying).
Either way, I think that "multiplication with carrying" might be close enough to work for you--if anything, it's a bit too inclusive (by including more complicated carrying problems), but the main point is that it's combining multiplication and carrying.
(Dr. Neil, is this really called "carry-over multiplication" in British English? There are almost no hits for this expression on google...)
1) What grade level is this?
2) Do you have any of the actual course materials related to this particular operation so we could look at them and know exactly what the operation is? That might be the easiest solution!
Hi and thanks to everyone for their help. Here's the related activities in the list:
• Problemas de suma, resta o multiplicación.
• Tablas de multiplicar hasta el 9.
• Inventar preguntas. Descubrir e inventar el dato que falta.
• Multiplicaciones llevando por un factor.
• Problemas de dos operaciones (suma o resta y multiplicación).
Are there any other references in the list to other types of multiplication? If so, we could eliminate some possibilities, just by knowing that they are mentiones separately.
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Answers
3 hrs confidence:
carry-over multiplications.
Explanation: At least one of the factors of the multiplication must be two-digit (otherwise it is not necessary to carry-over anything - e.g. 7 x 5 does not require any carrying-over) - 15 x 4...... is (5 x 4 = 20 or 'zero and carry the two' as we say in the UK) then 1 x 4 = 4 'plus the two carried-over' = 6.......the answer is 60 ;@)
All multiplications must have at least two factors so I see 'two-factor multiplication with carrying' as rather redunant (especially as primary school children are not likely to calculate more than 2-factor multiplications. Anyway the ST does not mention hwo many factors are included therefore how can one assume that it is 2?
Dr Neil Ashby Spain Local time: 10:19 Works in field Native speaker of: English
Explanation: My idea on this is that "llevando por un factor" is not actually a syntagm, and that it really means "multiplicaciones / llevando / por un factor", so "por un factor" is the type of multiplication and "llevando" is the method. In principle, it could have been expressed as "Multiplicaciones por un factor llevando".
"Factor" means one of the numbers you are multiplying: in A x B, A and B are the factors. (The number of digits is a separate issue, I think.) So "multiplication by a factor" is a tautology; all multiplication is by a factor, by definition. I think it means by one factor, as opposed to two or more factors (multiplication by two factors would be A x B x C).
In the following school programme, Educación matemática in Tercero Básico includes "Multiplicación por un factor" (and "División con un divisor"). From the following year, Cuarto Básico, they're doing "Multiplicación por uno y dos factores". http://www.colegiocarmenarriaran.cl/contADM.htm
Since there have to be at least two factors in all for a multiplication to take place, I think "por un factor" has to mean multiplying a number by one other number (or a multiplicand by one multiplier), and "por dos factors" means three factors in all (multiplying a multiplicand by two multipliers).
In English, you don't tend to find "multiplication/multiplying by one factor"; the more usual expression for a simple A x B calculation is "two-factor multiplication". Later you would get "three-factor multiplication".
"This study investigated the pedagogical content knowledge that a college learner who is a prospective teacher might construct for teaching two-factor multiplication." http://hopper.unco.edu/hauk/tport2006/node29.html
-------------------------------------------------- Note added at 12 hrs (2011-03-16 23:04:01 GMT) --------------------------------------------------
As I have said above, "por un factor" must mean "by one multiplier", as opposed to two or more; in other words, multiplying one factor (the multiplicand) by one other factor (the multiplier), and not more. Therefore this expression refers specifically to multiplying two factors, not to multiplication in general.
"Multiplication with carrying" or "Carry-over multiplication" are simply "Multiplicación llevando". So "multiplicación llevando por un factor" must mean something more than that. The primary maths syllabus in Spain does include 3-factor multiplication, which is why it specifies here "por un factor", as opposed to "por dos factores".
"Unidad 7: Practica la multiplicación
- Multiplicar por 10, por 100 y por 1.000
- Multiplicar por un número seguido de ceros
- Multiplicar números de dos cifras sin llevar
- La multiplicación llevando
- Multiplicar número de tres y cuatro cifras
- El producto de tres factores [...]" http://www.juntadeandalucia.es/averroes/loreto/sugerencias/V...
Charles Davis Local time: 10:19 Native speaker of: English PRO pts in category: 4
Explanation: From the list of activities, it looks as though this is the next step after learning the multiplication tables (ie, multiplying a single-digit number by another single-digit number). It seems logical that the next step would be to multiply a multi-digit number by a single-digit number, which involves carrying the tens to the next position to the left. After that, they would go on to multiplying a multi-digit number by another multi-digit number, but that looks like it doesn't happen in this year/grade.
(BTW, does anybody know how to stop an apostrophe getting a backslash pre-appended to it?)
pclews Local time: 10:19 Works in field Native speaker of: English PRO pts in category: 8
Reference: carrying--but we don't say it that way!
Reference information: Hi Simon,
"con llevar" and "sin llevar" / "con llevadas" and "sin llevadas" etc. means "with carrying" and "without carrying" respectively:
"Adiciones de un número de tres cifras con un número de una, dos, o tres cifras sin llevar y llevando a las decenas, centenas y unidades de millar."
From http://www.nicaraguaeduca.edu.ni/uploads/Prog_Mult_Tomo2.pdf... also in tons of "programaciones" you can find online.
The problem is that in English we have "multiplication with carrying" and "multiplication without carrying", but to my knowledge, we don't say "multiplication with single-digit carrying".
I guess "multiplication carrying only one digit/a single digit" might work...but it sounds unnatural to me, since, to my knowledge, we don't express multiplication this way!
Hope this helps.
Wordalia Spain Native speaker of: English, Spanish PRO pts in category: 4
Note to reference poster
Asker: Thanks very much for your help, Wordalia :)
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