How well do you understand fractions?

Use people.
For instance, there are twenty people in the house, and only 1/5 are in the kitchen cooking.
For larger numbers, go with people at a convention, and food preparation for the crowd.

All those examples seem intuitive to me, yes.

Other ideas…playdough. It provides a tactile dimension that helps humans learn.

Stick with halves when you introduce new concepts. Halves are intuitive to most everyone. Drive home the point that a half is one divided by two in the same way that a seventh is one divided by seven.

A simple introductory book might help. I like these, though you’d need to research or contact them to find out which level you want.

Those are all easy examples. But realize that half of the people understand a third of fractions about a quarter as well as they should.

Simple and obvious.
When I was in 5th grade and was doing arithmetic with fractions I asked my step dad (an electrical engineer and colleague professor) how adding and subtracting fractions could be useful when I become an adult. He said that he didn’t know. That told me a lot. HA!

I know if you have 9 people and only 8 slices of pizza, 2 people are fighting!

I understand fractions, and most grade-school math, quite well.

Many people (including US adults) struggle with fractions, apparently because (as far as I’ve ascertained) it’s very common that no one actually managed to really teach them much about what the concepts were.

They often learn some minimum tricks to survive math tests and do homework, and then they even forget that, because the tricks have little of no meanings attached to them (in their retained memory), so they’re pointless once people stop assaulting them with homework and tests.

Recent US public grade school math teaching (that I’ve encountered 2nd hand) focused on specific steps to get right answers to certain types of problems, with near-zero conceptual understanding. Not just for fractions, but for area, circumference, distance, etc.

I generated some intense interest in the answer to some simple math problems I made, by putting them in a Minecraft treasure hunt for some kids. They showed the clues (simple line equations for Minecraft map coordinates) to “the best kid in math in their class”, and that kid had no idea what to do with the clues.

And, they often have aversions, dislike, even fear and paralysis attached to the whole subject.

Even if they do have some pieces of information, they don’t trust those pieces enough to reason out answers, nor to confirm their answers.

Since a half of a half is obviously a quarter, that’s a good place to start multiplying fractions. Focus on the simple rules, and use a simple example to prove to them that it’s true. The pizza analogy is time tested. Everyone loves pizza, and it really does make an abstract concept feel more real and intuitive.

People in general are terrible with fractions. Use the pizza analogy thing.

About 50/50.

Use money. Why do we call a quarter a quarter? Because it is ¼ of a dollar. Or, a clock, why do we say quarter after 2? because it is ¼ of the way around.

After that, I would just teach the rules. MEMORIZATION is the way to go for math in my opinion in the most basic of concepts.

My grandpa drew pies in the sand with a stick at the beach to teach me fractions when I was very little, maybe 5 or 6 years old. I remember it was a little confusing to me, but then when I started learning it in school, what he had taught me started to fall into place. I was good at math though, and I enjoyed, and it sounds like your student isn’t. Most people I know who aren’t good at math don’t like to just memorize how to do a problem, they feel they need to understand, but I disagree, with the exception of setting up word problems, then you do need to have some understanding.

So, ok, just teach the steps. When adding, the denominators have to be the same, to you do the math to make the denominators the same, and then just add the top numbers, keep the bottom the same. After that you can reduce the answer if that is required. Reduce probably isn’t the right word, I don’t remember the word for changing 6/8ths to ¾ths.

When multiplying, the rules are….

Just teach the rules and have her practice a bunch of problems.

Eventually, the understanding might fall into place, but fake it till you make it and pass the test.

I would not start with a detonator of 7. I would use4 4 or 8 or 12. 8 slices of pizza. Numbers that are very simple to first try to understand the concept.

I visualize fractions as cutting things into pieces (denominator). That helps with the ¼ is smaller than ⅓. Then grouping the pieces would be adding the numerators. Adding fractions with different denominators requires some math (multiplying top and bottom by x/x), then you can add.

Yeah, people who really have trouble just can’t understand that 1/6 is larger than 1/7. 7 is bigger right?

A ruler can help too. 1/16th is smaller than ½ an inch.

Things they use every day so they can make sure whatever answer they get after working a problem makes sense. Always double check an answer.

@JLeslie , I tried just teaching the rules, but she forgot them in the next class. Fractions are so fundamental that I think it is worth the effort to try to create an understanding of what they mean.

Above average.

I understand them quite well. It is a concept that is not taught well in schools now and I see the difficulties that my daughter has with it.
The only advice outside the other ones here is to use recipe doubling, tripling or halving.

Recipes helped me a lot, but sofew people cook from scratch these days, many adults are mystified by terms, and how to follow a basic recipe.

Other intuitive metaphors for fractions include amounts of something easily divided by hand, such as uncooked rice or beans, or likening the divisor to sharing equally between a number of people who are getting equal shares of something.

i learned fractions, for size, by handing my dad wrenches out of his tool box, while was working on our family car. May 6 or 7 years old.

@LostInParadise Is the student getting frustrated? Or, is she willing to keep working at it? I think it’s important to have an understanding, but I’m not sure how advanced an understanding is necessary to get through life.

What about a recipe? Cut a recipe in half. Maybe young people don’t bake from scratch anymore and they don’t use that skill. I’m just trying to think of every day things so the student will see why it’s useful.

Maybe if you move on to another lesson and then go back to it.