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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
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
  • 21k
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
4 votes
Accepted

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

This topic seems to be called "Bridging 10s" or "Making 10s": http://www.helpingwithmath.com/by_subject/addition/making-10-1oa6.htm I'm not sure that you will find many discussions about the utility ...
Opal E's user avatar
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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
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
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
2 votes

Tricks for computing things in your head

Multiplying whole numbers times $25$ is counting quarters. Many American students find this easy. Getting a better that whole number approximation of square roots is possible using $$\left( a+\frac{...
Jim H's user avatar
  • 351
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
1 vote
Accepted

Math dyslexia is a big problem for me. I lag behind my classmates

Have you tried bringing this to your math teacher's superiors? It seems to me a perfectly good case for them to make an exception to the "no calculator" rule. Normally teachers/schools don't ...
cody benedict'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
1 vote

Tricks for computing things in your head

Let me give you some insight how I calculate things by heart: First we start with the simple formula: $a^2-b^2=(a-b)*(a+b)$ This can be used for two things: perform a multiplication calculate a ...
Dominique's user avatar
  • 2,165
1 vote

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

When I studied those things, in Spanish it's was called "suma algebraica", i. e., algebraic sum. Numbers in a term could be positive or negative.
Tavasanis's user avatar
  • 161
1 vote

Tricks for computing things in your head

It's not really mental math, but it is more useful that one might expect. And it encourages students to see factoring and grouping possibilities. Evaluate $P(x) = x^3-7x^2+6x-8$ at $x = 3$. $$P(3) = ...
Jim H's user avatar
  • 351
1 vote

Tricks for computing things in your head

To multiply two numbers from $11 - 19$, written in base ten as $1a$ and $1b$, we can use, $(10 + a)(10 + b) = 100 + (a + b)10 + ab$ It could be remembered as 'One add multiply'. For example, $ 12 ...
Tom's user avatar
  • 333

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