Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I like fraction wheels and cooking, but it's easy to waste a HUGE amount of time on manipulatives when you should instead be drilling on paper.

I suggest "Key to Fractions", a very inexpensive four-book workbook series. Get it either used or from Rainbow Resource. Also math-drills.com for printable worksheets for extra practice. (They have some with autofill for answers. Don't do that, just print them out.)

NB that fractions are the most difficult topic in elementary school math; IIRC in Liping Ma's blockbuster "Knowing and Teaching Elementary Mathematics", something like 40% of teachers failed to do a fractional division problem correctly, and only one out of twenty-five or so could come up with an example of fractional division, and the one she came up with wasn't that great.

Key to Fractions looks like a good set. Question for anyone, does adding and subtracting fractions typically come after learning multiplying fractions as laid out in this series? I think mine has learned how to add and subtract fractions at school but I’m not sure he knows how to multiply them. That seems more complicated.

Multiplying fractions (and dividing them, which is just flip and multiply) is conceptually easier than adding and subtracting. It's also fewer steps, as no common denominator is required.

That said, across two different math curriculums (FCPS and Math in Focus) my kids have learned adding and subtracting fractions before multiplying and dividing them.

The algorithm isn't that bad, but conceptually people absolutely flail at it. You can replicate Liping Ma easily. 1 3/4 ÷ 1/2 was the sample, iirc. Pick a couple of people, ask them to solve, then ask them give you an example that would go with the problem. An appalling number will fail to solve, fail to put in simplest form,or give you a word problem involving multiplication instead of division.

I will admit that if I saw that I would not remember how to do that by hand, because it’s been so many years since I had to do it. In would just use my phone calculator if I saw that in real life. I didn’t have any trouble with fractions while in school and I am confident that I could do it easily if I got a quick refresher on the strategy/rule. That’s not the same as not understanding fractions. I am sure there a lot of life science things that I remember from years ago that many other people forget, because I have continued reading about and using that information in my career. I have no use for math most days.

Flip and multiple! aka imagine you were baking and needed 1.75 cups of flour but only had 1/2 cup measuring cup. You'd figure out you need 3.5 of those 1/2 c scoops (1.75 x 2 divide by 1).

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I like fraction wheels and cooking, but it's easy to waste a HUGE amount of time on manipulatives when you should instead be drilling on paper.

I suggest "Key to Fractions", a very inexpensive four-book workbook series. Get it either used or from Rainbow Resource. Also math-drills.com for printable worksheets for extra practice. (They have some with autofill for answers. Don't do that, just print them out.)

NB that fractions are the most difficult topic in elementary school math; IIRC in Liping Ma's blockbuster "Knowing and Teaching Elementary Mathematics", something like 40% of teachers failed to do a fractional division problem correctly, and only one out of twenty-five or so could come up with an example of fractional division, and the one she came up with wasn't that great.

Key to Fractions looks like a good set. Question for anyone, does adding and subtracting fractions typically come after learning multiplying fractions as laid out in this series? I think mine has learned how to add and subtract fractions at school but I’m not sure he knows how to multiply them. That seems more complicated.

Multiplying fractions (and dividing them, which is just flip and multiply) is conceptually easier than adding and subtracting. It's also fewer steps, as no common denominator is required.

That said, across two different math curriculums (FCPS and Math in Focus) my kids have learned adding and subtracting fractions before multiplying and dividing them.

The algorithm isn't that bad, but conceptually people absolutely flail at it. You can replicate Liping Ma easily. 1 3/4 ÷ 1/2 was the sample, iirc. Pick a couple of people, ask them to solve, then ask them give you an example that would go with the problem. An appalling number will fail to solve, fail to put in simplest form,or give you a word problem involving multiplication instead of division.

I will admit that if I saw that I would not remember how to do that by hand, because it’s been so many years since I had to do it. In would just use my phone calculator if I saw that in real life. I didn’t have any trouble with fractions while in school and I am confident that I could do it easily if I got a quick refresher on the strategy/rule. That’s not the same as not understanding fractions. I am sure there a lot of life science things that I remember from years ago that many other people forget, because I have continued reading about and using that information in my career. I have no use for math most days.

Anonymous wrote:

Anonymous wrote:I like fraction wheels and cooking, but it's easy to waste a HUGE amount of time on manipulatives when you should instead be drilling on paper.

I suggest "Key to Fractions", a very inexpensive four-book workbook series. Get it either used or from Rainbow Resource. Also math-drills.com for printable worksheets for extra practice. (They have some with autofill for answers. Don't do that, just print them out.)

NB that fractions are the most difficult topic in elementary school math; IIRC in Liping Ma's blockbuster "Knowing and Teaching Elementary Mathematics", something like 40% of teachers failed to do a fractional division problem correctly, and only one out of twenty-five or so could come up with an example of fractional division, and the one she came up with wasn't that great.

I like to knock on FCPS all the time, but this stat amazes me. My kids upper ES teachers could all easily do this kind of math. I have no idea about lower ES, because they aren't doing fractional division. Maybe the problem was she was interviewing mostly kindergarten and 1st grade teachers?

23 or 24 US elementary school teachers, chosen among a group specifically interested in math. Some of them were probably teaching younger grades, some of them older. My guess is the ones in upper grades were much more likely to get the right answer, but even they were poor at explanations.

She also interviewed a group of Chinese ES math teachers, and they did much, much better. I do wonder to what extent this is still true, IIRC China is moving away from its old Normal School model, and in any case it is a lot richer and more modernized now, and the more bookish men and women may be heading into other parts of the economy.

Ma's thesis is that what you want out of math teachers for ES is something she termed "profound understanding of fundamental mathematics". It is an amazing read, one of those books that really did change my thinking.

9 is really young. He can circle back around years to come.
All the pies and blocks confused me. The shapes and colors took attention away from the numbers themselves.
I'd have him compare 1/5 and 3/5 for example. Also divided them using calculator or put them in %.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I like fraction wheels and cooking, but it's easy to waste a HUGE amount of time on manipulatives when you should instead be drilling on paper.

I suggest "Key to Fractions", a very inexpensive four-book workbook series. Get it either used or from Rainbow Resource. Also math-drills.com for printable worksheets for extra practice. (They have some with autofill for answers. Don't do that, just print them out.)

NB that fractions are the most difficult topic in elementary school math; IIRC in Liping Ma's blockbuster "Knowing and Teaching Elementary Mathematics", something like 40% of teachers failed to do a fractional division problem correctly, and only one out of twenty-five or so could come up with an example of fractional division, and the one she came up with wasn't that great.

Key to Fractions looks like a good set. Question for anyone, does adding and subtracting fractions typically come after learning multiplying fractions as laid out in this series? I think mine has learned how to add and subtract fractions at school but I’m not sure he knows how to multiply them. That seems more complicated.

Multiplying fractions (and dividing them, which is just flip and multiply) is conceptually easier than adding and subtracting. It's also fewer steps, as no common denominator is required.

That said, across two different math curriculums (FCPS and Math in Focus) my kids have learned adding and subtracting fractions before multiplying and dividing them.

The algorithm isn't that bad, but conceptually people absolutely flail at it. You can replicate Liping Ma easily. 1 3/4 ÷ 1/2 was the sample, iirc. Pick a couple of people, ask them to solve, then ask them give you an example that would go with the problem. An appalling number will fail to solve, fail to put in simplest form,or give you a word problem involving multiplication instead of division.