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I am teaching a group of 8 kids on fractions and I did not realize how difficult this can be. These kids were selected by their teachers for needing additional outside help. I really need some advice, it seems that only 1 kid understands me and what is going on whereas the others are confused.

They have troubles doing problems like these:

$\frac{1}{6} + \frac{1}{8} $

$ 2 \frac{1}{2} - 1 \frac{3}{4}$

I've explained them to go 1) find the LCD first and then 2) put the fractions in an equivalent form (i.e. 1/3 = 3/9) and then 3) add or subtract. At first I thought that by breaking it down to these steps the kids would understand but they get confused and forget.

For example $2 \frac{1}{2}$ could be rewritten as $2 \frac{2}{4}$. I then tell them to do the following operation: $2 \frac{2}{4} - 1 \frac{3}{4}$. I tell them that they're really figuring out this: (2 - 1) + ($\frac{2}{4}$ - $\frac{3}{4}$). They get really confused. Then I tell them to look at the fractions for now and ignore the whole number. They still get confused. I am up to my wits end. Not only that but they have trouble with LCM. All they want is to leave the room and not look at fractions. How can I get through these kids?!

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I would recommend an intuitive approach that they can grasp.

Buy a pizza and a cake.

Ask them how we would know how to cut them up to divide them equally.

This is fractions.

Now, show a picture of halfs and that each is represented by the fraction $\frac{1}{2}$.

What allows us to add the fractions together is the common denominator.

Repeat for $3, 4, 10$ and the actual number of students in the class.

Break, have pizza and cake as now, they'll have interest.

Now, change it up with denominators like a quarter and a half to show with some live training aid. You get the idea, use an intuitive approach with reward. Make sure to use pictures with colors to represent the fractions to show a real world application to them.

Regards

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  • $\begingroup$ Great examples to use for illustration/intuition! $\endgroup$ – Namaste May 6 '13 at 0:34
  • $\begingroup$ Sure is a motivation-builder! $\endgroup$ – Namaste May 6 '13 at 0:45
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Write it as $2 + \frac{1}{2}$ rather than $2 \frac{1}{2}$. This is simpler to understand.

Make sure they understand dividing even numbers by 2, triples by 3 etc. Before trying to use fractions that don't go.

Visualization works well to teach additions e.g. showing 2 circles and another sliced in half.

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  • $\begingroup$ I told them this but they have trouble using it and/or don't understand it. I'm dealing with kids who have severe math issues. $\endgroup$ – Low Scores Jan 26 '13 at 23:51
  • $\begingroup$ @LowScores, I mean consistently use it everywhere. Don't use the notation $2 \frac{1}{2}$ at all. $\endgroup$ – user58512 Jan 26 '13 at 23:51
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The answer for how ti should be done probably needs a lot of research. However, I have some ideas that may help researchers figure out the solution. Maybe those students are actually better students and the method of marking isn't very good. Maybe they feel really smart by their own standards and just aren't by the standards of society. If they refuse to blindly accept statements they don't understand why are true, that's a good thing, and it might be better to leave them not understanding than to be pushy about them performing calculations the way they were taught to when they don't want to do it because they don't understand the meaning of what they're doing. They might be like I know that the natural numbers satisfy the following properties

  • $\forall x \in \mathbb{N}\forall y \in \mathbb{N}\forall z \in \mathbb{N} (x + y) + z = x + (y + z)$
  • $\forall x \in \mathbb{N}\forall y \in \mathbb{N} x + y = y + x$
  • $\forall x \in \mathbb{N}\forall y \in \mathbb{N}\forall z \in \mathbb{N} (x \times y) \times z = x \times (y \times z)$
  • $\forall x \in \mathbb{N}\forall y \in \mathbb{N} x \times y = y \times x$
  • $\forall x \in \mathbb{N}\forall y \in \mathbb{N}\forall z \in \mathbb{N} x \times (y + z) = (x \times y) + (x \times z)$

but not jump to the conclusion that those properties hold for the real numbers also which is a good thing, and that might be why some of them are failing to understand what the teacher means by fractions and why doing calculations the way the teacher is trying to teach them works. They might also be less likely to make the mistake that some people would probably make such as assuming that the law $(a + b)^2 = a^2 + 2ab + b^2$ for quaternions and assuming the axiom of choice. To make matters worse, maybe they're requiring them to blindly accept the fundamental theorem of arithmetic in order to get the marks because maybe that's the statement they use to show that every fraction can be reduced to lowest terms. Taking the lowest common denominator is actually harder to teach them why it works than taking the product of the denominators. Maybe they don't explain that it means take the product of the denominators then reduce the fraction to the lowest common denominator.

Maybe they're moving onto that topic too soon. Maybe some people claim that there's a chance that if they don't hurry up and learn stuff, they will become too old to learn it. Maybe they're not addressing the concern that they're also a risk that if the curriculum moves too fast near the beginning, some students might start a vicious cycle where they're behind so they feel the curriculum is moving too fast so they continue being behind. I realize that Mary and Janelle from Sister Wives were raised very differently then were too old to learn each other's way of thinking until they got help from a therapist. That may be a good thing because it means they're also less likely to be able to be brainwashed when they're older and be old enough to understand that what other bad people are now trying to teach them is wrong and that they would have learned it wrong if they had been raised by them when they were younger. I'm not sure that's also the case for learning school material. https://www.inc.com/bill-murphy-jr/science-says-were-sending-our-kids-to-school-much-too-early-and-that-can-hurt-th.html seems to hint that kids will probably learn material better if they start later. That might be because those who start grade 1 earlier are more likely to have the curriculum move on before they're ready for it to move on.

Maybe for those who continue to fail to understand, the teacher could be like "Let's redefine the method of calculation I'm trying to teach you how to do as just simply a puzzle, that does not actually represent a real statement," and then teach them how to use number theory to derive general properties of that method of calculation. For example, that what they defined equality of fractions to mean is an equivalence relation and performing calculations on fractions from the same classes gets you a result from the same class.

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