Does Saxon teach FOIL for multiplying polynomials?

[Tiramisu]

I just think FOIL is easier than their method and would like to teach it if they don't.

[Dana]

I don't know if Saxon does or not, but I'd be careful with FOIL. It's a useful mnemonic, but I see a number of students who regularly get problems wrong because they only know FOIL and don't understand that all that's happening is distribution.

 

FOIL doesn't help if you have a binomial times a trinomial or two trinomials multiplied.

[bettyandbob]

I don't know if Saxon does or not, but I'd be careful with FOIL. It's a useful mnemonic, but I see a number of students who regularly get problems wrong because they only know FOIL and don't understand that all that's happening is distribution.

 

FOIL doesn't help if you have a binomial times a trinomial or two trinomials multiplied.

 

The box method helps you keep like terms together better IMO.

[Tiramisu]

The box method helps you keep like terms together better IMO.

 

I don't think I know what the box method is. 

 

If what Saxon does is the box method, it comes out exactly the same as FOIL in terms of how like terms come out close together.

[Tiramisu]

I don't know if Saxon does or not, but I'd be careful with FOIL. It's a useful mnemonic, but I see a number of students who regularly get problems wrong because they only know FOIL and don't understand that all that's happening is distribution.

 

FOIL doesn't help if you have a binomial times a trinomial or two trinomials multiplied.

 

I introduced the topic in terms of the distribution property. And the lesson in Saxon included trinomials multiplied by binomials.

[regentrude]

I don't know if Saxon does or not, but I'd be careful with FOIL. It's a useful mnemonic, but I see a number of students who regularly get problems wrong because they only know FOIL and don't understand that all that's happening is distribution.

 

FOIL doesn't help if you have a binomial times a trinomial or two trinomials multiplied.

 

I never heard of FOIL before I started reading on these boards.

 

Just want to share the visual method we were taught in school, which generalizes to any type of polynomial multiplication:

Let's take (a+B.)*(c+d+e)

You would draw arcs over the expression from a to each term in the second parentheses, so a to c, a to d, a to e and write down the products as you do so: ac+ad+ae,

then you'd go to the second term in the first parenthesis, B, and repeat the process with arcs B to c, B to d, B to e and add the corresponding products +Bc+Bd+Be to your expression

Thus you have kept track of really catching all the pairs. The visualization and kinesthetic experience helps cement the process.

After a while, students are no longer required to actually draw the arcs. But - don't laugh! - I still trace out the (imaginary) connections with my pencil when I do math, 35 years and hundreds of polynomial expressions later...

 

[LinRTX]

I don't think it does. My daughter just got introduced to FOIL this morning in a PSAT prep book. We do Saxon and she had never heard the term. Being very literary, she loved it! But quickly realized it only works when multiplying two binomials. The method Saxon teaches (distribution) can be used when multiplying any two polynomials, so is much more useful.

 

However, for my daughter's usual quirky math statement. "OK, the way Saxon does it is better and makes more sense, but from now on instead of multiplying binomials, I'm foiling them, I think they  would look pretty covered in foil." 

 

Gotta love the mind of a 13yo.

[Tiramisu]

I found a video of the Saxon lesson on youtube but they teach it as FOIL and not in the vertical way that's in the Saxon book. 

 

I went ahead and taught FOIL for multiplying two binomials but regentrude's way for other polynomial multiplication.

[Tiramisu]

I never heard of FOIL before I started reading on these boards.

 

Just want to share the visual method we were taught in school, which generalizes to any type of polynomial multiplication:

Let's take (a+B.)*(c+d+e)

You would draw arcs over the expression from a to each term in the second parentheses, so a to c, a to d, a to e and write down the products as you do so: ac+ad+ae,

then you'd go to the second term in the first parenthesis, B, and repeat the process with arcs B to c, B to d, B to e and add the corresponding products +Bc+Bd+Be to your expression

Thus you have kept track of really catching all the pairs. The visualization and kinesthetic experience helps cement the process.

After a while, students are no longer required to actually draw the arcs. But - don't laugh! - I still trace out the (imaginary) connections with my pencil when I do math, 35 years and hundreds of polynomial expressions later...

 

 

I draw the arcs mentally, too. And that's how I taught dd the distributive property. 

 

Now, I feel like I've been doing something right!!! :)

[bettyandbob]

here's a youtube of the box method

 

http://www.youtube.com/watch?v=pxmmJzB5ULs

 

here is a binomial times a trinomial

http://www.youtube.com/watch?v=wqOG4UXZOEY

 

I like how you can quickly gather like terms by looking at the diagonal. 

 

[Jann in TX]

I never heard of FOIL before I started reading on these boards.

 

Just want to share the visual method we were taught in school, which generalizes to any type of polynomial multiplication:

Let's take (a+B.)*(c+d+e)

You would draw arcs over the expression from a to each term in the second parentheses, so a to c, a to d, a to e and write down the products as you do so: ac+ad+ae,

then you'd go to the second term in the first parenthesis, B, and repeat the process with arcs B to c, B to d, B to e and add the corresponding products +Bc+Bd+Be to your expression

Thus you have kept track of really catching all the pairs. The visualization and kinesthetic experience helps cement the process.

After a while, students are no longer required to actually draw the arcs. But - don't laugh! - I still trace out the (imaginary) connections with my pencil when I do math, 35 years and hundreds of polynomial expressions later...

 

I agree that FOIL is very limiting--- only working with binomials.  I don't teach it (I do demonstrate it because it it so common).  I've found that students tend to focus more on the letters instead of the procedure and it does not carry over into other distributing patterns.

 

I teach regentrude's  method -- my students have dubbed it the 'rainbow method'.

 

For longer problems (like trinomials by trinomials) I use a 'stacked' method that looks like long multiplication.  To make the problem 'expand' to the right start with the highest degree term on the bottom polynomial and work left to right keeping like terms together.

 

Personally I cannot stand the 'box' method for multiplication of polynomials or worse yet- factoring polynomials... I've had to tutor/remediate too many students who were confused or were totally dependent on that box!

 

Below is sample of the 'rainbow' and 'stacked' methods

 

[bettyandbob]

I learned FOIL many years ago and it was the only method I used for a long time. It gets messy when you multiply trinomials. I work with students who have learning challenges. I have found the box method makes it easier to see what is happening for students who respond well to a multi sensory approach. I will show students more than one method so they can figure out what is easier for them to work with.

[Tiramisu]

I agree that FOIL is very limiting--- only working with binomials.  I don't teach it (I do demonstrate it because it it so common).  I've found that students tend to focus more on the letters instead of the procedure and it does not carry over into other distributing patterns.

 

I teach regentrude's  method -- my students have dubbed it the 'rainbow method'.

 

For longer problems (like trinomials by trinomials) I use a 'stacked' method that looks like long multiplication.  To make the problem 'expand' to the right start with the highest degree term on the bottom polynomial and work left to right keeping like terms together.

 

Personally I cannot stand the 'box' method for multiplication of polynomials or worse yet- factoring polynomials... I've had to tutor/remediate too many students who were confused or were totally dependent on that box!

 

Below is sample of the 'rainbow' and 'stacked' methods

multi.jpg

 

The link didn't work for me but the stacked method seems to be what Saxon is using. 

 

I think the "rainbow method" might be the best bet for us.

[kiana]

+1 to everyone who doesn't like FOIL.

 

I just don't see the point of teaching a mnemonic that only works on *some* of the problems. It makes those problems easy, but I frequently see that students don't understand what's going on with the process of multiplying and are unable to multiply anything *but* binomials times binomials.

 

The second issue is that for these students, it frequently makes learning to factor far more difficult than it should. Since they don't really see how they went together in the first place, they can't see how they come apart.