Where do you need math, square roots, or algebra?
Students often question whether they will need any math skills in real life. They probably recognize the need for simple math, such as addition, multiplication, fractions, and percents, but in middle school some students start wondering why even study certain concepts, such as square roots or integers. Then, in 8th or 9th grade, when they take algebra, many more teenagers start asking the age-old question, "Where will I ever need algebra?"
The answer is that you need algebra in any occupation that requires higher education, such as computer science, electronics, engineering, medicine (doctors), trade, commerce analysts, ALL scientists, etc. In short, if someone is even considering higher education, they should study algebra. You also need algebra to take your SAT test or GED.
Studying algebra also has a benefit of developing logical thinking and problem solving skills. Algebra can increase your intelligence! (Actually, studying any math topic — even elementary math — can do that, if it 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 studied in high school algebra, calculus, and beyond are not needed in every occupation. Geometry concepts are very useful though for just about everyone. You never know if you might build a house or a shed!
However, deciding to NOT study algebra presents a big problem, because most teens in middle school are not sure what they are going to do as adults. In that case, they are better off studying algebra and learning all the math they can so that they won't be stopped from a career because of not having studied it. There have been many students who have been bitterly disappointed when after high school they could not (at least not immediately) go into the field of study that interested them for lack of math skills.
And, even if students think they know what they want to be, how many times have young people changed their minds? Even we adults don't always 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 flipside of that is that they need to study a lot more to get a good education. Since they don't know all about their future, it's far better to study, 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.
Example: where do you need square roots?
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 real life outside of math class?"
Here is one idea that showcases an important real-life application of square roots and at the same time lets students ponder where math is needed. This idea will work best after you have already taught the concept of square roots 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 studied the Pythagorean theorem yet — but that is part of the "game". Have you ever seen an advertisement where you couldn't tell what they were advertising? Then, in a few weeks the ad would change and reveal what it was all about. It makes you curious.
So, let them think about it for a few minutes (don't tell them the answer at first). Hopefully it will pique their interest. Soon you will probably study the Pythagorean theorem anyway, since it often follows square roots 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 construction people who were measuring and marking on the ground where a building would go. 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 trapezoid or some other shape.
Now, beyond this simple example, students need to understand the CONCEPT of a 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, 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
Online resources for math in real-life - there exist lots of websites concentrating on this!