Anyone moved from Singapore to Math Mammoth a little later in the game?

[SFM]

We have been using Singapore since 2nd and my son is now in 5th and we have hit a snag. Should I keep pushing through, it seems suddenly like nothing was being retained and that I am having to walk through problem after problem. He is not (nor am I) mathematically inclined and I am starting to wonder if I need more hand holding and more explanations than Singapore PM US edition provides. What about Math Mammoth? Or should I just stick to this topic (dividing fractions and the whole fractions unit) until we are solid? I was already thinking about next year and I was going to us Singapore 6A/6B and now I am wondering if that isn't the most prudent idea. 

 

Any help, tips, or advice? Please tell me I am not the only one who thinks that the dividing fractions unit is difficult!?

 

Thanks.

[kateingr]

A couple thoughts:

 

1. Are you using the Home Instructors Guide with Singapore? If not, it's probably a good time to start using it. It'd be a great resource for ways to teach and explain the concepts to your son.

 

2. Math Mammoth is a great curriculum, but if it's just this topic that's causing your son grief, it probably doesn't make sense to jump ship away from what's worked for him since second grade. My hunch is that it's the topic and not the curriculum--dividing fractions is tough! That said, Math Mammoth does offer a one-topic worktext on multiplying and dividing fractions. Your son might just need to see dividing fractions in a different way, and the pdf is only six dollars, so it could be worth a try. Then, you'll get a good sense of MM and see if it has a style that might fit your son better. 

 

 

http://www.mathmammoth.com/preview/Fractions_2_Fraction_Dividing_Fractions2_Fitting_Divisor.pdf

 

 

 

[SFM]

That is what I was leaning towards. Thank you. Also, yes I use the HiG.

[MamaSprout]

HiG is useful. You can always buy a single MM blue topic book for whatever you are stuck on right now in Singapore and see how it works. We went from Singapore Stds 5b to MM 6a and it has been a good (if not fun) move for us.

[Momling]

We used Singapore and whenever my daughter got stuck, we just jumped over to math mammoth for a while until she was ready to move on... I think it was elapsed time word problems and fractions of sets and long division when math mammoth gave extra practice and a slightly different approach. They complimented each other really well.

[sbgrace]

We hit a snag there too. It's hard to understand/visualize. If my son doesn't understand, he won't remember.

 

I found c-rods were great for really understanding it. Here are the two links I have saved (one video, the other pictures and explanation; I can't now remember which helped me more).

 

 

and

 

http://www.learner.org/courses/learningmath/number/session8/part_b/modeling.html

 

FWIW, we jumped to CLE about a month ago...I'm using Math Mammoth and/or my Singapore materials to supplement the conceptual portion when we need it, but the spiral is really helping at this point.

[SFM]

Thank you very much for the resources and tips. I will check those out.

[letsplaymath]

Here is, hands down, the best way I've ever seen to help kids think through fraction division:

• Fraction Division via Rectangles

[MamaSprout]

<p>Here is, hands down, the best way I've ever seen to help kids think through fraction division:

• Fraction Division via Rectangles

Okay, this makes no sense at all to me. I like the presentation better than circles. Are there other explanations of this somewhere? My DC gets fraction division, but I think it will stick better if she can see it.

[letsplaymath]

Okay, this makes no sense at all to me. I like the presentation better than circles. Are there other explanations of this somewhere? My DC gets fraction division, but I think it will stick better if she can see it.

 

The basic question of division is, "How many of these are in this much?"

 

I will demonstrate how the rectangles work with a simpler example than Fawn used in her blog article, Fraction Division via Rectangles.

 

The trouble with fractions is that they can mean different things depending on what they are a fraction of, so the abstract question "How many thirds in a half?" can land you in a pit of trouble, if you aren't careful to make sure they are both thirds and half of the same amount, the same unit --- in this method, the same rectangle. If you make the units different, say, "How many third cups in a half gallon?" then you have a completely mixed-up mess.

 

So we draw a rectangle that will be the "one" unit for each of our fractions. The easiest way to make sure our rectangles are the same size and can be accurately compared is to draw them with each denominator being one side, so for thirds and halves we would draw a 3x2 rectangle. We make a second copy of the same rectangle. We divide one rectangle into half (or whatever fraction we need) and the other rectangle into thirds (or whatever fraction we need).

 

Now, our basic question "How many of these are in this much?" has a visual meaning: How many of this size piece could we cut out of that size piece?

 

If the division comes out even, that's simple. How many fourths are in a half? Two. Easy-peasy.

 

But if we have extra pieces, like with thirds and halves, then we have to do more thinking. 1/2 ÷ 1/3 = "How many thirds in a half?" When we draw our rectangle, we see that we can cut one "one-third" piece from the half, and then we have a bit extra. We could get PART of another third, but not quite a whole third. What size is the part? How close are we to getting another complete piece? Since our extra bit is one square, it is exactly HALF of a one-third size piece.

 

Therefore, 1/2 ÷ 1/3 = "How many thirds in a half?" = one whole third, plus an extra half a third = 1 1/2.

 

Does that help?

 

How this transitions to the standard flip-and-multiply method: As students draw example after example, focusing on the meaning of each division problem, they will begin to notice a pattern.

 

In particular, using the color code above, "How many blues in the red?", they will see that the number of red pieces they need to cut up is always the same as the red numerator times the blue denominator. And the number of blue pieces (the size they are cutting red into) is always the red denominator times the blue numerator.

 

In other words, flip-and-multiply has a very real, visual meaning in the model. It is a short-cut for exactly the procedure they have been doing. And if they forget the short-cut, they can always go back to the visual model to figure out their answer.

[MamaSprout]

 

But if we have extra pieces, like with thirds and halves, then we have to do more thinking. 1/2 ÷ 1/3 = "How many thirds in a half?" When we draw our rectangle, we see that we can cut one "one-third" piece from the half, and then we have a bit extra. We could get PART of another third, but not quite a whole third. What size is the part? How close are we to getting another complete piece? Since our extra bit is one square, it is exactly HALF of a one-third size piece.

 

Therefore, 1/2 ÷ 1/3 = "How many thirds in a half?" = one whole third, plus an extra half a third = 1 1/2.

 

Does that help?

 

 

This is the part where I was having trouble following the example before.

 

My dc found inverting to be somewhat intuitive (who ever does that? Hooray, Math Mammoth).

 

I also help tutor in an after school program. Having visual examples like this out when I need them "on the fly" is very handy. The students use the book in the blog post.

[letsplaymath]

I think a lot of the confusion in fraction division (and in other applications of multiplication and division as we move into middle school, like rates and ratios and conversion factors) is keeping track of what the numbers mean.

 

For instance:

1/2 ÷ 1/3 = 1 1/2

 

Elementary students are used to thinking of division as splitting something up into smaller parts. But how in the world could you split up 1/2 into smaller parts and end up with a number that's bigger than you started with?

 

It doesn't make any sense at all, as long as you are looking at abstract numbers without thinking about what they mean. You can memorize a rule (flip-and-multiply) that will give you the correct answer. But if you're like most kids, the rule will get jumbled in your head and lead to more confusion. High school students are notorious for committing nonsense with fractions due to half-remembered rules.

 

To make sense of the calculation, you have to go back to the original meaning of division:

1/2 ÷ 1/3 = "How many thirds in a half?"

So our answer will be the number of thirds (or of pieces that size):

1/2 ÷ 1/3 = 1 1/2 pieces the size of one-third.