# Questions tagged [arithmetic-operations]

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### Speed math appropriate for middle-school students

There are many "rules" for speed arithmetic. List of some reference links showing speed methods or rules: https://ofpad.com/multiplication-tricks-for-mental-math/ https://ofpad.com/mental-...
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### Order of operations pemdas

Why was the order of operations established in mathematics with multiplication taking precedence over addition, as dictated by the PEMDAS rule? What historical or practical factors influenced this ...
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### Why are there two inverses to exponentiation?

I'm not sure if this is more educational or more "pure math", but: For multiplication and addition, there is exactly one inverse operation, namely division and subtraction. For ...
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### Reduction of fractions

Last night I was fiddling with some equations and admittedly, I made a careless mistake because I was exhausted. However, in doing so, I began to question the process of what I used to understand as &...
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### Is it normal for a child to strongly prefer addition to subtraction?

My six-year-old daughter enjoys addition but not subtraction. When we walk together, I like to give her some "mental mathematics" questions, such as "What is 13 plus 33" and she ...
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### Math dyslexia is a big problem for me. I lag behind my classmates

I am a 17-year-old secondary school student from India studying math, physics, and other subjects. I lag behind other classmates only because I work slowly when doing addition, subtraction, ...
263 views

### How to convince a high school student that the $=$ symbol denotes identity?

In French language, arithmetic statements are often read, at the elementary school level, as , say, " deux et deux font quatre" , i.e. something like " two and two make four". Out ...
200 views

### Is there a name for this method of column addition and subtraction?

Suppose I want to subtract 46 from 52. Instead of the borrowing method, I can use this method: \begin{array}{r} & 5 & 2\\ -\!\!\!\!\!\!& 4 & 6 \\ \hline & & -4 \\ +\!\!\!\!\!\!&...
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### What is a good math "curriculum" for a mathematically precocious 4-year old?

I am parent to a 4-year-old son who is mathematically precocious. An example of what I mean (since I'm sure guys like Gauss were proving theorems at 4): He multiplies and divides small numbers easily,...
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### Analyzing an answer to the following problem: Give meaning to $\frac{4}{5} + \frac{2}{3}$

Case: Exam Problem given to student at university: Give a problem/context illustrating the operation $\frac{4}{5} + \frac{2}{3}$ Answer by student: Anna and Beatrice buy flowers for grandpa for his ...
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### Did Americans, before new math came in to schools, really say, 'three from two is nine carry the one", instead of borrowing ten from the tens column?

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one'. I never heard of this ...
5k views

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### What's the word for addition and subtraction without borrowing or carrying over?

Is it regrouping? Upon googling it seems regrouping is borrowing or carrying over collectively. What's the word for not borrowing and carrying over? It's supposedly to train mental computation. ...
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### How to use these actions words for subtraction?

Do the following sentences express 5-2? a. 5 fewer 2 is 3 b. 2 fewer than 5 is 3 c. 5 less 2 is 3 d. 5 gave 2 is 3 I also saw online that "shared" can also mean "...
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### Learning operator priorities by drawing trees

As far as I know (and here I am refering to my own math education), operator priorities of $+$, $-$, $\cdot$, $\div$, power and parenthesis are taught via some simple phrases like "pointy" ...
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### What is the pedagogical justification and history for using mnemonics to teach order of operations?

There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by ...
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### Why is modulo not an elementary operation?

Like it is just as primitive as makes intuitive sense in a way similar to division. I feel like teaching 4th graders the modulo function would complement learning division extremely well, as it helps ...
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### Proof of why BODMAS (or BIDMAS) works?

In my first full-time teaching post, it is very likely that I'll need to be teaching a small amount of GCSE Mathematics to students retaking it. One thing that has been bugging me is that I can't seem ...
378 views

### Teaching arithmetic operations ($+ - \times \div$) to a 3 year old

What is the best way to teach the standard arithmetic operations ($+ - \times \div$) to a 3 year old child? Also: How we do know if the child has really understood it? can a kid be 3 years old ...
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My daughter showed me the picture below, which came from 9GAG. It shows a question on an exam asking the student to "use the repeated addition strategy to solve: 5 x 3." The student answered "5+5+5" ...
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### Method for teaching factorization

A while back I stumbled on teacher's website that advocated a different way to teach factorization. Rather than jumping straight to factorization practice, the teacher first had their student's ...
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### Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
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### How do I help a 6-year-old understand the meaning of her sums

I am tutoring a Grade 2 girl in arithmetic. She has demonstrated an ability to add two-digit numbers with carrying. For example: $$\;\;14\\ +27\\ =41$$ I asked her to write this out horizontally, ...
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### Parse out 2/3 of 30 minus 11

Note - I am not a math teacher; I am seeking an answer from a math teacher. While helping my son with his 5th grade homework today we had one answer wrong. I'm not sure I agree with the book and ...
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### Is there any other procedure to find the square root?

If no calculator is allowed, and we want to find the square root of a square number if it is large and analyzing to prime factors is hard, how can one proceed? For example, what to do if the number ...
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