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44 votes

Explaining the order of negative integers

To my mind, the problem is the word smallest. If you asked me which is smaller, $-1$ or $-9$, I'd ask you to clarify in what sense. Colloquial use of small refers to magnitude rather than ordering. It ...
Dan Fox's user avatar
  • 5,869
36 votes

Parentheses around negative numbers

It is not a good idea to against a convention, unless you have strong reasons for it. That said, you might not want to punish those going against the convention, either. An obvious reason for having ...
Tommi's user avatar
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26 votes

Why don’t American school textbooks recognize negative numbers as whole numbers?

I’m more curious about incorrect things in them. Yet, this is the first thing I found. There's absolutely nothing "incorrect" about this. As Dave L Renfro noted in a comment: and whole ...
R.. GitHub STOP HELPING ICE's user avatar
20 votes

Why don’t American school textbooks recognize negative numbers as whole numbers?

I don't think that "textbooks" decided this, usage did. The term "integer" covers positive and negative, so it would be redundant for whole numbers to refer to that category. And ...
Acccumulation's user avatar
17 votes

Parentheses around negative numbers

Others have talked about legibility, so I want to address the importance of the parentheses in an expression like $$17\color{red}{-}(\color{blue}{-}59)$$ from the perspective of educational psychology....
Justin Hancock's user avatar
14 votes

Explaining the order of negative integers

It seems to me that what you asked wasn't really right. -9 is the "lowest one-digit integer" but (at least it can reasonably argued) 0 is the smallest. Maybe making this difference explicit would ...
MatthewJohnHeath's user avatar
12 votes

Why in the FOIL Method the terms are taken with their signs?

I'm going to answer with something of a polemical frame challenge: FOIL is evil, and probably shouldn't even be taught. Okay... that's a bit extreme. How's this: FOIL is a mnemonic that is, in my ...
Xander Henderson's user avatar
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12 votes

Why don’t American school textbooks recognize negative numbers as whole numbers?

You seem to describe "whole numbers" in this American usage as describing $\mathbb {N}$, the set of natural numbers, whereas you expected it to describe $\mathbb{Z}$, the set of integers. As ...
Oosaka's user avatar
  • 301
11 votes

Explaining the order of negative integers

All 8 answers so far seem to have missed the following issue: Ask the student why he picked $-1$ rather than $1$ or $0$. If he changes his mind and says that $0$ is the smallest, then he is using ...
user21820's user avatar
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9 votes
Accepted

Explaining the order of negative integers

He wants to know the why, not per se the logic behind it. So give him a reason he can understand. Explain to him that many hundreds of years ago the concept of zero didn't exist. There was no number ...
Tschallacka's user avatar
8 votes

Explaining the order of negative integers

So $-9$ is "smaller" than $-1$? By that terminology, a bank account overdrawn by $9$ dollars (balance $-9$) would be said to carry a "smaller debt" than a bank account overdrawn by $1$ dollar (...
509-249-3447's user avatar
8 votes

Negative Denominator in Fractions; Importance and Applications

I would say you're doing your student a disservice if you were to seriously disallow a negative denominator. A fraction is simply a ratio of two integers (where the denominator is not allowed to be ...
A.Ellett's user avatar
  • 390
7 votes

Parentheses around negative numbers

Are there any reasons why this notation is necessary? Yes, of course - it is necessary to avoid easily avoidable errors introduced by unclear writing. While it may usually be obvious from context if ...
AnoE's user avatar
  • 848
6 votes

Why in the FOIL Method the terms are taken with their signs?

The issue isn't unique to factoring or the FOIL process. The roots of $(ax^2 + bx + c)$ can be found via the quadratic equation. $$x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$$ Now, this prompts the ...
JTP - Apologise to Monica's user avatar
6 votes

Explaining the order of negative integers

I will only add to the other excellent answers that even the words "less than" (the conventional name of the $<$ sign) can reinforce the (incorrect) notion that $<$ is used to compare the ...
mweiss's user avatar
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6 votes

Exponents with Negative Base; with or without Parentheses

You might explain that BEDMAS is not the whole story when it comes to the order of operations. There is an operation called negation. It reverses the sign on numerical quantifies. It gives the ...
Dan Christensen's user avatar
6 votes

Exponents with Negative Base; with or without Parentheses

I like the presentation on the NCTM Math Forum/Dr. Math website: We don't usually list unary operators in PEMDAS because they're thought of as being implied by the rules for binary operations. You ...
Daniel R. Collins's user avatar
6 votes

Explaining the order of negative integers

If he's ignoring the + or - signs, then that needs to get remediated. My approach is to: Define negative numbers as running to the left on the number line. (In other words, the "-" means "in the ...
Daniel R. Collins's user avatar
5 votes

Explaining the order of negative integers

Help him first to understand that subtracting 1 make numbers lower, lower and lower. Each time you subtract 1, you have less than before. Just like adding 1 will make them higher, higher and higher. (...
Paulo Amaral's user avatar
5 votes

Exponents with Negative Base; with or without Parentheses

I tutored a student who had a hard time understanding this, and the way that helped him to understand it was this: Any time there is a negative sign on a number, we can read it as $(-1)$ . So $-5 \...
Davy M's user avatar
  • 150
5 votes

Is a clear distinction made between signs and operators?

It can definitely be confusing, and a clear distinction should be made when teaching. It's not always made, and students can in fact remain lost for a long time. I've seen students who thought $1 \...
DS.'s user avatar
  • 191
4 votes

Why in the FOIL Method the terms are taken with their signs?

Simple answer: Including the signs/negative numbers is algorithmic. Working out the sign afterwards requires thinking. Imagine writing computer code to multiply out the brackets. You would do it by ...
Jessica B's user avatar
  • 5,840
4 votes

Exponents with Negative Base; with or without Parentheses

If your students already understand that exponents precede multiplication, and that multiplying by $-1$ is the "negation" operator, then you should be able to convince them that $$-5^2 = -1*5^2 = -1*...
Nick C's user avatar
  • 9,729
3 votes

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

I won't try to give a specific explanation here because I think that depends highly on the level of knowledge of the student. Rather, I'd like to emphasize some general points that I think are helpful ...
Bill Dubuque's user avatar
  • 1,038
3 votes
Accepted

Why are fractions taught before negative numbers?

In the US, we have the controversial Common Core. A summary of it is available here. In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole ...
JTP - Apologise to Monica's user avatar
2 votes

Negative Denominator in Fractions; Importance and Applications

There are numbers that one (or many) may never use, is this a reason to eliminate them. Is there a reason to have 1 to any non-negative integer power? When responding to questions of this type "Why ...
Sid Hollander's user avatar
2 votes

Online Resources to Explain Negative Numbers and Scientific Notation

You can find lots of information on this site for mathematics: http://www.webmath.com/sn_convert.html
LCarvalho's user avatar
  • 193
2 votes

Explaining the order of negative integers

There is a great board game that I use with my third graders which teaches negative numbers. It's called Midnight Party or Ghost Party. In the game the students can get captured and get sent to a ...
Amy B's user avatar
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