So then how do you "teach" math

[choirfarm]

Let us take two examples:

 

4th grader is supposed to say whether 4/7 is equal or not equal to 16/35.

 

I've tried a couple of different ways:

Cross multiply- which she won't want to do because she has to do it on a separate piece of paper and write it out. If the multiplication like 4 x 35 and then 7 x 16 was on the sheet, then she could do it. But the extra step of figuring it out kills her.

 

Or.. look what would you multiply 7 by to get 35. ( After several minutes as she is NOT good at division AT ALL) 5. Ok.. yes. What happens if I multiply 4 x5. What do you mean that doesn't make sense. Ok, remember we have to multiply a fraction by the same number on the top and the bottom to get an equivilent fraction. That doesn't make sense. Sigh...

 

To me, this is SO incredibly EASY. I just look at it and KNOW they are not equal.

 

Or Geometry

 

There is a graph with a vector drawn on it. Ok write the ordered pair of the vector.

 

To which he writes ( -3, 1) ( This is the ordered pair for the intial point of the vector not the ordered pair of the whole vector.)

 

No.. remember we have to figure out the number with a formula.

 

Oh, yeah the (x2- x1) (y2- y1) and then the square root..(I don't know how to do the subscripts on here)

 

No that isn't quite right. You will just get one number from that formula. Remember we want the ordered pair not the distance. Although you are close. I don't know... Ok let us go back and look.

 

OH YEAH I just subract the x's and y's. YES.

 

I've had this conversation 3 different days.

[Free]

For the fourth grader, I would be showing either similar sized rectangular grids one having 7 partitions and the other 35 and ask her to compare the two. Another way of visualizing fractions is on a number line.

 

My son did plenty of fractions on grids and number lines before moving on to reducing fractions or finding equivalent fractions by multiplying the common factor.

 

ETA: I used MEP for teaching Fractions and it was wonderful in teaching the concepts visually.

Edited December 20, 2011 by Free

[Teachin'Mine]

I might explain that it's easier to compare apples to apples, so we'd get them divided into equal parts. So both denominators would become 35. To do that, the first has to be multiplied by 5. Since we don't want to change the value of the fraction, we have to multiply by one. So if we multiply the denominator by 5, then we do the same for the numerator. So 4/7 is equal to 20/35. Then it's obvious that that is larger than 16/35.

 

For the vectors, Saxon did all the teaching. : )

Edited December 20, 2011 by Teachin'Mine

[flyingiguana]

It's easier the second and third time around. The first time you teach it to a particular child, don't expect it will really all sink in. They might get it for a day, but then lose it completely by the next day.

 

But when you come back to it next year, they will understand it for a little longer. How you teach it this time or next is not really the issue. They just have to see it a number of times, over a span of time, in a number of different ways.

 

It may look like one particular method worked, but that will only be because that was the method you were using when their brain was finally ready to let the idea in for good.

 

By high school, hopefully, they will have this concept down and think it's really easy.

[choirfarm]

For the fourth grader, I would be showing either similar sized rectangular grids one having 7 partitions and the other 35 and ask her to compare the two. Another way of visualizing fractions is on a number line.

 

My son did plenty of fractions on grids and number lines before moving on to reducing fractions or finding equivalent fractions by multiplying the common factor.

 

ETA: I used MEP for teaching Fractions and it was wonderful in teaching the concepts visually.

 

What is MEP? She did all the problems where the fractions had pictures with them, but those crutches are gone now and they are expected to do it without them. So do I just keep drawing them for her. She could easily see that 4/8 was the same as 8/16. You just have more pieces but it takes up the same amount. She can't seem to handle it when it is just numbers.

[choirfarm]

I might explain that it's easier to compare apples to apples' date=' so we'd get them divided into equal parts. So both denominators would become 35. To do that, the first has to be multiplied by 5. Since we don't want to change the value of the fraction, we have to multiply by one. So if we multiply the denominator by 5, then we do the same for the numerator. So 4/7 is equal to 20/35. Then it's obvious that that is larger than 16/35.

 

. : )[/quote']

 

That is how I thought I was explaining it up above. I keep telling her she has to have the same amount of pieces on the bottom.

[choirfarm]

I would teach both of those concepts visually. I would not go on with the fractions until the concept is understood and the multiplicatin facts are down pat. I would use correct mathematical terminology: numerator, denominator and explain their meanings and the root word associations. You'll know that the concept is understood when they can draw it and explain it, and when they look at the two numbers and start estimating rather than calculating.

For ex. 4/7 is greater than a half because half would be 3.5/7.

16/35 is less than a half becauase half would be 17.5 parts out of 35.

 

 

 

 

Ok.. what do you mean by concept of fractions. She labels the parts numerator and denominator. She has that down. I have absolutely no idea what you are talking about with root word associations. Well, she is at 71 percent at x-tra math for multiplication after 20 days of it. We're still doing it every day. I will go on to division after that. Several people on here said not to hold her back even though she stil skip counts. So are you saying I should have her draw the fractions when she has to do the equivilent fraction problems?

[choirfarm]

But when you come back to it next year, they will understand it for a little longer. How you teach it this time or next is not really the issue. They just have to see it a number of times, over a span of time, in a number of different ways.

 

 

 

This looks like the last day we have any of these kind of problems in this 3rd grade book. ( We are doing lessons 121 and 122 today out of 160) Trying to get to the 4th grade book. Maybe when we cycle back around she'll get it.

[Teachin'Mine]

That is how I thought I was explaining it up above. I keep telling her she has to have the same amount of pieces on the bottom.

 

I read your post and missed that - sorry! I think that not having her math facts memorized is going to make it a slow go for everything else. I'd back up, and maybe use a different program, or even different workbooks. Those inexpensive workbooks each approach the math from a slightly different angle, and this can really help to solidify the math and make some connections. Saxon has built in work on the facts and lots of review with each lesson ... :leaving:

[choirfarm]

Yes, have her draw the pictorial representations of the numerical fractions, preferably on the marker board while you watch. Have her explain her reasoning as she works through the problems. Don't release her to independent work until she comprehends what she is doing..you want understanding, not algorithm memorization.

 

Numerator and denominator - it is not enough to id which is which. She needs to know and use the definitions as she thinks through the problem sets. 4/7 : 7 denotes the number of these peices needed for a complete unit. 4 is the number we have now. 16/35. 35 peices here for a complete unit and we have 16 of them. If we are to compare, we need to compare equal sized peices and the unit needs to be the same.

 

Ok.. now on the regular fractions she has no trouble doing this. I'll try it today. BTW, that is part of the reason I skipped representing ratios as fractions. She even said when we did the ratio of boys to girls as being 2:3 and they wanted a fraction, she tried to put 2/5 and 3/5...which is correct in fraction terms but of course the answer they wanted was 2/3 which to me is horribly confusing!!!

 

 

Also, trying to draw 24/45 and 16/35 is going to be hard!

[Teachin'Mine]

 

 

Also, trying to draw 24/45 and 16/35 is going to be hard!

 

I'm truly not understanding where 24/45 is coming from. :confused:

 

Wouldn't you be comparing 20/35 to 16/35? I'm taking the 4/7 and multiplying it by 5/5 to get the common denominator. No?

Edited December 20, 2011 by Teachin'Mine

[regentrude]

4th grader is supposed to say whether 4/7 is equal or not equal to 16/35.

 

I've tried a couple of different ways:

Cross multiply- which she won't want to do because she has to do it on a separate piece of paper and write it out. If the multiplication like 4 x 35 and then 7 x 16 was on the sheet, then she could do it. But the extra step of figuring it out kills her.

 

Or.. look what would you multiply 7 by to get 35. ( After several minutes as she is NOT good at division AT ALL) 5. Ok.. yes. What happens if I multiply 4 x5. What do you mean that doesn't make sense. Ok, remember we have to multiply a fraction by the same number on the top and the bottom to get an equivilent fraction. That doesn't make sense. Sigh...

 

First of all: I would only begin fractions if my student was completely solid on arithmetic (addition, subtraction, multiplication and division) with integers.

Second: Before beginning to compare fractions, I would make sure the student is solid in simplifying fractions and can do so without much thought (i.e. seeing that 20/35 = 4/7 by canceling). This requires practice to make the process automatic.

Next, I would teach the student the reverse process and make sure he learns to expand fractions to a larger denominator by reversing the canceling process. Again, practice until mastered. Make sure the student understands exactly what he is doing and does not simply memorize a recipe.

Not until all these skills are mastered would I introduce comparison of fractions that are so complicated that drawing does no longer work (1/2 and 2/3 you can draw- 4/7 and 16/35 you can no longer draw).

 

There is a graph with a vector drawn on it. Ok write the ordered pair of the vector.

To which he writes ( -3, 1) ( This is the ordered pair for the intial point of the vector not the ordered pair of the whole vector.)

No.. remember we have to figure out the number with a formula.

 

Oh, yeah the (x2- x1) (y2- y1) and then the square root..(I don't know how to do the subscripts on here)

 

No that isn't quite right. You will just get one number from that formula. Remember we want the ordered pair not the distance. Although you are close. I don't know... Ok let us go back and look.

 

OH YEAH I just subract the x's and y's. YES.

 

I've had this conversation 3 different days.

Use graph paper for these kind of problems.

First: Teach student to graph points on the Cartesian plane (practice) and to read coordinates of a point off a graph (practice)

Second: Teach student to graph pairs of points on the Cartesian plane (practice), line segments, and to read end point coordinates off graph.

Third: Help student discover what the relationship between the points and the ordered pairs for your vector is. Then develop a formula and practice.

 

The problems you describe sound to me as if your 4th grade student is trying to learn skills for which he does not have the adequate preparation.

 

For your 7th grader, it would help if he was involved in the process of discovering WHY things work the way they do - rather than you repeating which formula to use. Knowing the formula does not teach him anything - he needs to understand why.

Edited December 20, 2011 by regentrude

[choirfarm]

I'm truly not understanding where 24/45 is coming from. :confused:

 

Wouldn't you be comparing 20/35 to 16/35? I'm taking the 4/7 and multiplying it by 5/5 to get the common denominator. No?

Here are the problems. You must tell whether they are = or not =

 

4/7 and 16/35, 4/9 and 24/45

[choirfarm]

See my questions inside.

 

First of all: I would only begin fractions if my student was completely solid on arithmetic (addition, subtraction, multiplication and division) with integers. Ok, if not is that all you do??? So we should only be doing multiplication?? She is doing division with remainders and is now showing the steps instead of doing it in her head. ( And yes she is doing all of this in her head while skip counting..don't ask me how.) x-tra math so far has been the most helpful by far. She typically does 70 or so multiplication in the progress section each day as well as 2 race the teachers that I think have 30 problems or so each. I don't know how much more to have her do..

 

Second: Before beginning to compare fractions, I would make sure the student is solid in simplifying fractions and can do so without much thought (i.e. seeing that 20/35 = 4/7 by canceling). This requires practice to make the process automatic.

Next, I would teach the student the reverse process and make sure he learns to expand fractions to a larger denominator by reversing the canceling process. Again, practice until mastered. Make sure the student understands exactly what he is doing and does not simply memorize a recipe.

Not until all these skills are mastered would I introduce comparison of fractions that are so complicated that drawing does no longer work (1/2 and 2/3 you can draw- 4/7 and 16/35 you can no longer draw).

OK, so just skip those problems. As I said, today is the last day for these kind of problems. It doesn't do anymore of those for the next 40 lessons. It does have subtraction with like denominators. I think she could do that.

 

 

 

The problems you describe sound to me as if your 4th grade student is trying to learn skills for which he does not have the adequate preparation.

 

.

 

All right I did Saxon 1st- half of 3rd with supplementing with Singapore. Then we switched to Horizon. If Horizon isn't teaching things correctly then what?? I am so tired of switching curriculum. What do I use so she won't fall behind? She is such a strange girl. As I said, she was doing division with remainders in her head until I made her go through the steps and subtract and all of that since it will be introducing the harder ones later where she will HAVE to. She can also do the problems like n+5= (2x4) + 5 in her head. ( I still can't figure out why Horizons has this in a 3rd grade book. To me, this seems like a prealgebra problem. But she thinks these are easy and fun.)

[choirfarm]

Use graph paper for these kind of problems.

First: Teach student to graph points on the Cartesian plane (practice) and to read coordinates of a point off a graph (practice)

Second: Teach student to graph pairs of points on the Cartesian plane (practice), line segments, and to read end point coordinates off graph.

Third: Help student discover what the relationship between the points and the ordered pairs for your vector is. Then develop a formula and practice.

 

.

 

For your 7th grader, it would help if he was involved in the process of discovering WHY things work the way they do - rather than you repeating which formula to use. Knowing the formula does not teach him anything - he needs to understand why.

 

First of all this is my 9th grader in Geometry. He can easily draw cooridinates on a graph. He can easily read co-ordinates on a graph. I just tested him.

 

Third: Help student discover what the relationship between the points and the ordered pairs for your vector is. Then develop a formula and practice.

 

I don't understand this at all. How do you discover what the relationship?? I've always just used formulas.

[Teachin'Mine]

Here are the problems. You must tell whether they are = or not =

 

4/7 and 16/35, 4/9 and 24/45

 

 

See the way I read that is that it's two separate questions. The first being are 4/7 and 16/35 equal, and since 20/35 is more than 16/35, they're not equal.

 

In the second, you would again multiply the first fraction by 5/5 and would get 20/45. 20/45 is less than 24/45, so they are not equal either.

 

I think that's what they're asking ... or by "and" do they mean to add the two and then compare the results? One would be 36/35 and the other 44/45, so this may be what they mean. One is slightly more than 1 and one slightly less. Strange way of wording a question.

 

Oh ... duh lol ... now I see why you'd be trying to show 24/45. : P Eventually I catch on! lol

 

FWIW - probably less than 2 cents - I'd be working on multiplication tables and trying Saxon 5/4.

Edited December 20, 2011 by Teachin'Mine

[regentrude]

Third: Help student discover what the relationship between the points and the ordered pairs for your vector is. Then develop a formula and practice.

I don't understand this at all. How do you discover what the relationship?? I've always just used formulas.

 

That is exactly the problem: using formulas without understanding. How can he memorize this lifelong if he does not know WHY?

If I had to teach this, I might start like this:

Draw the vector. Draw a right triangle with the hypotenuse being the vector itself, and sides parallel to teh x-axis and parallel to the y-axis. Color the sides two different colors. Find out how long they are from graph. Look at coordinates of points. Do you notice something interesting? Yes, the x-side length is x2-x1. Does that work for the y-side too? Oh yes, it does.

Let's investigate this more systematically. Look at a vector that is parallel to the x-axis. Then take one that's parallel to the y-axis.

Now let's take another slant vector, repeat the procedure, see if it works out agian. Yep, it does.

Can we pout our discoveries into a formula? Come up with formula.

Does the formula work for the extreme cases of vectors that are parallel to the axes? Yes, it does. Cool.

Now go practice using formula.

 

Same procedure will also lead to discovering that length of vector (measure!) can be found from side lengths using the Pythagorean theorem. (Again, try out on the extreme cases of vectors parallel to axes)

[regentrude]

OK, so just skip those problems. As I said, today is the last day for these kind of problems. It doesn't do anymore of those for the next 40 lessons. It does have subtraction with like denominators. I think she could do that.

Sounds like Saxon?

I think she might benefit from a more structured program that is mastery based and does not jump between topics as much.

 

And yes, I would personally work on arithmetic with integers until mastery BEFORE moving on to fractions- since you see that division is an essential skill to make sense of the fraction operations.

If she is ready, I would then pick a curriculum that focuses on fractions and stays on topic without jumping for a dozen lessons off to a different subject.

[choirfarm]

That is exactly the problem: using formulas without understanding. How can he memorize this lifelong if he does not know WHY?

If I had to teach this, I might start like this:

Draw the vector. Draw a right triangle with the hypotenuse being the vector itself, and sides parallel to teh x-axis and parallel to the y-axis. Color the sides two different colors. Find out how long they are from graph. Look at coordinates of points. Do you notice something interesting? Yes, the x-side length is x2-x1. Does that work for the y-side too? Oh yes, it does.

Let's investigate this more systematically. Look at a vector that is parallel to the x-axis. Then take one that's parallel to the y-axis.

Now let's take another slant vector, repeat the procedure, see if it works out agian. Yep, it does.

Can we pout our discoveries into a formula? Come up with formula.

Does the formula work for the extreme cases of vectors that are parallel to the axes? Yes, it does. Cool.

Now go practice using formula.

 

Same procedure will also lead to discovering that length of vector (measure!) can be found from side lengths using the Pythagorean theorem. (Again, try out on the extreme cases of vectors parallel to axes)

 

 

I'll have to go try this, but you lost me a little bit. IS the triangle itself what the vector is?? I mean all they show is a little ray for the vector. To be honest, I don't remember doing this in school. And what else is strange is I got the Cliff Notes Geometry and vectors aren't even in there!! I can do all the Geometry in the Cliff Notes book.. Sigh.. I'm not sure how to do this...

[regentrude]

I'll have to go try this, but you lost me a little bit. IS the triangle itself what the vector is?? I mean all they show is a little ray for the vector. .

 

A vector is a ray or piece of line that has length and direction - a vector is NOT a triangle!

The vector is typically at some angle with respect to the axes, so the triangle I was talking about is what you can construct if you use this vector as hypotenuse and draw what is commonly known as the components: lines parallel to the x-axis and the y-axis that close with the hypotenuse to a right triangle.

[Teachin'Mine]

Sounds like Saxon?

I think she might benefit from a more structured program that is mastery based and does not jump between topics as much.

 

And yes, I would personally work on arithmetic with integers until mastery BEFORE moving on to fractions- since you see that division is an essential skill to make sense of the fraction operations.

If she is ready, I would then pick a curriculum that focuses on fractions and stays on topic without jumping for a dozen lessons off to a different subject.

 

Sounds nothing like Saxon to me. Saxon has continual built in review - concepts may not be built on within a teaching lesson for a while - but they are always reviewed in the daily problems and often built on within the problems themselves.

[happyhomemaker]

Dd went through Horizons 3 last year and I remember thinking that the section on fractions and ratios was too advanced. We went over it, but I didnt stress out about perfect mastery. I went for exposure to the concept and we went on. Since it's a spiral program, you will hit it again. We havent covered it again this year yet, but if I dont like how they teach fractions again, I might get the blue book from MM or go through Key to Fractions with her and just skip the fractions stuff in Horizons. I am not loving Horizons, but I dont want to switch her again so I think I will supplement the weak points as best I can.

 

For the specific problems you mentioned, I believe they want the kids to make the fractions have the same denominator and then determine whether or not they are equal. I tried explaining cross multiplication and got a :001_huh: face from dd so we went back to making everything have the same denominator.

[Julie Smith]

Let us take two examples:

 

4th grader is supposed to say whether 4/7 is equal or not equal to 16/35.

 

I've tried a couple of different ways:

Cross multiply- which she won't want to do because she has to do it on a separate piece of paper and write it out. If the multiplication like 4 x 35 and then 7 x 16 was on the sheet, then she could do it. But the extra step of figuring it out kills her.

 

Or.. look what would you multiply 7 by to get 35. ( After several minutes as she is NOT good at division AT ALL) 5. Ok.. yes. What happens if I multiply 4 x5. What do you mean that doesn't make sense. Ok, remember we have to multiply a fraction by the same number on the top and the bottom to get an equivilent fraction. That doesn't make sense. Sigh...

 

For this one if my son didn't get it, I would have a big smile on my face and say, "Okay we are done math for the day. I'll explain it tomorrow."

 

Then the next day I would....

 

Lesson 1:

I would have some paper ready and scissors and be ready to re-explain fractions. We would cut paper into different equal sizes and I would make sure that my son had a good understanding of fractions.

 

First I would take a red piece of paper and cut it in half and right 1/2 on each side.

 

Then I would cut a green piece of paper into three pieces and write 1/3 on each on.

 

Then I would cut a blue piece of paper in four pieces and write 1/4 on each side

 

... all the way up to 1/10

 

We would examine the pieces and master being able to tell which is bigger, and which is smaller when the top number is the different, and the bottom one the same. It will be discovered that it is easier / possible to compare fractions when the bottom number is the same.

 

Lesson 2:

The next lesson we would then do comparisons. I would show that 1/4 and 1/4 is the same as 1/2 and vice versus. This would then turn into a pencil and paper project that teaches how to convert 1/2 to 1/4.

 

We would then redo this lesson with 1/3 and 1/3 being equal to 2/6.

Then again with 1/4 being equal to 1/8 + 1/8

And so on and so on....

 

This will cement the understanding of fractions. It will also start gently how to work with fractions in a math sense, instead of just pieces of paper cut into fraction size.

 

Lesson 3:

This lesson would teach the mathematical way to convert fractions so that they have a different bottom number. We would know that it is easier to compare the size of fractions if they have the same bottom number because of lesson 1.

 

Lesson 4:

My son would then try to do the question he got stuck on.

 

I would also reserve all the library books I could on fractions. Or any math subject that shows fractions. :)

 

And this is why my son gets that fear look in his eyes when I say, "Don't worry if you can't get it. We'll work on it tomorrow." He doesn't like having these re-lessons. So he tires hard to get it himself. :)

[kiana]

I'll have to go try this, but you lost me a little bit. IS the triangle itself what the vector is?? I mean all they show is a little ray for the vector. To be honest, I don't remember doing this in school. And what else is strange is I got the Cliff Notes Geometry and vectors aren't even in there!! I can do all the Geometry in the Cliff Notes book.. Sigh.. I'm not sure how to do this...

 

The vector has an x-component and a y-component when you write it as an ordered pair.

 

The x-component is how far right/left you're going and the y-component is how far up/down you're going.

 

So if your vector is (2, 3) starting at the origin, you'd plot (2, 3) and draw a line segment from the origin to (2, 3). Right? To get to (2, 3) you can move along the path of the vector itself, or you can move right 2 and then up 3. These are the lines that regentrude was telling you to draw in -- the moving right 2 and then up 3.

 

Now, if your vector is going from (1, 1) to (3, 4), you'd plot both the points and draw the line segment between them. To visually find the x-component and y-component of the vectors, you can do the following.

 

Add in the point (3, 1), and draw a line from (1, 1) to (3, 1) and thence to (3, 4). You can see that with the additional two lines drawn in, there is a right triangle with the vector at the hypotenuse.

 

To find the x-coordinate, move along the horizontal line. You've gone 2 to the right, (from (1, 1) to (3, 1)), so your x-coordinate is +2. To find the y-coordinate, now move along the vertical line. You've gone 3 up (from (3, 1) to (3, 4)), so your y-coordinate is +3.

 

Or you can just memorize the formula. But ... if you don't understand why the formula *works*, you're just picking formulas out of a hat until you hit the right one.

 

The same thing goes for the distance formula, which you've mentioned your son struggling with before. Once the horizontal and vertical lines are drawn in (using the same triangle as above), you can see that the length of the vector is the hypotenuse, the length of the base is 2 and the length of the side is 3, and use the pythagorean theorem to find the length/distance of the vector. This is the origin of the formula.

 

I do apologise for the inherent limitations of a text-based interface. :P

[choirfarm]

For this one if my son didn't get it, I would have a big smile on my face and say, "Okay we are done math for the day. I'll explain it tomorrow."

 

. :)

 

But that is only 4 problems. Then there are 4 problems on Roman numerals, 4 solve the equation for n problems, 6 division with remainder problems, 10 math problems adding 5 digit numbers with decimal, 4 problems to find area, and 2 word problems. So would you just skip the fractions?

 

I did your suggestions for 1 and 2 when it was easy with pictures. These are much harder.

[regentrude]

But that is only 4 problems. Then there are 4 problems on Roman numerals, 4 solve the equation for n problems, 6 division with remainder problems, 10 math problems adding 5 digit numbers with decimal, 4 problems to find area, and 2 word problems. So would you just skip the fractions?

 

If fractions is the only thing where she has difficulties, maybe.

But seriously: A program like this makes my head spin. It would have driven both my children nuts.

Are you SURE that your DD learns best this way? From your posts about math frustration, I would really, really try to switch to a program that covers ONE topic until mastery and then moves on to the next in a LOGICAL sequence. Not random stuff like this.

[Julie Smith]

But that is only 4 problems. Then there are 4 problems on Roman numerals, 4 solve the equation for n problems, 6 division with remainder problems, 10 math problems adding 5 digit numbers with decimal, 4 problems to find area, and 2 word problems. So would you just skip the fractions?

 

I did your suggestions for 1 and 2 when it was easy with pictures. These are much harder.

 

Well I am doing Singapore math, right now we are about to start 3A. I have found with my son if he doesn't get a concept we will work on that concept till he gets it. Then move onto the next concept. It is rare for him to not 'get' a question. I think this is in part to the fact we master it before moving on to the next concept. Also he hates doing hands on math - so having me explain something to him bugs him. :)

 

If the curriculum I choose says he needs to know how to do something I assume he needs to know it and I don't move on till he understands it. I would rather he fully understands a little math then partially understands lots of it.

 

I think for him this has worked out because he doesn't find math a mystery. It always makes sense for him. If something confuses him we work on it till he sees the light. :)

 

If you work on mastering fractions. Then, if you have a good library follow up with fraction related books. Then it is likely the next time you kid gets to a fraction question it will be easy. That way you will have more time to focus on a different difficult concept.

 

If it takes a long time before I can move onto the next page, then so be it.

 

Once we spend 3 weeks mastering the understanding of the number 6. (As in number bonds totaling 6. Addition and subtraction questions totaling 6. The many different ways to make 6. ....) I was so HAPPY to finally move on when the time came. But he needed to spend that long on that subject to master it, so we did.

 

When my eldest gets a question he can't answer I try to figure out what information he is missing that makes it impossible to get that question. We then work on every little step that can help him understand it before moving on.

 

It sounds like the curriculum you are using repeats subjects. So if you take the time to master fractions, and roman numerals, and.... then the next time those subjects get repeated you wouldn't have to re-master and re-teach them on every page.

 

In other words if you take the time to master those hard subjects now (fractions, roman numerals) it will make it easier in the future.

[choirfarm]

If fractions is the only thing where she has difficulties, maybe.

But seriously: A program like this makes my head spin. It would have driven both my children nuts.

Are you SURE that your DD learns best this way? From your posts about math frustration, I would really, really try to switch to a program that covers ONE topic until mastery and then moves on to the next in a LOGICAL sequence. Not random stuff like this.

 

 

I'm just not sure what that is. To be honest, my oldest one taught himself math. My middle one looked at the textbook/computer ( Horizon upper elementary, then TT for 7th then Chalkdust Alg) I just helped him when he got stuck. This is the first year I've actually tried to "teach" him.

 

I've gotten votes for Saxon and MM. Anyone know which one would be better. I'm going to the curriculum store on Thursday anyway to redeem coupons that are about to expire and I have some credit from other things I've bought.

[Teachin'Mine]

Look at any of the texts you are interested in before buying them. Skip to a lesson in the middle of the book, and really read it, and see if it makes sense to you since it sounds like you'll be teaching them. If your student will be doing the book on their own, then let them look through and see if they understand how things are being taught. HTH

[kiana]

I'm just not sure what that is. To be honest, my oldest one taught himself math. My middle one looked at the textbook/computer ( Horizon upper elementary, then TT for 7th then Chalkdust Alg) I just helped him when he got stuck. This is the first year I've actually tried to "teach" him.

 

I've gotten votes for Saxon and MM. Anyone know which one would be better. I'm going to the curriculum store on Thursday anyway to redeem coupons that are about to expire and I have some credit from other things I've bought.

 

Firstly, I'd do my very best to preview the books for myself.

 

But IMO, given that you've stated before that you often understand how to do a problem but not how to explain it, I would choose MM first. It's also easier to pick out a specific topic to work on. Saxon has a wide variety of problems every lesson. I think Saxon might appeal to you more personally, but I think MM will make it easier for you to explain in more than one way. Again, JMO and I'd try very hard to preview before switching.

 

A main focus of MM's 3rd grade was on learning the multiplication tables. Maybe her method would help your dd if she's still struggling on that?

[choirfarm]

F

A main focus of MM's 3rd grade was on learning the multiplication tables. Maybe her method would help your dd if she's still struggling on that?

 

Actually, I bought MM multiplication when currclick had it on supersale. We were bored out of our mind doing only multiplication day after day after day... But maybe if you get the whole curriculum then you could do a page from the each section??? I guess I don't see her doing 45 minutes of just one topic: multi-digit multiplication, division with remainder. I don't know...

[Caroline]

I would ask for the components of the vector as opposed to the ordered pair. Ordered pair implies a point. Components implies vector.

 

 

 

Or Geometry

 

There is a graph with a vector drawn on it. Ok write the ordered pair of the vector.

 

To which he writes ( -3, 1) ( This is the ordered pair for the intial point of the vector not the ordered pair of the whole vector.)

 

No.. remember we have to figure out the number with a formula.

 

Oh, yeah the (x2- x1) (y2- y1) and then the square root..(I don't know how to do the subscripts on here)

 

No that isn't quite right. You will just get one number from that formula. Remember we want the ordered pair not the distance. Although you are close. I don't know... Ok let us go back and look.

 

OH YEAH I just subract the x's and y's. YES.

 

I've had this conversation 3 different days.

[Julie in MN]

Here are the problems. You must tell whether they are = or not =

 

4/7 and 16/35, 4/9 and 24/45

 

I'm agreeing with Teachin'Mine:

 

I think that not having her math facts memorized is going to make it a slow go for everything else.

 

It should jump out at her that 4 x 4 is 16,

but 7 x 4 is 28, not 35.

So they aren't equal.

 

If she sees 4 & 24, she should automatically know it's 6 that gets you from one to the other...

but if you use 9 x 6 is not 45, it's 54.

So, again not equal.

 

I don't think you have to do any long, drawn-out explanation there. Her math facts should jump right out, 4x4=16. If it doesn't jump out, then it's those math facts that need work first.

 

Julie

[creekland]

You might want to remember that it takes an average person 7 times of seeing something to "get it." Some can be above average and "get it" with seeing it once or twice. Others might need 10 - 14 times. Training the brain is a process.

 

Visually is great. We're coloring parts of rectangles in my pre-alg class to have a better understanding of fractions this week. We're doing it with probability, but one can do it for sheer comparisons as well.

 

Then learn the "short cut" of cross multiplying to check.

 

Drawing vectors and components usually helps to visualize those. Three days? Four more to go to be "average." ;)

[choirfarm]

I'm agreeing with Teachin'Mine:

 

 

I don't think you have to do any long, drawn-out explanation there. Her math facts should jump right out, 4x4=16. If it doesn't jump out, then it's those math facts that need work first.

 

Julie

 

Ok, but we are doing it and I am sick of it. She only has her addition facts automatically. I've been doing multiplication since 3rd grade: flashcards daily, songs, timed sheets with Saxon for the first half of the year. Someone told me x-tra math and when she started 22 days ago she had 33 percent in multiplication. After those 22 days she is at 76 percent. ( She got up to 95 percent in addition in 5 days before that.) After this I will go back to subtraction and then division. She will be 10 in less than 2 weeks. Sigh.. it seems like she should know her multiplication by now. But even the ones x-tra math says she knows, she will skip count when doing the problems on the worksheet.

[1Togo]

Sending a pm about math fact memorization.

[Halftime Hope]

here's a nice link to playing war to solidify number fact families for your younger one:

 

http://letsplaymath.net/2006/12/29/the-game-that-is-worth-1000-worksheets/

 

This was what we did for ds1 and ds3, both of whom had a hard time getting math facts to stick.

 

Also, I would not teach the 4th grader to cross multiply at this point. The cross multiplying is a short cut, and she needs to thoroughly understand the concept of fractions and have automaticity in her fact families, before you teach her a short cut. Cross-multiplying leaves out so many steps that she doesn't really get yet.

[Julie in MN]

Ok, but we are doing it and I am sick of it. She only has her addition facts automatically. I've been doing multiplication since 3rd grade:

 

I used to tutor at Kumon. We had high schoolers who came in and started with addition facts. They required doing problems every day of the week (well, we skipped Sundays at our house), repeating until a set was mastered (both oral recitation and worksheets). Tests could not be passed in the required time limits without facts having been committed to memory, so no moving ahead until conquered.

 

Since math facts build on themselves, it just makes sense to start at the beginning and stay there until mastered. Your other math doesn't have to stop, though.

 

Julie

[LizzyBee]

I can so commiserate! My 10 yo dd is solid on arithmetic up to fractions. She really is. She had her annual standardized test last week and scored at a solid mid-5th grade level for math, 6th grade 6th month for applied word problems. She knows her basic math facts. I thought fractions would be easy for her. She's dyslexic, but good at math. I have explained equivalent fractions every which way, used blocks and fraction towers, drawn pictures.... and she is just not getting it. I've explained and shown her that multiplying or dividing by 3/3, 4/4, 5/5, etc. is the same as multiplying or dividing by 1, but that didn't help.

 

When she was 6-7, she really struggled to learn the "language" of math, but she could do word problems easily when you put them into regular English. IOW, she couldn't understand 2 + 2 = 4, but could easily understand and calculate that if she had 2 apples and I gave her 2 more, she would have 4. I am trying to figure out what the language barrier is with fractions, but I'm running out of ideas and I'm about to pull my hair out!

Edited December 21, 2011 by LizzyBee

[flyingiguana]

Did anyone post the MEP link?:

http://www.cimt.plymouth.ac.uk/projects/mep/default.htm

 

At the least, these are really good for review and extra practice, even if they're not used as the main curriculum. There are some nice online interactive problems.

[LizzyBee]

After I typed out my post yesterday, I remembered that we have Right Start C. I pulled it out and dd is loving math again. RS introduces equivalent fractions slowly, incrementally, visually, and hands-on.