confusing math concept ratios

[choirfarm]

Ok.. My oldest math genius kid tried to explain this to me, but I just don't get it. Horizons introduced ratios today to my 4th grader. Let us say you have 2 girls to every 3 boys. I completely understand the 2:3 or 2 to 3 concept. But then they also have 2/3. Ok... that makes NO sense. If 2/3rds are girls then 1/3 are boys!!! She is having enough trouble with equivilent fractions which is in the same lesson. ( She can understand looking at the pictures the 2/3 and 4/6 take up the same amount of the pie, but dividing each by 2 just loses her.) My oldest just said that 2/3 is just two different things... 2/3 as a fraction which means two out of three pieces of pie or 2 girls to 3 guys if it is a fraction. Good grief. That doesn't make sense to me, much less will my daughter get it. Math people. Help. What am I missing.

[Lang Syne Boardie]

Is this the fourth grade book? What lesson?

[jennynd]

draw the bar diagram (I am Singapore user). than you can see girls are 2/3 of boys. boys now is 3 unit and girls is 2 unit. therefore ration g:b = 2:3

[Dana]

You're comparing different things.

 

In the ratio 2 girls : 3 boys, the fraction form is 2 girls / 3 boys.

 

What you're thinking of is a ratio of girls to students: 2 girls / 5 students

So 2/5 OF THE CLASS is girls and 3/5 OF THE CLASS is boys.

 

2/3 here is just girls to boys - not to the class.

 

HTH... units are really useful!

[choirfarm]

You're comparing different things.

 

In the ratio 2 girls : 3 boys, the fraction form is 2 girls / 3 boys. Yes I completely get this. But in a lesson when she is labeling a picture 2/3 in the fraction section then she is going to think that a 2/3 ratio is refering to the same kind of picture.

 

What you're thinking of is a ratio of girls to students: 2 girls / 5 students

So 2/5 OF THE CLASS is girls and 3/5 OF THE CLASS is boys. So why doesn't the ration work like this in fraction form???

 

2/3 here is just girls to boys - not to the class. Yes, I am not dumb. I understand that. I do. But how is she supposed to know ( and how am I supposed to explain) that when she sees a fraction 2/3 that sometimes it means 2 out of 3 and sometimes it means 2 people are one way and 3 people are another way. To me this just totally makes the regular fraction work confusing when fractions are confusing enough for some people. Does that make sense?

 

HTH... units are really useful!

 

 

I guess I just tell her the fractions mean different things depending on what you are doing. She won't understand that, thoughl

[wapiti]

There are 2/3 as many girls as there are boys, or the girl group is 2/3 as big as the boy group.

 

There are 3/2 as many boys as there are girls, or the boy group is 3/2 of the girl group.

[choirfarm]

Is this the fourth grade book? What lesson?

It is actually the 3rd grade book ( we are behind) lesson 103.

[choirfarm]

There are 2/3 as many girls as there are boys, or the girl group is 2/3 as big as the boy group.

 

There are 3/2 as many boys as there are girls, or the boy group is 3/2 of the girl group.

 

????? 2/3 as many girls...even I don't understand that.

[wapiti]

????? 2/3 as many girls...even I don't understand that.

 

The girl group is 2/3 as big as the boy group. Draw bar diagrams - a bar for the girls with two units, a bar for the boys with three units.

 

[----][----] girls

[----][----][----] boys

[blondeviolin]

Your ratio of 2/3 is per boy. So for every 1 boy, there is 2/3 girl. It's not out of the class. So, if you have 6 boys, that is the number you would multiply the 2/3 by, which would give you 4 girls. The ratio of boys to girls is saying 2/3 of boys is the number of girls...NOT 2/3 of the class.

[choirfarm]

The girl group is 2/3 as big as the boy group. Draw bar diagrams - a bar for the girls with two units, a bar for the boys with three units.

 

[----][----] girls

[----][----][----] boys

 

 

Yes I get that but 2/3 also means 2 out of 3 pieces of pie!!!

[choirfarm]

Your ratio of 2/3 is per boy. So for every 1 boy, there is 2/3 girl. It's not out of the class. So, if you have 6 boys, that is the number you would multiply the 2/3 by, which would give you 4 girls. The ratio of boys to girls is saying 2/3 of boys is the number of girls...NOT 2/3 of the class.

 

Ok, yall are telling me to have a 9yo who doesn't completely get the concept of fractions yet.. (She can label them easily but coming up with equivilent fractions is hard. ) that she needs to multiply something by 2/3rds... She will never understand this.

[choirfarm]

I understand the concept. HOnestly, I do. IT makes sense TO ME all of the ways you are explaining it. My question is can I just skip the fraction part of ratios for now and just do the 2:3 and 2 to three part until she has fractions more solidified. I like math and it is intuitive to me. I do see what all of you are saying, but she doesn't understand things I say when I make them more simple.

[wapiti]

Yes I get that but 2/3 also means 2 out of 3 pieces of pie!!!

 

The whole pie has 3 pieces.

 

But what is your whole pie in the girl/boy ratio? The whole pie is the boy group. If you want the whole pie to be the whole class, then the fraction will be 2/5.

 

I'm sorry, I'm so not helping :tongue_smilie:

[wapiti]

My question is can I just skip the fraction part of ratios for now and just do the 2:3 and 2 to three part until she has fractions more solidified.

 

I vote yes.

[blondeviolin]

I understand the concept. HOnestly, I do. IT makes sense TO ME all of the ways you are explaining it. My question is can I just skip the fraction part of ratios for now and just do the 2:3 and 2 to three part until she has fractions more solidified. I like math and it is intuitive to me. I do see what all of you are saying, but she doesn't understand things I say when I make them more simple.

 

Yeah, I'd work on the understanding of fractions because that's all ratios are!

[Candid]

Yes I get that but 2/3 also means 2 out of 3 pieces of pie!!!

 

I think part of the problem is what I've bolded above. It's time to introduce other visual ways of showing fractions than round cirucular objects because that way of talking about fractions is limited and I'm afraid you've hit a limit with this example.

 

For more see:

 

http://math.berkeley.edu/~wu/fractions1998.pdf

 

It is likely that teachers would expose students to other pictorial repre-

sentations of fractions at this point, such as a square divided into 4 equal

parts, or a pie cut into 6 equal parts, etc., so a caveat is in order. There is

certainly no harm in introducing these models, but I would suggest doing

so only after students have become procient at working with the number

line and the division of line segments. One reason is that our reasoning

throughout the development of fractions is done with the help of the number

line. But there is another reason: the pie representation of fractions, for

instance, has the drawback of being clumsy at representing fractions > 1

because teachers and students alike balk at drawing many pies. Reason-

ing done with the pie model therefore tends to accentuate the importance

of small fractions. Could this be the explanation of the passage on p. 96

of the NCTM Standards ([2]) quoted in the introduction? On the other

hand, the number line automatically puts all fractions, big or small, on

an equal footing so that they can all be treated in a uniform manner. An

additional advantage is the exibility of this model in all kinds of discus-

sions, and this advantage would become most apparent when we come to

the multiplication of fractions.

 

If it is not clear from this section, he suggests using fractions as points on a number line as your base method of talking about them.

 

For more on this try this longer paper:

http://math.berkeley.edu/~wu/EMI2a.pdf

[zoo_keeper]

I must not be understanding the issue. The OP is using the numbers 2 and 3 in multiple, unequal contexts.

 

2/3 of the class is girls means that 2 out of every 3 students are girls. The "whole" fraction is 3/3. If there are 30 students in the class, then 30 times 2 divided by 3 or 20 of the students are girls (so 20/30 are girls). Hopefully, even before you do the math, you should be able to intuit that if 2/3 of the class is girls, then there are more girls than boys and that 3/3 - 2/3 = 1/3 of the class is boys.

 

If there are 2/3 as many girls in the class, then this should send off bells that there are fewer girls in the class then boys. In fact, for every 3 boys there are 2 girls. This is synonymous with saying the odds or distribution of girls to boys is 2:3. The "whole" fraction is no longer 3/3, it's now 5/5. Or, 2 out of every 5 students are girls. So now if there are 30 students in the class, the number of girls is 30 times 2 divided by 5 or 12. The remainder, 30-12=18 (of which 12/18=2/3 are girls) are boys. So now 12/30=2/5 are girls.

[letsplaymath]

Ok.. My oldest math genius kid tried to explain this to me, but I just don't get it. Horizons introduced ratios today to my 4th grader. Let us say you have 2 girls to every 3 boys. I completely understand the 2:3 or 2 to 3 concept. But then they also have 2/3. Ok... that makes NO sense. If 2/3rds are girls then 1/3 are boys!!!

 

Ratios are kind of like percent discounts. It depends on what you're buying (or in the case of ratios, what you're comparing).

If you buy a $100 coat on sale at 50% off, they would subtract $50 from the price of the coat, right?

 

And then if you buy a $48 blouse on sale at 50% off, would you expect them to subtract another $50? After all, we just proved that 50% off means subtract $50, right?

Of course, you are familiar enough with sales that you wouldn't get confused that way. But ratios are unfamiliar enough that you (and your daughter) WILL get confused, which means you have to be VERY careful.

Whenever you want to take a percent discount, you have to look at the price of

the thing you are buying

(not something else you may have bought some other time). That is what we treat as "one whole pie" or 100%, and we make our discount according to that.

 

Whenever you turn a ratio into a fraction, you have to look at

the

thing you are comparing to

(that's the

second number

in the ratio). That is what we treat as "one whole pie" or 100%, and the first part of the ratio is a fraction of the second part.

Therefore, because your ratio is comparing girls to boys, when you turn it into a fraction, it will tell you what "part of a pie" (what fraction) the girls would be compared to one "whole pie" that was the boys.

 

What part each group is compared to the entire class doesn't matter, because that isn't what we were comparing to---that would be like trying to apply the coat's discount amount to the blouse.

 

Does that help at all?

 

I do think you could just ignore the fraction notation for ratios, if you had to. I am surprised the book teaches it in 4th grade. But since they do teach it, they will probably be including it in future reviews and on tests, so you will have to watch out for that and avoid those sections, which is a hassle. You may want to see if your daughter can understand it this way first.

 

She is having enough trouble with equivalent fractions which is in the same lesson. ( She can understand looking at the pictures the 2/3 and 4/6 take up the same amount of the pie, but dividing each by 2 just loses her.)

 

When you have 2/3 of a pie left, and you want to cut it into more pieces (to share with some friends who come to visit), you cut each piece into two pieces. Now you have 4 pieces (2 times 2), but they are only half as big. They are 6ths, not 3rds. It would take twice as many of them (3 times 2) to make a whole pie.

Can your daughter see why both the top and bottom numbers of the fraction are multiplied by the same number?

How many pieces you have goes up in the exact same way that the size of the pieces goes down (or the number of them it takes to make a whole pie goes up).

To go from 4/6 back to 2/3 (put the fraction in simplest form), it is just the reverse. It's like you are gluing the pieces back together. You glue the pieces together in pairs, so now you have half as many pieces (4 divided by 2). But the pieces are bigger, so it won't take as many to make a whole pie. In fact, it only takes half as many of the big pieces to make a pie as before, when they were little (6 divided by 2).

 

You may want to practice this with actual pies cut out of construction paper, cutting them into equivalent fractions and then taping them back together. Try cutting each piece into 3 pieces, or 4 pieces, to see how those numbers multiply and divide, too.

[choirfarm]

Ratios are kind of like percent discounts. It depends on what you're buying (or in the case of ratios, what you're comparing).

 

 

If you buy a $100 coat on sale at 50% off, they would subtract $50 from the price of the coat, right?

 

 

 

And then if you buy a $48 blouse on sale at 50% off, would you expect them to subtract another $50? After all, we just proved that 50% off means subtract $50, right?

Of course, you are familiar enough with sales that you wouldn't get confused that way. But ratios are unfamiliar enough that you (and your daughter) WILL get confused, which means you have to be VERY careful.

 

 

Whenever you want to take a percent discount, you have to look at the price of

the thing you are buying

(not something else you may have bought some other time). That is what we treat as "one whole pie" or 100%, and we make our discount according to that.

 

 

 

Whenever you turn a ratio into a fraction, you have to look at

the

thing you are comparing to

(that's the

second number

in the ratio). That is what we treat as "one whole pie" or 100%, and the first part of the ratio is a fraction of the second part.

Therefore, because your ratio is comparing girls to boys, when you turn it into a fraction, it will tell you what "part of a pie" (what fraction) the girls would be compared to one "whole pie" that was the boys.

 

What part each group is compared to the entire class doesn't matter, because that isn't what we were comparing to---that would be like trying to apply the coat's discount amount to the blouse.

 

Does that help at all?

 

I do think you could just ignore the fraction notation for ratios, if you had to. I am surprised the book teaches it in 4th grade. But since they do teach it, they will probably be including it in future reviews and on tests, so you will have to watch out for that and avoid those sections, which is a hassle. You may want to see if your daughter can understand it this way first.

 

 

 

When you have 2/3 of a pie left, and you want to cut it into more pieces (to share with some friends who come to visit), you cut each piece into two pieces. Now you have 4 pieces (2 times 2), but they are only half as big. They are 6ths, not 3rds. It would take twice as many of them (3 times 2) to make a whole pie.

 

 

Can your daughter see why both the top and bottom numbers of the fraction are multiplied by the same number?

How many pieces you have goes up in the exact same way that the size of the pieces goes down (or the number of them it takes to make a whole pie goes up).

To go from 4/6 back to 2/3 (put the fraction in simplest form), it is just the reverse. It's like you are gluing the pieces back together. You glue the pieces together in pairs, so now you have half as many pieces (4 divided by 2). But the pieces are bigger, so it won't take as many to make a whole pie. In fact, it only takes half as many of the big pieces to make a pie as before, when they were little (6 divided by 2).

 

You may want to practice this with actual pies cut out of construction paper, cutting them into equivalent fractions and then taping them back together. Try cutting each piece into 3 pieces, or 4 pieces, to see how those numbers multiply and divide, too.

 

Sigh... I understand, I do. But trying to explain it to her. This is actually in the 3rd grade HOrizons as we are behind. As far as seeing that they are multiplied by the same number..no . HOrizons has a picture of a rectangle divided into 4 pieces, then shades 2 of them. Then it has a picture of a rectangle with 8 pieces, then shades 4 of them. So then below the picture they have her label them, which she does 2/4 and 4/8. Then it has a space in between those to have her put what each is multiplied by and then she gets completely stuck. She says it makes no sense. She understands that they represent the same amount of the figure, but doesn't understand what multiplying or dividing if you are reducing the fraction has to do with it. To me this is EASY. That is why although I understand what all of you are saying with ratios, for me to try to explain how 2/3 means TWO DIFFERENT THINGS would only confuse her more. Does that make sense??

[zoo_keeper]

But 2/3 does not mean 2 different things. The difference is what follows the fraction, i.e., 2/3 "of what". If 2/3 of a 30 student class are girls, then the whole against which you apply the fraction is the 30 student class. If, instead, the number of girls in the class are 2/3 of the number of boys, then the whole against which you apply the fraction is the number of boys (which is smaller than the 30 student total). If you want to apply the fraction to the whole of the 30-person class, you'll need to transform it by adding the girls back into the denominator, i.e., 2/(3+2)=2/5 against 30. Either way, 2/3 always means 2 parts out of a 3 part whole.

 

(Sorry to belabor the point. Maybe it's just the math teacher in me, it's just bothering me that you keep asserting that the fraction's meaning changes in different settings.)

[morosophe]

Maybe we could change the ratio to something a little more intuitive for a kid who doesn't even have large classes--the "two girls to every three boys in class" thing is already pretty abstract for her, isn't it? (Off-topic: does anyone else have the Beach Boys running through his head reading this thread?)

 

How about this, since pies have gone over so well:

 

You have two tarts, and three people eating dessert. That's a ratio of 2 tarts to 3 people, or 2:3, or 2/3. Your child is probably going to try to divide the tarts among the people to see how much each person can get so that it's "fair," and she'll easily see how the 2/3 fraction fits the rest of it. But it's still a 2:3 ratio.

 

Dividing girls among the boys doesn't make as much sense at this (or any) stage, I'll admit. (Even the Beach Boys preferred a very different ratio, right?)

 

As for how to increase and decrease fractions... They introduce that as the same time as the concept of ratios? Really? Wow, how mind-bending for a kid! I'd try to teach that concept separately, myself. Or you could point out that you'd actually figured out that 2/3 of a tart was about a perfect amount of dessert. Now you're having a Christmas party, and there will be fifteen people there, and you want to have 2/3 of a tart for all of them: How many tarts will you need?

 

Edited because: Wow, I misspelled dessert? Really?

Edited December 1, 2011 by morosophe

[choirfarm]

But 2/3 does not mean 2 different things. The difference is what follows the fraction, i.e., 2/3 "of what". If 2/3 of a 30 student class are girls, then the whole against which you apply the fraction is the 30 student class. If, instead, the number of girls in the class are 2/3 of the number of boys, then the whole against which you apply the fraction is the number of boys (which is smaller than the 30 student total). If you want to apply the fraction to the whole of the 30-person class, you'll need to transform it by adding the girls back into the denominator, i.e., 2/(3+2)=2/5 against 30. Either way, 2/3 always means 2 parts out of a 3 part whole.

 

(Sorry to belabor the point. Maybe it's just the math teacher in me, it's just bothering me that you keep asserting that the fraction's meaning changes in different settings.)

 

 

Ok, this is so confusing to the English teacher. In my head I see a picture of 2 out of every 3. That is what I see when I see a fraction. But let us take the 30 students. If you say that 2/3 are girls then you are saying 2o girls and 10 boys. But the ratio 2/3 means something completely different. It doesn't mean 2 out of every 3 like the first one. It means 2 girls and 3 boys for a total of 5. So basically the fraction 2 means 2 out of 5 and 3 out of 5. AT least to me. I can figure it out intuitively. I did very well on the ACT in math, but I just figure it out. Explaining it to a math phobic girl is impossible for this brain.

[morosophe]

Back to two girls for every three boys, since I'm determined to make this work:

 

Due to it being scheduled at the same time as cheerleading and gymnastics practice, there are two girls for every three boys in the dance class. How many of the boys are going to be able to practice with the correct-gendered partner for each dance?

 

You have to make the terms in the ratio mean something to each other, particularly when teaching ratios to kids.

 

Here's another way to do it:

 

There are two girls to every three boys in the class. They decide to play tug-of-war, girls against boys. Which team do YOU want to be on, so you don't get dragged through the dirt? If your daughter has 2/3 of the class confused with 2/3 of the number of boys, she'll say she wants to be on the girl's team, because it's bigger. (Well, plus because she's a girl, but I digress...) If she understands that there are half again as many boys as girls, she'll hopefully understand that the boys are probably going to win, because they have numbers going for them as well as machismo.

[Snickerdoodle]

This reminds me of the Andre Toom article where he wrote:

In the course of this kind of teaching I came to the conclusion that

teaching to understand and intelligently use the natural language, in the

present case English, is one of the most urgent functions of mathematical

education.

[go_go_gadget]

Ok, this is so confusing to the English teacher. In my head I see a picture of 2 out of every 3. That is what I see when I see a fraction. But let us take the 30 students. If you say that 2/3 are girls then you are saying 2o girls and 10 boys. But the ratio 2/3 means something completely different. It doesn't mean 2 out of every 3 like the first one. It means 2 girls and 3 boys for a total of 5. So basically the fraction 2 means 2 out of 5 and 3 out of 5. AT least to me. I can figure it out intuitively. I did very well on the ACT in math, but I just figure it out. Explaining it to a math phobic girl is impossible for this brain.

 

The question had to do with there being 2/3 the number of girls compared to the number of boys, not compared to the number of total students. I think that's where you're becoming confused when you say that 2/3 means two different things. It doesn't, but you're using two unequal candidates for the number to take 2/3 of. If you take 2/3 of 30, then yes, you get 20. But if you take 2/3 the number of boys, you get a different answer, because you're taking 2/3 of a different number.

 

edited to add: Let's just do it. There are 30 kids in the class, and the group of girls is 2/3 the size of the group of boys. Let x = number of boys, in which case the number of girls is (2/3)x. The equation is x + (2/3)x = 30. To add the fractions you need a lowest common denominator, so you consider x to be (3/3)x, because 3/3 = 1. (3/3)x + (2/3)x = (5/3)x. So now your equation is (5/3)x = 30. To solve for x, divide both sides by (5/3), which gives x = 18. So there are 18 boys, and the number of girls is 2/3 the number of boys. 2/3 of 18 is 12, so there are 12 girls. 12/18 = 2/3.

 

Here's another way to do it:

 

There are two girls to every three boys in the class. They decide to play tug-of-war, girls against boys. Which team do YOU want to be on, so you don't get dragged through the dirt? If your daughter has 2/3 of the class confused with 2/3 of the number of boys, she'll say she wants to be on the girl's team, because it's bigger. (Well, plus because she's a girl, but I digress...) If she understands that there are half again as many boys as girls, she'll hopefully understand that the boys are probably going to win, because they have numbers going for them as well as machismo.

 

I think it might be too much to introduce the idea that 1/3 is 1/2 of 2/3 at this point. Also, in this case, it would probably be easier to just think in terms of two groups of kids, not boys vs. girls, to control for the "I want to be on the girls' team!" and "Boys are stronger anyway!" variables. So one team is 2/3 the size of the other, and all the rest of your logic applies.

Edited December 1, 2011 by go_go_gadget

[Carol in Cal.]

In a fraction, the denominator (bottom part) is ALWAYS the whole.

 

In a ratio, it's not ALWAYS the whole, so you have to assess the word problem to see whether it's the whole or not.

 

A fraction is fundamentally a division problem.

The denominator (bottom) tells HOW MANY PARTS add up to ONE WHOLE.

The numerator (top) tells HOW MANY PARTS YOU HAVE.

 

If you have a ratio, and you want to turn it into a fraction, the FIRST thing to do is to figure out how many makes up ONE WHOLE. That becomes the denominator, and then everything else falls into place.

 

HTH

[boscopup]

Ok, this is so confusing to the English teacher. In my head I see a picture of 2 out of every 3. That is what I see when I see a fraction. But let us take the 30 students. If you say that 2/3 are girls then you are saying 2o girls and 10 boys. But the ratio 2/3 means something completely different. It doesn't mean 2 out of every 3 like the first one. It means 2 girls and 3 boys for a total of 5. So basically the fraction 2 means 2 out of 5 and 3 out of 5. AT least to me. I can figure it out intuitively. I did very well on the ACT in math, but I just figure it out. Explaining it to a math phobic girl is impossible for this brain.

 

I think the bar diagrams someone posted earlier would be an easy way to explain the ratio to a young child.

 

As to why it's 2 girls out of 5 and 3 boys out of 5, but the ratio is 2/3... You have 2/5 of the class is girls and 3/5 of the class is boys, so the ratio is:

 

2/5......2x1/5.......2.......1/5

---- = ------- = ---- x -----

3/5......3x1/5.......3.......1/5

 

Any number divided by itself is 1, so the 1/5 over 1/5 is just multiplying by 1. You're left with 2/3. (this is explanation for YOU, not your DD... I would assume she hasn't learned how to multiply fractions ;) ).

 

I agree with a PP that you should make some paper pies and have her practice dividing them up and really seeing how they are equal. If you have your pie split into 2 pieces and have 1 pie colored, then you draw lines to split each half into 2 more pieces, you now have 2 of the 4 pieces colored. So you can see that 1/2 = 2/4. Then point out that you multiplied both top and bottom by 2. I think when explaining to my son, I went ahead and taught him multiplication of fractions, as that just seemed easiest, but he's mathy and understands fractions, so I'm not suggesting that you should necessarily do that for your DD. Perhaps hit fractions from a different angle... Math Mammoth fractions download? Kahn Academy video on fractions? Something else? Then take a break from fractions until January and see if the time off helped it sink in. Just some ideas.

[morosophe]

I think it might be too much to introduce the idea that 1/3 is 1/2 of 2/3 at this point.

 

Yeah, I was being a little less strenuous than that ended up sounding, sorry. I didn't mean that you should teach that it was "half again," just that it (hopefully) might look something like that in her head.

 

Though I completely agree with you on the making-them-gender-neutral thing. I'm still trying to figure out why the example ratio is two girls to three boys. (For one thing, the girls always outnumbered the boys at my school. :p) It's really hard to figure out how this would ever matter to a kid, except in that the girls are outnumbered.

 

(You should take computer science as a minor in college--the classes there have three boys for every two girls, most of them extremely intelligent and socially stunted enough that you expressing interest in them will make their year! I mean, really, when does this exact ratio come into play as being important to ANYBODY? Except maybe for statisticians, who find all sorts of weird numbers interesting. Are there any statisticians around who can find a reason to make this exact ratio interesting to me?)

 

By the way, I'm still singing, "Two girls for every (three!) BOOOOOOOOOY(s)!" here, so you can tell I'm not the person with the most to contribute to this thread.

[Brenda in FL]

Ok.. My oldest math genius kid tried to explain this to me, but I just don't get it. Horizons introduced ratios today to my 4th grader. Let us say you have 2 girls to every 3 boys. I completely understand the 2:3 or 2 to 3 concept. But then they also have 2/3. Ok... that makes NO sense. If 2/3rds are girls then 1/3 are boys!!! She is having enough trouble with equivilent fractions which is in the same lesson. ( She can understand looking at the pictures the 2/3 and 4/6 take up the same amount of the pie, but dividing each by 2 just loses her.) My oldest just said that 2/3 is just two different things... 2/3 as a fraction which means two out of three pieces of pie or 2 girls to 3 guys if it is a fraction. Good grief. That doesn't make sense to me, much less will my daughter get it. Math people. Help. What am I missing.

 

Isn't your issue that the notation used for fractions and ratios are the same? So how is your daughter supposed to know if she's dealing with a fraction or ratio?

 

How are the ratio problems worded? Teach your child to recognize the key words in the ratio problems. When she recognizes those words mean a ratio, also teach her that although it looks like a fraction - it is not. it is a ratio and ratios just happen to use the same symbol as a fraction.

 

I understand that it would be confusing to a child as to why ratios and fractions are written the same way but don't mean the same thing. That's why I'd try to focus on recognizing the type of problem first. And helping her understand that a ratio problem is not asking about a fraction.

 

Mathematicians - please don't blast this explanation. You do need to use fractions to solve computations regarding ratios - but a ratio stated in this notation is not a fraction and at 3rd grade - that's what the child needs to understand.

Edited December 1, 2011 by Brenda in FL

[choirfarm]

In a fraction, the denominator (bottom part) is ALWAYS the whole.

 

In a ratio, it's not ALWAYS the whole, so you have to assess the word problem to see whether it's the whole or not.

 

A fraction is fundamentally a division problem.

The denominator (bottom) tells HOW MANY PARTS add up to ONE WHOLE.

The numerator (top) tells HOW MANY PARTS YOU HAVE.

 

If you have a ratio, and you want to turn it into a fraction, the FIRST thing to do is to figure out how many makes up ONE WHOLE. That becomes the denominator, and then everything else falls into place.

 

HTH

 

This actually makes sense. I may try this. She might understand that.

[Beth in SW WA]

I told hubby as he was leaving for work this morning that I am SO glad that dd is doing ratio challenging word problems with her Singapore tutor online today. I understand ratios in computation problems....but when they are strategically placed in a challenging word problem -- without a clear step-by-step solutions guide -- I get stumped.

 

OP, I feel your pain. I'm more confused after reading this thread. Let's Play Math offered us a fabulous explanation. As did Boscopup and others.

 

Khan Academy has a few videos on ratios. The series starts here. These videos are found in his algebra series.

[Carol in Cal.]

This actually makes sense. I may try this. She might understand that.

 

Just be ready to say it over and over. That's what I had to do when I was teaching DD this. (That's why I could just rattle it off like that, LOL--I have it memorized.)

[choirfarm]

Isn't your issue that the notation used for fractions and ratios are the same? So how is your daughter supposed to know if she's dealing with a fraction or ratio?

 

How are the ratio problems worded? Teach your child to recognize the key words in the ratio problems. When she recognizes those words mean a ratio, also teach her that although it looks like a fraction - it is not. it is a ratio and ratios just happen to use the same symbol as a fraction.

 

I understand that it would be confusing to a child as to why ratios and fractions are written the same way but don't mean the same thing. That's why I'd try to focus on recognizing the type of problem first. And helping her understand that a ratio problem is not asking about a fraction.

 

Mathematicians - please don't blast this explanation. You do need to use fractions to solve computations regarding ratios - but a ratio stated in this notation is not a fraction and at 3rd grade - that's what the child needs to understand.

 

THANK YOU> Yes. That is exactly it.

[choirfarm]

Just be ready to say it over and over. That's what I had to do when I was teaching DD this. (That's why I could just rattle it off like that, LOL--I have it memorized.)

 

Yes, but actually I have decided to shelve ratios entirely and just work on equivilent fractions and save ratios for later. I think part of the problem is her division facts are not there. She sort of understands the concept. We started doing x-tra math a few weeks ago. She screamed and we started with addition and she could only do a progress report at a time not 3 like they wanted. But after awhile she caught on and quit screaming and after she hit about 94 percentile we switched to mult. She started at 33 percent, but now is at about 80. But she does 3 of them ( progress and 2 race the teacher seem to be what it asks her to do each lesson) without screaming and says that it is helping her. We'll switch to division when she gets to 95 percent or so.

[choirfarm]

I told hubby as he was leaving for work this morning that I am SO glad that dd is doing ratio challenging word problems with her Singapore tutor online today. I understand ratios in computation problems....but when they are strategically placed in a challenging word problem -- without a clear step-by-step solutions guide -- I get stumped.

 

OP, I feel your pain. I'm more confused after reading this thread. Let's Play Math offered us a fabulous explanation. As did Boscopup and others.

 

Khan Academy has a few videos on ratios. The series starts here. These videos are found in his algebra series.

 

Actually I am going to use KHAn today with her about equiv fractions. I'm shelving ratios until later.

[Beth in SW WA]

Actually I am going to use KHAn today with her about equiv fractions. I'm shelving ratios until later.

 

Not a bad idea. Equivalent fractions are critical. Once you cross into prealg/alg you need to have your mult/div facts down solid and must understand fractions upside-down and backwards. I am surprised your Horizons book taught you ratios before fractions mastery.

 

Good luck. You are doing awesome. Isn't is great that we can ask the expert moms here for advice? I'd be lost without the mathy moms who have helped me here over the years. Dads, too. (Hi, Bill! :))

 

Have you seen Let's Play Math blog? It's wonderful! She posted above. I read her section on percents a few weeks ago. Good stuff.

[choirfarm]

 

 

Have you seen Let's Play Math blog? It's wonderful! She posted above. I read her section on percents a few weeks ago. Good stuff.

 

 

NO.. wow. It is great. I have actually started some of the more living math with her. She reminds me of that student in the struggling student post in the blog. She can do equations with variables easily. She can add things together in her head and make correct change in her head. ( She loves money.) But you ask her what 6 plus 8 is and she looks like a deer in the headlights. ( Well, not anymore thanks to x-tra math.) She get things I think are hard easily and gets confused on things that I think are easy. She loves the Mathematicians are People too series. She begs me to read those. I'm going to start Murderous Math soon, too.

[siloam]

Actually I am going to use KHAn today with her about equiv fractions. I'm shelving ratios until later.

This is what I was going to recommend. This could be completely developmental...she just hasn't developed the higher level think necessary to get it. Doesn't mean she never will.

 

All my kids are developmentally behind in math. It is always a struggle here. I have one child this week who was multiplying fractions and half way through the assignment she started reducing by finding the lowest prime factor (other than 1) and reducing to that instead of dividing both top and bottom by the same number. :confused: I had her redo the page the next day, and she did well except for on the last about 5 problems she suddenly started adding the denominators instead of multiplying them. This is the child most likely to get 100% on a worksheet and tests high 90's in math on standardized testing. Getting it into her brain the first time is another thing entirely, and has always been like this. I will probably pull her out of what she is doing, pull out MM fractions and have her go through that and hope that is enough to get her beyond this. It might be signs of a developmental delay and I might have to find other math for her to do for a while.

 

You are not alone. (((hugs)))

 

Heather

[Beth in SW WA]

She loves the Mathematicians are People too series. She begs me to read those. I'm going to start Murderous Math soon, too.

Dd8 wrote a letter to Santa yesterday asking for history, science and math books -- and a jewelry box :). She is obsessed with the I Hate Math book by Burns from the library. She wants her own copy.

[zoo_keeper]

Isn't your issue that the notation used for fractions and ratios are the same? So how is your daughter supposed to know if she's dealing with a fraction or ratio?... a ratio stated in this notation is not a fraction and at 3rd grade - that's what the child needs to understand.

 

Just to be clear, ratios should not be stated as fractions. They should use the proper notation, e.g., the number of girls and boys in a class is 2:3 (a ratio), respectively. The same distribution across genders could be said with a fraction, but with different words, e.g., there are 2/3 (a fraction) as many girls as boys. If your book is actually expressing a ratio as a fraction, then you have a problem. Otherwise, it's just an interpretation issue.

[choirfarm]

Just to be clear, ratios should not be stated as fractions. They should use the proper notation, e.g., the number of girls and boys in a class is 2:3 (a ratio), respectively. The same distribution across genders could be said with a fraction, but with different words, e.g., there are 2/3 (a fraction) as many girls as boys. If your book is actually expressing a ratio as a fraction, then you have a problem. Otherwise, it's just an interpretation issue.

 

The directions say Write the ratio two other ways. There are then three boxes with 9 squares to a box. Here is one square:

 

2/3 _____ ______

 

____ 4:5 ______

 

_____ _____ eight to two

 

So, she is supposed to write 2:3 in the second box, two to three in the third box. On the next line she should write 4/5 and then 4 to 5 in the last blank. To me, that is confusing. If the book had put it the way you did above I wouldn't have a problem. The problem on ratios today has a picture like 4 blue circles and 5 red stars and they are supposed to write 4/5 below it. But to me, I would say, do you want me to do the circles and write 4/9 or the stars 5/9?

Edited December 1, 2011 by choirfarm

[zoo_keeper]

The directions say Write the ratio two other ways. There are then three boxes with 9 squares to a box. Here is one square:

 

2/3 _____ ______

 

____ 4:5 ______

 

_____ _____ eight to two

 

So, she is supposed to write 2:3 in the second box, two to three in the third box. On the next line she should write 4/5 and then 4 to 5 in the last blank. To me, that is confusing. If the book had put it the way you did above I wouldn't have a problem. The problem on ratios today has a picture like 4 blue circles and 5 red stars and they are supposed to write 4/5 below it. But to me, I would say, do you want me to do the circles and write 4/9 or the stars 5/9?

Are you sure the answers to the first line are 2/3, 2:3, and two to three? Is that what it says in the TM? I'm wondering instead if the answers should be 2/3, 2:1, and two to 1. IOW, maybe the book wants the student to be able to convert ratios to fractions? If the TM really has it the way you suggest, I'd simply tell your child that the book is being sloppy. This is Horizons?

[Lang Syne Boardie]

choirfarm, I can't seem to locate my third grade materials. I think they're in storage. Going on memory, I agree with those who say to shelve the ratio concept for now and work on fractions. You'll spend much more time with ratio in second semester of the fourth grade book.

 

But I wanted to tell you that, although I like Horizons and have used K-5, I don't recommend it for anyone who can't/doesn't understand it all, inside and out, and can't teach the concepts more than one way. There's just not enough help in that teacher guide.

 

You've said you understand this, which is great, but the bridge between your understanding and your daughter's ability to understand needs something other than Horizons to connect it.

 

Since she's not getting her fraction skills down, either, I would suggest looking into different curriculum. Either to switch entirely, or to fill in some gaps before going on with Horizons if you really love Horizons.

 

If everything else is going well, maybe you'd both enjoy Math Mammoth just for fractions. If you want some refreshing on ratio just to help you find some other ways to explain it to your daughter, Math Mammoth also has ratio worksheets.

 

I've certainly had to switch curriculum before, especially for math. That's a pain to do, but worth it if those lightbulb moments will start happening as a result.

[choirfarm]

Are you sure the answers to the first line are 2/3, 2:3, and two to three? Is that what it says in the TM? I'm wondering instead if the answers should be 2/3, 2:1, and two to 1. IOW, maybe the book wants the student to be able to convert ratios to fractions? If the TM really has it the way you suggest, I'd simply tell your child that the book is being sloppy. This is Horizons?

 

Positive. I just relooked to make sure. And here are the directions in the teacher's material: Discuss with the student the meaning of ratio ( a relationship or comparison of two numbers) Show them three ways a ratio can be written ( 3:4, 3 to 4, or 3/4) The students should be able to complete Student Activity Three independently.

 

To me this is totally confusing. Plus, I really want to firm up equiv fractions before I touch this. I mean, she could get/can get 3:4 and 3 to 4. That I will do. But I will ignore the fraction part for now.

[choirfarm]

 

Since she's not getting her fraction skills down, either, I would suggest looking into different curriculum. Either to switch entirely, or to fill in some gaps before going on with Horizons if you really love Horizons.

 

.

 

 

I'm tired of switching. I used Singapore and Saxon 1st - 3rd grade.. Wasnt getting it. So We started Horizon 3 last spring. In the summer I did TT4 and then came back to Horizon 3 this fall. We still do TT 4 sometimes, but it is so much easier that she does 2 lessons in it. ( But she hates it. She basically hates all math and thinks she is stupid in it.)

[zoo_keeper]

I would ignore it as well. Or better yet, rewrite it as 3X/4Y or whatever. To continue with the previous example, that would be like 2 girls/3 boys. A ratio expressed like this would be acceptable because the units are specified, cluing the reader into the fact that the numbers do not imply a fraction.

[choirfarm]

I would ignore it as well. Or better yet, rewrite it as 3X/4Y or whatever. To continue with the previous example, that would be like 2 girls/3 boys. A ratio expressed like this would be acceptable because the units are specified, cluing the reader into the fact that the numbers do not imply a fraction.

 

GREAT idea. That would make sense!!!!

[wy_kid_wrangler04]

Ok I just got out dd's 3rd grade book and I am looking at the problem. When I taught this to dd we did not look at the fraction bar as a fraction bar. I told her that in a ratio problem to look at that bar and say to. like this

 

 

2 boys

to

3 girls

 

 

You just need to help her to be clear when she is doing a ratio problem to not confuse that as 2 thirds of 1 whole. In ratio its not a whole to parts situation its a comparison!

 

 

I haven't read all the replies and I am on my way out the door. I read the first page and saw where you were. When I get home I will read through the thread and see if you still need help or if I am to late ;)

[Beth in SW WA]

Here is the link to RR's first video on ratios on the AOPS website. He does a fantastic job explaining it.