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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.

5
votes
7answers
252 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 ...
6
votes
5answers
477 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 ...
6
votes
2answers
230 views

On fractions and 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 primer number, prime factorization and calculus of least common multiple. In ...
8
votes
6answers
293 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 $1/2$ ...
11
votes
7answers
1k 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. ...
3
votes
4answers
134 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 ...
18
votes
3answers
547 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 ...
16
votes
6answers
528 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?" ...
5
votes
0answers
67 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
337 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
201 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
261 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: ...
4
votes
0answers
201 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 ...
36
votes
13answers
7k 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 ...
16
votes
4answers
802 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 ...
11
votes
8answers
7k 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 ...
19
votes
4answers
1k 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 ...
10
votes
6answers
904 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 ...
9
votes
2answers
181 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 ...
7
votes
2answers
198 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 ...
27
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 ...
4
votes
2answers
615 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 ...
18
votes
5answers
2k 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 ...
45
votes
14answers
4k 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 ...