# Tagged Questions

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### Intuition for high school students regarding square roots and logarithms [duplicate]

These are some common mistakes high schoolers make: $$\sqrt{a + b} = \sqrt{a} + \sqrt{b}$$ $$\log(a+b) = \log (a) + \log(b)$$ So I can obviously show numeric examples to say why these are wrong, ...
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### When $n$ is divided by $14$, the remainder is $10$. What is the remainder when $n$ is divided by $7$?

I need to explain this to someone who hasn't taken a math course for 5 years. She is good with her algebra. This was my attempt: Here's how this question works. To motivate what I'll be doing, ...
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### $2^{1/4} \times 4^{1/8} \times 8^{1/16} \times 16^{1/32} \times \ldots\to2$

$2^{1/4} \times 4^{1/8} \times 8^{1/16} \times 16^{1/32} \times \ldots\to2$ How can I explain this to a school student who doesn't know what a limit is?
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### Transitioning to Higher Level Mathematics

I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are ...
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### Teaching School Algebra via Programming

It seems that there are ideas to teach school algebra (i.e. using variables, working with algebraic expressions and solving equations) via computer programming. I need a book or a collection of ...
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### Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...
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### How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
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### What is an effective means to make divisibility tests a mathematical 'habit', particularly for algebra?

Divisibility tests are a useful problem-solving technique for particularly dealing with larger numbers (thousands etc) and algebraic problems. However, I have always found that many students will just ...
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### Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
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### Turning an ellipse into a parabola

Today I was discussing circles, ellipses, hyperbolas, and parabolas in my precalculus class. We did the usual: completing the square, finding the center and radius (radii), etc. etc. But I like to ...
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### Is this way of teaching how to solve equations dangerous somehow?

Two years ago, I bought the book Mathematics for the Nonmathematican, by Morris Kline. There I learned a new way of solving equations, which is related to the principle that states that any ...
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### How can I introduce complex numbers to precalculus students?

I teach a precalculus course almost every semester, and over these semesters I've found various things that work quite well. For example, when talking about polynomials and rational functions, in ...
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### Polynomials and exponentials: showing that $n^k \le c\cdot a^n$

If $k$ is any real and $a>1$, prove that there exists a $c>0$ such that for any integer $n\ge 1,$ $$n^k \le c\cdot a^n$$ To forestall any complaints about the imperative nature of this ...
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### “Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
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### “the product of the factors” versus “the factors of the product”

Could somebody please compare and contrast the meanings of the two phrases: "the product of the factors" and "the factors of the product." In terms of expressing possession. Thank you.
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### High school math definition of a variable: the first step from the concrete into the abstract…

variable: A symbol used to represent one or more numbers. High school students are justifiably confused by the two distinct concepts: a variable as something that “varies” in an expression, such ...
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### When my teacher gives me a question involving summation notation, do they expect us to calculate it by hand?

Assuming we don't have a calculator that can do summation notation. My class is not up to summation yet, but I'm asking a question involving this concept because I'm not all that experienced using it. ...
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### Should the domain of a function be inferred?

It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...