Questions tagged [fractions]
For questions about the teaching of fractions and their interpretations. Fractions are numbers of the form $p/q$, where $p$ and $q \neq 0$ are integers.
34
questions
17
votes
15answers
17k views
How to explain the difference between the fraction a / b and the ratio a : b?
I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...
8
votes
4answers
1k views
Why do some students struggle so much with fractions?
I read on multiple web pages something that implies that that some students really struggle with fractions but I could never find a detailed explanation of why. This question is different from Are ...
1
vote
2answers
213 views
How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?
I am teaching math to a 10 year old student. He learned that
$$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$
and
$$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
6
votes
5answers
253 views
Concrete way to teach addition and subtraction of fractions
I am teaching 4th-grade kids. The topic is Fraction. Basic understanding of a fraction as a part of the whole and as part of the collection is clear to the kids. Several concrete ways exist to teach ...
0
votes
1answer
82 views
Applications of unreducible fractions in Basic School
An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (...
7
votes
10answers
2k views
How to explain fractions to 7 year old kid
I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out ...
9
votes
5answers
797 views
Don't these word problems seem designed to be confusing?
I'm a fairly new private math tutor, and I'm good at math (I have a BS from Caltech with lots of graduate level math), but becoming good at teaching math is something else, which I strive to improve ...
5
votes
3answers
227 views
Algebra/trig/precalculus review questions that elicit common student errors
This semester I have decided to give students a simple question or two at the beginning of every calculus class that will trap them into making the most common errors that we all know...e.g. the ...
43
votes
17answers
9k views
How to explain the flipping of division by a fraction?
This question is inspired by @DavidButlerUofA's discussion of
"$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in
"Are fractions hard because they are like algebra?"
Q. How can one best convey to ...
7
votes
4answers
327 views
How is $\frac{a}{b}$ interpreted?
I was having a discussion with a colleague who is in the process of writing some curriculum, and we ended up having a discussion about what $\frac{a}{b}$ (with all the standard restrictions) meant. We ...
18
votes
6answers
3k views
Models and strategies for teaching fractions in 7th grade mathematics
I'm a first year student at a university college, and I'm currently teaching 7th grade for a few weeks as a part of my education. I'm struggling a bit with finding models and strategies to develop an ...
12
votes
7answers
1k views
How to teach quick multiplication and division in head?
I recently started giving maths lessons and it seems like I am at my wits end. My own background is: I'm a masters student in physics, already did several tutorials for younger students, especially ...
12
votes
8answers
2k views
How to teach sum of fractions to students?
I think almost every middle school student in my country has learned sum of two fractions in this non reflexive way (I'm included when I was kid), doing the following steps:
They calculate the lcm.
...
7
votes
3answers
331 views
On fractions and the least common multiple
At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of prime numbers, prime factorization, and the calculation of the least common ...
3
votes
2answers
210 views
Where to find good exercises for term operations?
I'm searching for exercises for practising operations with terms. They should involve
working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like ...
3
votes
3answers
202 views
How to explain to pupils that “$\frac n{100}$ OF $a$” is equivalent to “$a$ TIMES $\frac{n}{100}$”?
How to explain to pupils that "$\frac n{100}$ OF $a$" is equivalent to "$\frac{n}{100}\times a$"?
There is some difficulty in explaining that the first sentence, containing "OF" (which could suggest ...
2
votes
4answers
219 views
What is the standard for “simplifying your answer”?
Most problems require the student to simplify the final answer and in many context the meaning is obvious: For example, $3/9$ should be simplified to $1/3$ and $\sqrt{16}$ should be simplified to $4$.
...
-4
votes
2answers
365 views
Could schools jump straight into teaching real numbers first then teaching fractions later?
Some students really struggle to learn fractions. Not only that but also, once they've mastered an understanding of real numbers, they can learn about fractions so much faster and more efficiently ...
4
votes
0answers
223 views
Is there a meeting place for fraction education stakeholders?
Is there a meeting place where all fraction education stakeholders (students, teachers, parents, researchers, fraction software developers) meet and collaborate? If not, do you have an advice on ...
19
votes
3answers
689 views
Constructive refutation of student misconception
Although @Gareth Shepherd recently posted Addressing fundamental math errors close to the issue, I experienced my problem of misunderstanding in class, where two good K10 students were asked to ...
8
votes
6answers
1k views
How to explain multiplying and dividing by fractions with real-world examples
I'm looking for a good way to explain how multiplication and division by fractions applies in the real-world the mechanics are receiving reasonably straight forward.
How can $2$ divided by $1/2$ ...
51
votes
14answers
5k views
Should we say that fractions “are” or “represent” numbers?
I never gave this a second thought until a friend who works in education brought it up the other day. Should we say that a fraction like $\frac{1}{2}$ "is" a number, or "represents" a number? In ...
3
votes
4answers
151 views
How do you explain the whole integer and fractions subject to a kid in 6th grade?
Problems like
There is 30 students in the class. $\frac13$ of the students study biology, $\frac15$ of the students study physics and the rest study chemistry. What part of the class studies ...
28
votes
6answers
1k views
What is the rationale for the absent (+) in mixed fractions?
Why are students taught to represent one and a half as $1 \frac{1}{2}$ rather than $1 + \frac{1}{2}$? This mode of expression seems standard at least throughout North America. I believe that it is bad ...
18
votes
6answers
815 views
How to teach students when they can and can't cancel factors in a fraction?
I mainly tutor adults in college algebra classes or lower. Sometimes an expression like $\dfrac {x+5}{5}$ will come up, and the students will say:
"We can cancel out the $5$'s and get $x+1$, right?"
...
6
votes
0answers
79 views
Resources for teaching algebraic fractions to a dyscalculic pupil
I have a new student in math class (high school) since last month, and she's being diagnosed with dyslexia and dyscalculia. We are about to go into conic sections and she should be able to do some ...
7
votes
3answers
766 views
Negative Denominator in Fractions; Importance and Applications
Why do we need fractions such as $\dfrac{3}{-5}$? I need a convincing answer suitable for 8th grade students. Here's what I've already thought of (which don't fully satisfy me!):
Solving the equation ...
7
votes
3answers
606 views
A good antonym for reducing/simplifying equivalent fractions
I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply ...
4
votes
3answers
286 views
The meaning of equal sign in unit conversion
Recently, I read a paper about student's understanding of fraction. Most students mentioned in the paper had given $5/8$ as their answer to the following question:
...
18
votes
4answers
1k views
Are fractions hard because they are like algebra?
It occurs to me that to really understand the ways that people work with fractions on paper requires a good grasp of the ideas that numbers have multiple representations and that expressions can be ...
19
votes
4answers
2k views
Is algebra really the gatekeeper to higher math, or is it multiplicative reasoning?
The National Mathematics Advisory Panel final report states that algebra is the gateway to higher math, to a college degree, and higher earnings from employment. It also states that success in algebra ...
8
votes
2answers
227 views
Teaching “and a half” early, possibly before general proper fractions
Fractions are a well-recognised issue in maths learning, with all sorts of complex issues involved. One particular aspect of this is difficulty recognising fractions as numbers which describe the size ...
10
votes
2answers
206 views
Using terminology for the different concepts of rational number
In elementary maths education literature, they distinguish multiple concepts that rational numbers are used to represent: fractions, quotients, ratios, rates, and possibly more. These words seem to be ...
4
votes
2answers
1k views
Teaching fractions: the generalization problem
I've been thinking about how you would go about teaching fractions, and there seems to be a problem in that every basic fact needs to be proven/explained twice, using two different layers of ...
