Notas importantes:

•El resultado de la división de llama “quotent”.

•Y el resto de la división se llama “remainder”.

•Los estudiantes suelen confundirse mucho al escribir la división, sobre todo identificando cuál es el numero que está dividiendo.

The post 5 Diferencias en matemáticas entre Estados Unidos y Latinoamérica first appeared on LatinHire Online Tutoring.

Comentario del Tutor: Elegí esta sesión ya que abarca un tema que no es muy usual de ver en Argentina , división de polinomios , por otro lado , en esta sesión el alumno no tenia un problema puntual para resolver , sino que necesitaba practica,  esto no es muy común , ya que normalmente los alumnos nos piden ayuda para resolver problemas particulares, a su vez trae una complicación , ya que se debe proveer un ejercicio adecuado al nivel del alumno , ni muy básico ni muy elevado . Por eso mismo en esta sesión comenzamos con un ejercicio simple , para comprobar que el alumno tuviese los conocimientos básicos necesarios , y luego optamos por resolver uno mas complicado , logrando que el alumno se esfuerce para resolver el ejercicio.

Student

I need help understanding division of polynomial a by monomials and polynomials.

Tutor

Welcome to Tutor.com ! My name is Javier . How are you ?

Student

Hello Javier. I am great. How are you?

Tutor

Im fine , thanks for asking :)

Student

Can you give me an example of a polynomial divided by a monomial and I will give it a shot?

Tutor

sure

x^5 +3x^3 + 4x^2 / x^2

Student

is that right?

Tutor

perfect ! :D

Student

Sweet. I am starting to understand them I think

how about division by a polynomial?

Tutor

ok lets try this one

x^3+2x^2 +x+1 / x+1

perfect :D

right !

and you have a remainder

Student

not for this one right?

oh yes I do

Tutor

mmm let me check something

oh thats right :)

because you erased the 1 now , that was confusing me :)

now its perfect !

Student

hmmmm. lets try one like that again that comes out with a remainder. I got a little iffy there at the end

Sweet

can we try another one that will come out with a remainder?

Tutor

ok

let me think another example

ok

4x^3 + 2x^2 + 5 / x-3

Student

How does that look?

Tutor

lets check that :)

dont forget the 5 :)

Student

ummm ok, lets back up. I’m confused

Tutor

sure

up to that step its perfect :D

Student

so in order to get 14x^2 I must multiply by 14x

Tutor

right

Student

now I switch the signs and add

Tutor

wait

we are doing 42x +5

we cannot add something with an X to something without an X , right ?

Student

oh, it just came to me…I needed a place holder

Tutor

right hehe

Student

may we start this over again

tricky little devil

:-)

Tutor

sure :)

Student

Thank you for throwing that in because I had forgotten all about that

Tutor

ok , lets start again :)

perfect !

wait please

how did the 5 transformed into 126 ?

oh sorry

Student

so in order to get 42x I must multiply by 42

Tutor

because of the 42 :)

yeah i missed that , sorry :)

continue please

Student

no problem

does that look right now?

Tutor

yes it does :)

its perfect :D

Student

OK, great

so I need to remember to watch out for the exponents

and use a place holder whenever needed

Tutor

right :D

do you have any questions about what we have covered today ?

Student

I think I am good for now. I need to practice a little more but I am starting to grasp this. Thank you so much for the help.

Have a nice evening!

Tutor

your welcome :)

Colaborador: Javier Verde, Tutor Argentino de Álgebra

The post División de Polinomios first appeared on LatinHire Online Tutoring.

Comentarios del Tutor: Elegí esta sesión dado que , a diferencia de la manera en que resolvemos este tipo de problemas en algunas partes de Sudamérica , en EEUU optan por hacerlo utilizando esta «regla» en lugar de emplear la identidad trigonométrica Pitagórica. Además, se utilizan los recursos que se nos sugieren constantemente, chequeo de entendimiento. Un cierre de las sesión adecuado.

Student sec A = -4 , cot B =2/3 with A in QII and B in QIII. Find: Sin 2A cos(A-B) tan B/2 csc A/2

Tutor Welcome! How are you today?

Student im ok. Frustrated

Tutor oh, wellIll help you with this

Student thank you!

Tutor Any ideas about it?

Student I know I will need to use a few different Identities. But im not sure how to find Sin andCos to make them work

Tutor okay , first of all we need to get sin and cos for each angle
let’s think about angle A

Student yes , 1/cos

Tutor right, So how much is cos?

Student -4x?

Tutor we know sec is -4 and you told me sec is 1/cos
so how much is cos?

Student right

Tutor if you have sec you flip it , and you get cos

Student -1/4

Tutor perfect! Now we will use a triangle to get sin

Student i cant believe I didnt get that

Tutor we know cos is adj/hyp right?

Student yes

Tutor so we place the 1 and the 4 , like this…
How can we get the missing side?

Student then solve for b

Tutor yes, how much is it?
great! So how much is sin?
perfect!

Student where did the neg go from cos A

Tutor  now we should work on angle B?
sec was negative and we also know the angle is in quad II is negative there

Student  oh okay, but we dont nee that on the triangle?

Tutor nope its the same

Student oky

Tutor just think about the quadrant

Student ok

Tutor what about B? Ideas?

Student cot = cos/sin

Tutor right

Student so would cos be 2 and sin be 3?

Tutor [09:43] not exactly you should place the values in the triangle

Student [09:54] ok

Tutor and get the hypotenuse
great!
so , how much is sin B? and cos B?
can we leave a root in the denominator?

Student nope

Tutor so?
great!
let me tell you something angle B, Its in quadrant III, what do we know about the sin and cos values in q III?

Student cos is neg  and so is sin

Tutor [15:49] okay, so we place the neg sign for them, now we can get the asked values

Student sin (A+A) is SinAcosA+CosAsinA

Tutor okay , you can plug the values

Student do i include teh negative here?

Tutor yes! How much is that?

Student do they cancel out?

Tutor both are negative
hmmm, you cant do that , you must combine both then you can reduce

Student oh!

Tutor perfect!

Student ok thx

Tutor now let me tell you something we forgot about angle B

Student ok

Tutor its in quadrant III , so what do we know about sin and cos?

Student cos is neg

Tutor and sin?

Student and so is sin

Tutor so we place the neg sign for them

Student i will try the others on my own and log back on if I cannot figure it out

Tutor oh ok  great idea!

Student thank you

Tutor Thank you for using our service
Please, do me the favour of completing the survey and comment before leaving

Student yup

Tutor Have a great day! Bye bye

Student bye

Colaborador: Juan Belluscio, Tutor Argentino de Trigonometría

The post Funciones Trigonométricas: Tutoría Online completa con estudiante first appeared on LatinHire Online Tutoring.

Student I’m working on composite functions, but do not understand what the «domain» is or how to find it. I can work through the problem, but am lost when it comes to the domain. Please help!

(Tutor) Hi, my name is Juan. How are you today?

Student I’m well. How are you?

(Tutor)  I’m good :D, ok let’s get started!

Student ok. I’m needing to understand, what the «domain» is and how to find it?

(Tutor)  Sure!

the domain is all the values that «x» can take
for example
let’s find the domain of f(x)
f(x)=4x+1
in that case does x have any restriction?
I mean is there an x value that we can’t use?

Student no. I don’t think so

(Tutor) correct
so the domain of that function is all real numbers
for example
this function
is there an x value that we can’t use?

Student 0

(Tutor) You got it!

Student ok

(Tutor)  so the domain of this function is
all real numbers except zero
is it more clear?
or not?
should I try to explain it in a different way?

Student yes.. domain is all values that x can be for the given function

(Tutor)  correct! :D

Student ok

(Tutor) let’s go back to the problem

Student ok

(Tutor)  in this case
the domain of f(x) is all real numbers
how about g(x)?

Student I think i’m still slightly confused.

 (Tutor) in that function
is there any x value that we can’t use?

Student no, i don’t think so

(Tutor) Correct

Student ok

(Tutor) so the domain is all real numbers

Student yes

(Tutor)  Clue: the domain of a polynomial is always all real numbers
f(x) and g(x) are polynomials

Student ok. i see

(Tutor) so the domain will be all real numbers
and how about (fog)(x)

Student f(g(x))

(Tutor) correct :D
but they are asking for gof

Student yes

(Tutor)  ok do you know how to find it?

Student g(4x+1)

(Tutor)  yeah!
then
we have to use g
how would it be?
do you need help?

Student i think i’ve got it. I had trouble with the buttons

 (Tutor)  ohhh
what are you trying to do?

Student  2(4x +1)squared + 5(4x+1)

(Tutor)  yeah!

Student  2(16x ² + 8x + 1) + 20x + 5
32x ² + 16x + 2 + 20 + 5

(Tutor)  it is 20x
but well done!

Student  equals 32x ² + 36x +7

(Tutor)  :D
You got it!
And what’s the domain of that function?
I understand what you wrote
but it should be written
like…

Student  right, negative on the left

Student Thank you so much for your help! :)

(Tutor)  No problem! It was great to work with you!
Bye

Student  thanks. Bye

 Colaborador: Juan Cruz, Tutor Colombiano de Álgebra

The post Funciones compuestas first appeared on LatinHire Online Tutoring.

Generalmente, entre más cómodo se sienta el alumno, será mucho más fácil que entienda los conceptos y si no logra entender alguno, facilita mucho el intentar otro enfoque sin que exista frustración.

Student Write each percent as a fraction and as a decimal. Write fractions in simplest form.

Tutor Hi! How are you today?

Student hello!

Tutor Welcome! Let’s get started.

Student alrighty

Tutor So, your problem is 0.4 percent right?

Student correcto

Tutor Awesome! So, let’s try this together!

Student k !

Tutor Do you remember what the word «percent» means?

Student yes

Tutor Ok What would be your definition?

Student i think its stands for over 100

Tutor Exactly! So, «0.4 percent» would be the same as «0.4 over 100»

Student alrighty

Tutor So, we can actually put that on the board

Student ok oops messed up a bit on the 4

Tutor It’s ok

Student lol

Tutor So, based on the drawing, what do you think we should do next?

Student simplify?

Tutor Oh almost Let’s take a look at this part!

Student okey dokey

Tutor In that part, we’re asked to multiply by 10, right?

Student yep

Tutor Why do you think we multiply times 10?

Student i am not sure

Tutor Oh, the 0.4 was a decimal, so to make it become a whole number we would multiply by 10 That way it’s easier!

Student oh i see!

Tutor So, we’re multiplying 0.4 by 10 Let’s write 0.4 here

Student ok

Tutor Ok! Awesome! So, now, let’s multiply What do you get when you do 0.4 times 10?

Student alrighty want me to do it on the board?

Tutor Sure !

Student 4

Tutor Yup! So, let’s write 4 here

Student ok!

Tutor Ok good! So, now, let’s multiply 100 x 10

Student ok! 1000

Tutor Yup! so, 1000 goes in this box

Student ok!

Tutor Ok! Now, we have our fraction 4/1000 and the next step says «simplify» . How would you simplify?

Student by 4?

Tutor Ok, that works !

Student 1/250?

Tutor Perfect! So, let’s write that here!

Student OK! sorry i made that a small box

Tutor It’s ok So, one more step to go.

Student lol ok!

Tutor Ready? ?

Student as ready as i could ever be

Tutor Ok! So, from the fractions we got here, we have to find the equivalent decimal Do you have any ideas on how to do that?

Student um…. no

Tutor Oh ok It’s really really easy. Let’s take at this 4/1000

Student ya

Tutor Isn’t that fraction also called «four thousandths» ?

Student yes

Tutor And how do you write «four thousandths» as a decimal?

Student ohhhhh!!!!!! i see .004

Tutor You got it! You got it! You got it! You got it! Awesome!

Student Tutor Perfect job today! Do you have any questions about anything we went over today?

Student no but thanks for the help!

Tutor No problem! :) I hope you enjoyed it! Bye and have a great rest of the day

Student bye!

Colaborador: Juan Pablo Rodríguez, Tutor Mexicano de Matemáticas

The post Comunicación asertiva para incentivar al estudiante: Tutoría de Matemáticas first appeared on LatinHire Online Tutoring.

Esta sesión muestra una resta de dos fracciones mixtas. Para facilitar el proceso, sugerí convertir las fracciones mixtas en fracciones impropias. El estudiante trabajó paso a paso para realizar esta conversión. Primero, multiplcando el número entero por el denominador y luego sumándolo al numerador. Una vez convertidas las fracciones mixtas a impropias, se encuentó el LCD (Least common denominator o mínimo común múltiplo). Ahora debemos encontrar el equivalente de nuestras fracciones impropias pero con el LCD como nuevo denominador. Para hacer esto, el estudiante dividió el LCD por el antiguo denominador, luego lo multiplicó con el antiguo numerador. Este resultado es el nominador de nuestra fracción equivalente. Finalmente se tiene una resta de fracciones con denominador común en donde simplemente se restan los numeradores y el resultado, si es posible, se reduce a su mínima expresión.

Colaborador: Carlos Armendia, Tutor Boliviano de Matemáticas

The post Resta de fracciones mixtas first appeared on LatinHire Online Tutoring.

 Colaborador: Giovanny Espinal, Tutor Colombiano de Álgebra

The post Utilizando colores para los ejemplos first appeared on LatinHire Online Tutoring.

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