# Questions tagged [arithmetic-operations]

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### Generating system of equations with unique solutions

I have a similar problem addressed in System of Equations Generator. What I need is an automatic way of generating a system of equations with unique solutions, but the equations are not exclusively ...
196 views

### At what age are most children able to convert between rational fractions and decimals?

At what age are most children able/taught to convert between rational fractions and decimals? For example Convert 0.25 to a fraction consisting only of whole numbers. What is 3/4 expressed in ...
209 views

### How to naturally encounter the properties of identity, commutativity, associativity, and distributivity (to define rings)?

(Cross posted at MSE: https://math.stackexchange.com/questions/3742948/how-did-we-isolate-the-properties-of-identity-commutativity-associativity-and) In elementary school, I remember learning about ...
218 views

### Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...
1k views

### Different ways to multiply decimals

I am an undergraduate secondary math education major. In $2$ weeks I have to give a Number Talk in my math ed class on the problem "$3.9$ times $7.5$". I need to come up with as many different ...
6k views

### Is short division taught these days and if not, why not?

tl;dr I'm interested in opinions on short division. Below I discuss my experience dealing with young children and long division versus short division. For those that don't know of it, wikiHow has a ...
186 views

### Introductory exercise for the addition of large natural numbers

I'm starting a repetition with my students in 5th grade after they learned in elementary school how to sum up larger natural numbers (also 5- to 6-digits) by writing down that calculation. As ...
3k views

### A PEMDAS issue request for explanation

This question made the rounds recently - $8÷2(2+2)=?$ Now, I glanced at this, answered "1" and then saw the full article printed in the New York Times, The Math Equation That Tried to Stump the ...
155 views

### Is a clear distinction made between signs and operators?

This question about FOIL, comments and answers made me think about the two roles of $-$: as a sign and as an operator. This struck me because the title "Why in the FOIL Method the terms are taken ...
242 views

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

That was the most boring title I could choose but in all honesty, it is what the question is. Here is a reminder of the FOIL method that is used for multiplying two binomials. For example, to multiply ...
187 views

### Teaching three-year-old subtraction using the number line

I am aware of questions such as this one. On the other hand, I still believe that teaching a bright three year old subtraction is possible. He counts from $0$ to $100$ and backwards from $10$ to $-10$,...
160 views

### Viewing arithmetical operations as processes-possibly wrong and detrimental to long term math performance of the students [duplicate]

I think that the standard practice in the first grades when addition (or other operation) is taught as a "process" may be not so good. I always wondered why so many children lose interest in math ...
831 views

### How to correct visualization of mathematical expressions?

This happens a lot when I try to explain the commutative property, mostly in elementary grade levels. I say 2 + 3 = ? and then the student usually replies with 5. Albeit they're not wrong, it's not ...
712 views

### Third Grade Question — This makes no sense to me

Third grade grandchild had this for homework. Can someone explain the intent here?
374 views

### Has Benezet's teaching experiment ever been reproduced?

In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6: In the fall of 1929 I made up my ...
117 views

### How to present the order of factors and summands for the usual multiplication procedure

In the following multiplication example, \begin{align} 34\;& \\\underline{\times\;\; 7\;}& \end{align} first one would multiply the units digits, producing the partial product $28$ as ...
447 views

### Subtraction using Addition (Austrian Method), is it useful to learn this method instead of the usual “borrow” method?

I came across this method to perform subtraction using addition and not using the "borrow" concept, apparently because it is harder to learn it that way. Video - https://www.youtube.com/watch?v=...
572 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 ...
388 views

Some teachers teach multiplication between integers with the following rules: plus with plus gives plus plus with minus gives minus etc. So for example in order to deal with the multiplication $2\... 2answers 231 views ### What's the word for addition and subtraction without borrowing or carrying over? Is it regrouping? Upon googling it seems regrouping is borrowing or carrying over collectively. What's the word for not borrowing and carrying over? It's supposedly to train mental computation. ... 1answer 67 views ### How to use these actions words for subtraction? Do the following sentences express 5-2? a. 5 fewer 2 is 3 b. 2 fewer than 5 is 3 c. 5 less 2 is 3 d. 5 gave 2 is 3 I also saw online that "shared" can also mean "... 3answers 148 views ### Learning operator priorities by drawing trees As far as I know (and here I am refering to my own math education), operator priorities of$+$,$-$,$\cdot$,$\div$, power and paranthesis are taught via some simple phrases like "pointy" operators (... 3answers 587 views ### What is the pedagogical justification and history for using mnemonics to teach order of operations? There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by ... 3answers 563 views ### Why is modulo not an elementary operation? Like it is just as primitive as makes intuitive sense in a way similar to division. I feel like teaching 4th graders the modulo function would complement learning division extremely well, as it helps ... 8answers 10k views ### Proof of why BODMAS (or BIDMAS) works? In my first full-time teaching post, it is very likely that I'll need to be teaching a small amount of GCSE Mathematics to students retaking it. One thing that has been bugging me is that I can't seem ... 4answers 315 views ### Teaching arithmetic operations ($+ - \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 ...
4k views

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 ...
149 views

### 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 ...
217 views

### 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, ...
650 views

### 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 ...