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Questions tagged [negative-numbers]

For questions on teaching students about negative numbers. Both formally and intuitively.

8
votes
5answers
422 views

Exponents with Negative Base; with or without Parentheses

How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$? I used to add "negation" to the order of operations, in the same row as multiplication and ...
5
votes
1answer
161 views

Why are fractions taught before negative numbers?

I'm not a math educator but I'm curious about this. Is this always true, or are there some schools/educational programs where students are shown negative numbers before fractions? Why is it done in ...
7
votes
3answers
343 views

Negative Denominator in Fractions; Importance and Applications

Why do we need fractions such as $\dfrac{3}{-5}$? I need a convincing answer suitable for 8th grade students. Here's what I've already thought of (which don't fully satisfy me!): Solving the equation ...
17
votes
12answers
2k views

Explaining the order of negative integers

Today I happen to have an interesting discussion with a primary school kid. I asked him "Which is the smallest one - digit integer?" He instantly replied $-1$. I told him that he's wrong and the ...
8
votes
3answers
352 views

Subtraction to Addition Conversion; how important is it?

Is it important to convert subtractions to addition, while simplyfing algebraic expressions (For example converting $3x-2y+7x-7y$ to $3x+(-2y)+7x+(-7y)$)? If yes, why and when?
7
votes
2answers
161 views

Online Resources to Explain Negative Numbers and Scientific Notation

I have to teach someone whose English isn't her native language (and her English skills aren't advanced) the concept of negative numbers + exponents, and how to read scientific / engineering numbers. ...
1
vote
2answers
130 views

How to preserve axioms from the positive numbers in the negative numbers?

It isn't so hard to convince students of grade 8. 9 that $-2$ is greater than $-4$, but it still make some confusion with an axiom says that ( The whole is greater than part ), which is true in the ...
8
votes
4answers
304 views

Should we rename the greater than sign?

As math teachers, sometimes we may wish that we could enter our students' minds to see how they think. In early years, while children are learning language, they build the concept of the word greater ...
25
votes
17answers
2k views

How to explain that a negative number multiplied by a negative number is a positive number, and that $-(-x)=x$?

Actually, there is no algebraic problem to show that $-(-x) = x$. This proof can be build upon the concept of the addition of the opposite like this: $- x + x = - x + [- ( - x) ]$, and thus by ...
32
votes
18answers
2k views

How to teach someone that $-3>-4$?

I am trying to teach a teenage person math, but he doesn't seem to be able to grasp the concept of negative numbers and $0$. Again and again he finds $-4$ greater than $-3$ because he has spent ...