# Formula triangles: do you use them?

Discussion in 'Science' started by msuxg, Jun 30, 2015.

1. ### msuxgNew commenter

Jenny Koenig has written a blog post on why she dislikes them.

2. ### SupertechnoNew commenter

As both a parent and a former teacher, I hate them with a passion. I used to tell my pupils that they are circus tricks for weak maths teachers. I'd like to see them use triangles to rearrange the kinetic energy equation to solve for 'v'!

One of the jobs of the maths department is to teach the pupils the skills that they need for science, especially physics. It does not take long to teach pupils how to rearrange equations: I used to do it in physics lessons to compensate for the triangles rubbish they were taught in maths. It might take two to three lessons, but by then all but the very weakest pupils could do it.

As a parent, I wanted my son taught how to rearrange equations, not poxy triangles. I ended up doing it myself and, again, it wasn't difficult.

At a push, I would possibly use them with the very weakest pupils. However, my caveat was that I always told them that using triangles was their choice: I never used them.

Also, the last time I looked at exam papers the equations were given in linear form, with a divide symbol if necessary. The pupils have to rearrange the equation from the form in which it is given in order to put it into the triangle form anyway.

Get maths teachers to teach algebra properly. After all, the pupils will definitely need that skill to rearrange the kinetic energy equation to solve for 'v', as I mentioned above. And they should know how to do it, as life skill.

3. ### Ssn77New commenter

I used formula triangles when I started teaching after pupils introduced them to me, and told me they relied on them. Having seen them in use, I too hate them with a passion and ban my pupils from using them. Pupils now learn the equations and gain confidence in rearranging equations because they have to. I also encourage them to use units to help them with unfamiliar or tricky problems.

4. ### blazerStar commenter

I will show them as an extra tool for handling some equations but they are just another thing to remember so I doubt they help much. I was asked for help during registration by one of my year 10s struggling with her maths revision. She was trying to solve equations (work out the value of x). After 10 minutes of sitting with her she could do them herself however the method she had been taught made absolutely no sense to me even though it did produce the right answer eventually.

5. ### ScienceGuyEstablished commenter

I use them with low ability students who struggle with the mathematical concepts. In the past, when no formula sheet was available, I used them more as they were a simple way of not only remembering the formula but automatically helped them rearrange it.

6. ### PaulDGOccasional commenter

Hate them and, as a maths teacher, I've always thought "I wish the Science department didn't teach these!"

But to see you're blaming us...?

Hmm. Someone, somewhere is teaching these as a short cut to gaining that next sub-level that will make the performance data look good.

Yet another thing we have to thank Ofsted for, I guess...

7. ### PaulDGOccasional commenter

This is the problem, isn't it?

That you're trying to teach them science the system hasn't given them the tools to access.

8. ### blazerStar commenter

If they don't understand algebra then they probably won't be able to use the triangles anyway.

9. ### BelleDuJourStar commenter

I use them. They work.

Bright students don't need them. Weak students find them simple.

I teach science and I leave the maths dept to teach the maths.

Really cannot see any issues using them.....just a simple tool that works.

10. ### wanetStar commenter

There is always one!

11. ### blazerStar commenter

Believe me Belle is worth 2!

12. ### steve_cookeNew commenter

It's difficult isn't it? You get used to finding kids who have no idea how to rearrange and therefore wonder why you are doing the maths department's job for them. In such circumstances it is no wonder science teachers opt for triangles.

However, when you challenge the maths department on rearranging they'll show you all these difficult equations being solved without a hint of a triangle. My suspicion is that the numbers habitually used in maths textbooks are so easy (eg x=2) that many of the kids may well be giving lip service to rearranging, but have worked out that it is actually more economical to be running trial and error calculations to find a small integer that will fit the equation. Those same kids get into Science where small integer answers are the exception, and give up before even really trying.

I've taught them in the past, but only as a tool and not spent loads of time on them.

14. ### PaulDGOccasional commenter

I think you've hit on something there.

Not that the kids are using trial & improvement or inspection but:

Yes. With the current (though it's hopefully changing) culture that was imposed on maths departments where there has to be progress every 20 minutes, doing enough practice to actually get to equations where the numbers aren't simple was rare.

As a result, we conditioned kids to be suspicious they'd made an error if their answer wasn't a simple, small integer.

We get kids in higher GCSE who are convinced they've made a mistake because they've an answer of 10.2 and "that can't be right" (because equations always result in small integer answers).

And we never have equations that result in answers that are best expressed in standard form.

That's definitely something maths departments should be looking at. (Though I will mention that I was disappointed when I was training to find that the attitude in even "outstanding" schools might be 'we don't need them to be able to do that [because it's not in GCSE] and so we can't afford the time to have them learn it'.)

15. ### steve_cookeNew commenter

Whichever of us right about the exact mechanism - and I think if you question them closely you'll be surprised how many "know" that x=2 long before they write down some workings to get there, just to pacify you - this also explains why they find basic trig so tough. It ought to just be rearranging a three term equation, with one extra step on the calculator added in, but there are no small integers anymore so in their heads it is something very different.

The other thing that I find them doing is memorising the pattern, they know, for example, that F=ma rearranges to give something equals something over something and will randomly assign variables into those slots in the hope that they have got it right! And that of course is the issue with triangles - it encourages the memorisation approach to problem solving.

16. ### BelleDuJourStar commenter

Cheers Blazer...................your cheque is in the post!

17. ### jsdcorreoNew commenter

http://TrianCal.esy.es - Open in Google Chrome. (Triangles online calculator developed by Jesus S.)

I propose this free online calculator triangles without advertising to help students with geometry, does not perform the duties, because their calculations formulas are not displayed. It is designed in a didactic way to check and view the realized duties.

TrianCal is online calculator triangles that works with any combination of values including sides, heights, angles, the area or perimeter of any triangle, calculating it with the minimum possible value (typically three).

Other functions:
- Draw the triangle (s) with GeoGebra.
- Set the range of values in each element.
- The type of angle.
- The type of triangle by its angles and sides.
- Selection of language (English or Spanish).
- Select the angle type [degrees (°), radians, degrees, minutes and seconds (° ' ") or degrees and minutes (° ')].
- Number of decimal places shown in the results (0-15).
- You can use the arrow keys and the Tab key to navigate through the settings.
- Drop-down menu to select the values comfortably.
- Create a link (URL) to the current triangle.
- An icon mail to communicate with the author.

NOTE: You must use the Google Chrome browser to display correctly TrianCal.

Examples of possible combinations:
- The area, perimeter and other data (side, height or angle), if the outside equilateral triangle would not need the third data.
- 2 angles and other data (if the value of the other data is not put aside the value of "a" at the time of drawing the triangle is 10).
- One side, one high and one angle.
- 3 heights.
- 3 sides.
- 2 heights and perimeter.
- Any other combination of values.

18. ### JameslabtechNew commenter

Formula triangles are great little tools if used right. They give a simplified visual idea on how to rearrange an equation. While I can see why people don't like them, they are something for lower years to use, possibly just KS3 or maybe just years 8 and below.

19. ### ah3069Occasional commenter

They are a means to an end, but I do think that as other people have said, allows the students not to gain the rearranging skills needed for equations with more than 3 components. So I think they're a double edged sword!

20. ### DonutBoy99New commenter

I'm surprised people dislike them so much. For me they are a tool useful for weaker students. More able ones don't need them. It'd be nice if weaker ones didn't need them, but one has to be pragmatic about it.

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