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Where do you need math, square roots, or algebra?

Students often wonder where in real life they would need any math skills. They do recognize the need for simple math, such as addition and multiplication, but in middle school, there are some topics where kids can start wondering why even study them (such as square roots or integers).

Then, in 8th or 9th grade, when students take algebra, many more can start asking this age-old question, "Where will I ever need algebra?"

The answer to that is that you need it in any occupational field that requires higher education, such as computer science, electronics, engineering, medicine (doctors), trade and commerce analysts, ALL scientists, etc. In short, if someone is even considering higher education, they should study algebra. You need algebra to take your SAT test or GED.

Algebra also lets you develop logical thinking and problem solving skills. It can increase your intelligence! (Actually, studying any math topic—even elementary math—can do that, if the mathematics is presented and taught in such a manner as to develop a person's thinking.)

You can admit to your student(s) that many mathematical concepts in algebra and beyond are not needed in every single occupation, especially in those of mostly manual labor. That is no big secret. Check Math Careers Database for the math requirements of 277 major occupations.

The website Algebra in the Real World has short movies, lesson guides, and student worksheets that show how algebra is used in with real word applications, such as roller coasters, banking, rice production, skyscrapers, solar power, and lots more.

Also, ask your students if they know for sure what they are going to do as adults. Most kids in middle school are not sure. If they are not sure, they'd better study algebra and learn all the math they can so that when they finally have some idea, they won't be stopped from a career because of not having studied algebra, geometry, or calculus.

And, even if students think they know what they want to be, how many times have young people changed their minds? Even we as adults don't necessarily know what kind of job or career changes are awaiting us. In times past, you could pretty well bank on either becoming a housewife (girl), or continuing in your father's occupation (boy). In today's world this is not so. Young people have more freedom in choosing - but the other side of that is that they need to study more to get a good basic education. Sometimes young people just need an adult to tell them that since they don't know all about their future, they need to keep studying, even math.

To futher help students see how mathematics and algebra are used in real world, check the free sample worksheets from Make It Real Learning activity books. These books focus on answering the question, "When am I ever going to use this?" and use REAL-LIFE data in the problems.

Another site to check out is Micron: Math in the Workplace, which contains a collection of real-world math problems and challenges contributed by a variety of businesses, demonstrating the relevance of math in today's world. Choose the "Math in the Worplace" tab.

Example: where do you need square roots?

As an example, let's say your students wonder, "Why do I need to know how to calculate the square root of a number? Are square roots really needed in life outside of math class?"

Here is one idea of how to show students one important real-life application of square root AND at the same time let them ponder where math is needed (and hopefully pique their interest into math problems in general). This lesson plan will work best when you have already taught the concept of square root but have not yet touched on the Pythagorean theorem.

  • Draw a square on board or paper, and draw one diagonal into it. Make the sides of the square to be, say, 5 units. Then make the picture to be a right triangle by wiping out the two sides of square. Then ask students how to find the length of the longest side of the triangle.

    The students probably can't find the length if they haven't yet studied Pythagorean theorem. But that is part of the "game". Have you ever seen an advertisement where you couldn't tell what they were advertising? Then, later, in a few weeks the ad would change and reveal what it was all about. It makes you curious, doesn't it?

    So, try to let them think about it for a few minutes and not tell them the answer. Hopefully it will pique their interest. Soon you will probably study the Pythagorean theorem anyway, since it often follows square root in the curriculum.
  • Then go on to the question: In what occupations or situations would you need to find the longest side of a right triangle if you know the two other sides? This can get them involved!

    The answer is: in any kind of job that deals with triangles; for example, it is needful for carpenters, engineers, architects, construction workers, those who measure and mark land, artists, and designers.

    One time I observed people who needed to measure and mark on the ground where a building would go. Well, they had the sides marked, and they had a tape measure to measure the diagonals, and they asked ME what the measure should be, because they couldn't quite remember how to do it. This diagonal check is to ensure that the building is really going to be a rectangle and not a parallelogram. It is not easy to be sure that you have really drawn the two sides in a right angle.

Now, beyond this simple example, you need to understand the CONCEPT of square root in order to understand other math concepts. Studying math is like building a block wall or a building: you need the blocks on the lower part so you can build on them, and if you leave holes in your building, you can't build on the hole.

The concept of a square root is a prerequisite to, and ties in with, many other concepts in mathematics:

  • square root → 2nd degree equations → functions & graphing
  • square root → Pythagorean theorem → trigonometry
  • square root → fractional exponents → functions & graphing
  • square root → irrational numbers → real numbers

See also:

Online resources for math in real-life - there exist lots of websites concentrating on this!

What can you do with a math degree? and Who hires math majors?
Math majors find employment in a variety of interesting and challenging fiels such as engineering, business, robotics, healthcare, and actuarial science, just to name a few.


Instead of using the shotgun approach, schools should be teaching either professional or trade schools as appropriate at high school level. You could then teach specific math principles as appropriate. I am looking at my kids geometry, calc. classes and thinking what a waste of valuable teaching time. You would need higher math skills to figure out the billions of wasted dollars spent teaching upper math skills for no reason. What a shame.

truth you

I've always hated math but I never thought it would keep me from getting a college education. I found it so difficult to pass that I just quit. I still haven't graduated...
You need math so you can graduate high school and go to college.


what kind of math skills do you need to be a construction worker
David Kutz

I think the best people to ask this about would be construction workers.... which I'm not. BUT I think construction workers would first of all need to know their geometry well, and everything about measuring and area and volume and such.

Then, you would probably need good grasp of percent and ratios... say maybe you're having to mix concrete, and you maybe need cement and sand and water in certain proportions in there...

And then, since construction work may involve all kinds of basic calculations, a construction worker probably needs to be able to do lots of mental math, and needs to be able to do rough estimates, as well as know how to do the exact calculations.

why do nurses study mathematics?
raizel magsalay

They need to know how to measure various things, understand metric system well with milliliters, milligrams, kilograms etc. They need to know how to calculate the right amount of medicine to give. Like for example, if you need to give 5mg of medicine per 10kg of body weight, then how much this person would need. Or, say 200mg of medicine as a tablet is equivalent to certain amount of the same stuff in liquid; then calculate how much is needed. They especially need to understand well decimal numbers and proportions.

I'm a bridge builder (carpenter) in San Diego, California who wishes I'd paid more attention in math class back when I was attending school. Every day now is a little bit of a math challenge. So in order to keep mt competitive edge in this high turn over industry I've desided to brush up on my math skills.

adrian chavira

what kind of maths do you need if you are a doctor? Is it the same as in nursing?

Medical doctors need a solid understanding of chemistry to understand the workings of the human body and how medicines work, and for that, they need to know math well. Doctors also need logical thinking and be able to understand scientific writing and reasoning, and good math skills are essential for that as well.

All in all, to-be doctors should study all possible math courses in high school: algebra, geometry, trig, calculus, statistics.

what kind of What jobs use pythagorean theorem?

Check this link Jobs using Pythagorean Theorem from Math Careers Database. You can see it is various engineers, architects, surveyors, carpenters and other construction specialists, machinists, etc. Basically if you need triangles when designing things, then you need Pythagorean Theorem. Also if you're making big rectangles on land, such as when planning a building or farmland, Pythagorean Theorem is useful to know so you can check your 'rectangle' has right angles.

Math Lessons menu
You'd be surprised at the level of mathematical expertise required in some "manual" jobs. I teach technical math at a community college, and constantly have students telling me they're using the trig and algebra concepts we're studying in class. One of the nicest things a student ever said to me is, "I do this stuff (meaning trig) in my machining class, but then I come here and I learn to understand it." When I taught technical math II, I was surprised at the sophistication of the course. Electrical technicians do lots of trig, vectors, complex numbers. The technical math sequence is not "easy". Never tell a student he won't need math in insert-profession-here. You just don't know.