Tiramisu Posted January 7, 2014 Share Posted January 7, 2014 I just think FOIL is easier than their method and would like to teach it if they don't. Quote Link to comment Share on other sites More sharing options...
Dana Posted January 7, 2014 Share Posted January 7, 2014 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. Quote Link to comment Share on other sites More sharing options...
bettyandbob Posted January 7, 2014 Share Posted January 7, 2014 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. Quote Link to comment Share on other sites More sharing options...
Tiramisu Posted January 7, 2014 Author Share Posted January 7, 2014 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. Quote Link to comment Share on other sites More sharing options...
Tiramisu Posted January 7, 2014 Author Share Posted January 7, 2014 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. Quote Link to comment Share on other sites More sharing options...
regentrude Posted January 7, 2014 Share Posted January 7, 2014 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... Quote Link to comment Share on other sites More sharing options...
LinRTX Posted January 7, 2014 Share Posted January 7, 2014 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. Quote Link to comment Share on other sites More sharing options...
Tiramisu Posted January 8, 2014 Author Share Posted January 8, 2014 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. Quote Link to comment Share on other sites More sharing options...
Tiramisu Posted January 8, 2014 Author Share Posted January 8, 2014 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!!! :) Quote Link to comment Share on other sites More sharing options...
bettyandbob Posted January 8, 2014 Share Posted January 8, 2014 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. Quote Link to comment Share on other sites More sharing options...
Jann in TX Posted January 8, 2014 Share Posted January 8, 2014 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 1 Quote Link to comment Share on other sites More sharing options...
bettyandbob Posted January 8, 2014 Share Posted January 8, 2014 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. Quote Link to comment Share on other sites More sharing options...
Tiramisu Posted January 8, 2014 Author Share Posted January 8, 2014 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. Quote Link to comment Share on other sites More sharing options...
kiana Posted January 8, 2014 Share Posted January 8, 2014 +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. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.