14
votes
5answers
2k views

Is $ 5 $ nearer to $ 0 $ or $ 10 $?

My 6-year-old’s homework was “to find the nearest $ 10 $.” For example, $$ 42 \to 40 \quad \text{and} \quad 28 \to 30. $$ For $ 55 $, she answered “$ 50 $” and was marked wrong. How is this wrong? ...
2
votes
3answers
49 views

Commutativity or Distributivity - Which One to Use to DEFINE Multiplication of Negative Numbers?

It's easy to calculate $3 \times (-4)$, using the meaning of multiplication: $3 \times (-4)=(-4)+(-4)+(-4)=-12$. But it's not the case about $(-4)\times 3$! To DEFINE $(-4)\times 3$ we can choose ...
0
votes
0answers
143 views

Gauss' Summation Trick; Applications and Generalizations

I'm going to write an article about the summation trick attributed to Guass and its applications and generalizations. I'm sure you know what is the trick I mean: $1+2+\cdots+100=101+101+\cdots+101$ ...
3
votes
5answers
375 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
79
votes
24answers
6k views

Why is there no “remainder” in multiplication

With division, you can have a remainder (such as $5/2=2$ remainder $1$). Now my six year old son has asked me "Why is there no remainder with multiplication"? The obvious answer is "because it ...
82
votes
12answers
10k views

How to convince a math teacher of this simple and obvious fact?

I have in my presence a mathematics teacher, who asserts that $$ \frac{a}{b} = \frac{c}{d} $$ Implies: $$ a = c, \space b=d $$ She has been shown in multiple ways why this is not true: $$ ...
4
votes
3answers
152 views

Operations on negative integers

I was trying to teach my younger sister some math, and it drifted on to integers, and operations on negative integers. So questions like: a) $-3+2 = ?$ b) $2- (-3)= ?$ c)$-3 -2 = ?$ had to be ...
4
votes
3answers
89 views

First-grader problem in arithmetic

I found this problem in a text book on arithmetic for first graders (7 y.o.) of the former USSR* . The problem comes from the section that covers single-digit addition and subtraction. Here is the ...
2
votes
1answer
385 views

Complex division: polar form vs complex conjugate

The original problem In an electricity course which I volunteered to help with, the students solve circuits using phasors. Using phasors requires a good knowledge of complex numbers arithmetics, ...
4
votes
3answers
210 views

Cancel before multiplying!!

$$ \binom{12}6 = \frac{12\cdot11\cdot10\cdot9\cdot8\cdot7}{6\cdot5\cdot4\cdot3\cdot2\cdot1} = 924. $$ Sometimes it's hard to talk students out of computing both the numerator and the denominator in ...
1
vote
3answers
196 views

“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.
1
vote
0answers
560 views

How can I use an abacus to teach concepts to a toddler?

My 18-month old son got a $10\times10$ abacus as a Christmas present, and he enjoys it as a toy. I'm fine with him just playing with it, but I don't want to miss an opportunity to introduce ...
2
votes
1answer
356 views

what is teaching kids the rules and exceptions in multiplication called?

I recall reading a website quite some time ago about the rules and exceptions of multiplication with regards to teaching children. For instance: ...
2
votes
2answers
202 views

Can a rule be formulated to explain this to 7 year old?

I'm trying to teach math to my 7 year old daughter. I'm teaching following type of equations. $$\cdots - x = y$$ I'm able to explain her the rule that: when $\cdots- x = y$, we can always ...
40
votes
14answers
12k views

Why negative times negative = positive?

Someone recently asked me why a negative * a negative is positive, and why a negative * a positive is negative, etc. I went ahead and gave them a proof by contradiction like so: Assume $(-x) * (-y) ...
20
votes
15answers
17k views

How do I explain 2 to the power of zero equals 1 to a child

My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero. I have tried explaining it, but I guess not well enough. How would you explain the ...