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17 votes

Is This Trick Helpful?

I do not think that such tricks are helpful: in fact I believe they are deeply damaging. These types of basic relationships should not be memorized: they should be derived on the fly from an ...
Steven Gubkin's user avatar
16 votes
Accepted

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

I think the heuristic \begin{align*} \frac{8}{4} \quad \longleftrightarrow \quad 8 \textrm{ out of every group of } 4 \end{align*} still makes sense if you emphasize that you want $8$ slices of pizza ...
Justin Skycak's user avatar
11 votes

How is $\frac{a}{b}$ interpreted?

A US specific answer: The Common Core State Standards define $\frac{1}{b}$ by saying it is one of $b$ equal parts making up a whole $1$. $\frac{a}{b}$ is then defined as $a$ of these. Connecting $\...
Steven Gubkin's user avatar
8 votes

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

If you are tutoring, it's important to value whatever algorithms work. Your frustration with the (new to me) lovely algorithm you show concerns me. It shows why each step makes sense, which is much ...
Sue VanHattum's user avatar
  • 20.8k
8 votes
Accepted

Determining the first digit of the Quotient using hand long division efficiently?

The awkwardness of "guessing" in the division algorithm is an artifact of the base-ten representation of numbers. If you represent in binary, then your only possible "guess" is 1. In binary, your ...
user52817's user avatar
  • 11k
7 votes

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

Not a teacher here, but I noticed when my kids went to school there was far less emphasis than I remember on techniques that require above average insight or intuition. I think there's more pressure ...
Cristobol Polychronopolis's user avatar
6 votes

What are strategies that a 10-13 year old could use to convert 6/27 into decimal notation?

I prefer method 2, which has the student simplifying first. Even if the student doesn't know that $ \frac{1}{9} = 0.\overline{1} $, the student can still divide 2.00 by 9. If the student uses ...
Amy B's user avatar
  • 8,017
5 votes

How is $\frac{a}{b}$ interpreted?

A key idea in maths education, that at least becomes more visible at university level, is that people tend to start thinking of new ideas as processes, but to do more advanced maths they need to move ...
Jessica B's user avatar
  • 5,822
4 votes

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

Long division is a useful thing to teach because at some point, polynomial long division is going to be something that someone is going to want to teach them, and it helps if they've seen something ...
user3482749's user avatar
4 votes

How is $\frac{a}{b}$ interpreted?

By definition, a rational number is a number that can be expressed as the quotient of two integers. This quotient is called fraction and is written as $\frac{a}{b}$. Hence, division and fraction are ...
Rusty Core's user avatar
  • 1,317
4 votes

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

Justin Skycak wrote a great answer that you can use with your kids, but I'd like to explain how what you're telling them relates to what they might be seeing right now and later on in school. I'll be ...
Justin Hancock's user avatar
3 votes

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

Justin H has a good answer emphasizing how fractions are a complex topic and we learn more and more about them over the years. To your specific question, I would emphasize the need to spend a ...
Guest troll's user avatar
3 votes

What are strategies that a 10-13 year old could use to convert 6/27 into decimal notation?

Simplify first. Then do the problem by long division. With a number of such problems, the student will quickly realize that 2/9 gives .222... and 4/9 gives .4444 and the like. It's actually a good ...
guest troll's user avatar
3 votes

Is This Trick Helpful?

I teach Year 7 and I’m with Steven on this. Sort of. If a “trick” reminds you of a correct understanding that you’ve already established, then it is a procedural memory aid and shortcut. Nothing ...
lukejanicke's user avatar
3 votes

Is This Trick Helpful?

$$a=\frac bc\implies \;c=\frac ba.$$ What you propose above is one of the if/thens that students should pick up after seeing it in practice a couple times. The 'long' way has them multiplying both ...
JTP - Apologise to Monica's user avatar
3 votes

Determining the first digit of the Quotient using hand long division efficiently?

Round. Check. Correct. What we need is $436\div48$. Rounding to remove the last digit reduces the problem to $44\div5$. This gives us an educated guess of either $8$ or $9$. From here we then ...
Simply Beautiful Art's user avatar
3 votes

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

Both of my sons are learning division right now (or rather, just finished the section), one in a public school using Eureka Math (in 4th grade level math), one in a Montessori (in Primary, at 1st ...
Joe's user avatar
  • 161
2 votes

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

Doing a quick google search for "why do students struggle with division?" made me realize myself why long division is difficult for a lot of students. Common reasons claimed include: The long ...
Simply Beautiful Art's user avatar
2 votes

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

I know I am late to the party, but I absolutely hate short division. It works for simple division problems, for those that you can almost do in your head. But try dividing 35/43 or 692/37. This is ...
CherG's user avatar
  • 21
2 votes

How to solve the simple elementary school math issue--calculate increase rate

A company will use NM indicating, as you noted, "No Meaning". This is less of a right/wrong problem as it is a problem that opens up a discussion. The actual meaning of these +/- percents ...
JTP - Apologise to Monica's user avatar
1 vote

Is there a way to extend the analogy that fractions means "x out of y" to show that fractions are also dividing?

We teach that there are two basic ways of understanding division. På norsk they are called delingsdivisjon and målingsdivisjon; sharing division and measurement division would be rough translations. ...
Tommi's user avatar
  • 7,202
1 vote

How is $\frac{a}{b}$ interpreted?

Adding another view to the point, one could view a fraction $\dfrac{a}{b}$, as a symbol indicating a change of measure unit. More precisely, talking about integers, at first, what does e.g. $7$ mean? ...
Vassilis Markos's user avatar
1 vote

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

One of the benefits of the partial quotients division method as illustrated above with 186 / 3 is NOT in dividing by single digit divisors but in multi-digit divisors. Students are generally taught ...
Slowworm's user avatar

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