Singapore 4B, Specific Lessons

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cbollin

Singapore 4B, Specific Lessons

Unread post by cbollin » Thu Sep 09, 2010 3:09 pm

Singapore Math Question
courthart246 wrote:I have a question about math. We are on Singapore 4b. We are working on decimals to the hundredth and thousandth. They have to convert them to fractions and then to the simplest form. What is the easiest way to find the simplest form of a fraction? For instance, 216/1000?

My ds keeps dividing by 2's and it took four different fractions to get it to its simplest form. He's been getting frustrated because it is taking him so long to get down to the simplest form. Perhaps this will be a lesson in perseverance and patience as well!

I know that he could have started out dividing by 4's, but how would he know that? How do I explain that? Is there a quick way to find out what to divide the fraction by in the beginning so that you don't have to keep dividing it by 2?

Any help would be greatly appreciated. Thanks!
I know with my oldest last year in 4A/4B we started with 2's since both were even.
then, she learned through trial and repetition that "oh yeah...if it is a 100 or 1000, I might try 4 first b/c 25 *4 = 100, and 250*4 is 1000"

Memorize some of the common factors as you learn the math facts up through 12 x 12

A little at a time as taught in the Singapore books (so it becomes easier later with factoring). It's ok if it takes a few steps right now. (imo)

-crystal

Julie in MN
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Re: Singapore Math Question

Unread post by Julie in MN » Thu Sep 09, 2010 8:04 pm

courthart246 wrote:I have a question about math. What is the easiest way to find the simplest form of a fraction? For instance, 216/1000? My ds keeps dividing by 2's and it took four different fractions to get it to its simplest form. I know that he could have started out dividing by 4's, but how would he know that? How do I explain that? Is there a quick way to find out what to divide the fraction by in the beginning so that you don't have to keep dividing it by 2? Any help would be greatly appreciated. Thanks!
It sounds like your ds senses intuitively that somehow there must be an easier way. If he's ready, I can think of a few methods that I see math-y kids use:

1. Do a google for "rules of divisibility" and learn those rules. For example:
http://math.about.com/library/bldivide.htm

2. Memorize some of the common factors as you learn the math facts up through 12 x 12

3. I don't know if I can explain this on the computer, but the method my kids have used in algebra involves starting with 2 until you run out of 2's, and then going to 3's, until you get all of the lowest factors. Then the child has to understand that they can be combined...

2|216
2|108
2|54
3|27
3|9
1|3

So then you know that the factors of 216 are 2 x 2 x 2 x 3 x 3 x 1.
Then you find the factors of 100 (2 x 2 x 5 x 5 x 1).
Then you cross off all the common factors (cross out 2 x 2 x 1 from top & bottom).
Then you have what is left (2 x 3 x 3 over 5 x 5).


Okay, that may be overboard for what you need ?? !!
Maybe just the general idea that you want to find the biggest numbers that are in both the top & bottom? If he explores what he thinks the biggest numbers might be, he may easily come up with 4 in this problem (especially if he thinks about coins)...

Just offering some ideas for the kind of kid who wants to learn math techniques outside of the book. Kind of an extension of math facts, which were outside of the lesson. The kids I work with and the kids on my son's math team are that way -- they want to dig in & try things, and learn new stuff!

Not every kid is that way. Some are overwhelmed by an idea outside of what has been taught in the lesson. Ignore my ideas if he is that kind of kid :)

Julie
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cbollin

Re: Singapore Math Question

Unread post by cbollin » Thu Sep 09, 2010 8:18 pm

Julie in MN wrote:Just offering some ideas for the kind of kid who wants to learn math techniques outside of the book.
my oldest does it the way you suggested with factoring, and probably learned it in elementary! LOL LOL
My middle wasn't ready for the connection like that. LOL.

It reminds of early days of AP calculus...... some of us got the picture and pattern real fast with first derivative... others, didn't... but eventually everyone got it.

Julie in MN
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Help with Geometry

Unread post by Julie in MN » Tue Nov 29, 2011 2:59 pm

saralynn wrote:I am having a difficult time with the Singapore geometry. Is there a resource that teaches Geometry from beginning to end?

I skipped it with my 8th grader who is now in Saxon, but it made his 7th grade year more difficult. I have never had geometry, and my brain will not go there with Sing. My 8th grader says that he still doesn't see how to teach the geometry sections with the Sing. even though he is fine with the Saxon geometry. (I have to admit that makes me feel a little better about my struggle with it. lol

We have completed 4A and are a good way through 4B. I do have the text book and the home instructors guide. I am lost with the angles and measuring and which one is which etc. If it was in just one place I could probably dig in and sort it out, but there is a little in several books.

Thanks in advance for any suggestions that you have. At this point I think I just need an additional resource that will take me straight through a basic geometry class.
Sara
With angles, my son had an easy time because he skateboarded & snowboarded, and he knew what a "360" was (i.e. a complete circle). So your snowboard starts flat on the ground at 0 degrees. Everything is based off that -- flipping over (around in a half circle) so you end up flat on the ground again (facing the other way, but flat on the ground again) is 180 degrees; therefore, any two angles that "add up" to that straight line have to "add up" to 180 degrees. Etc. Angles made sense to him based on what he was doing with them in real life.

Does your son relate to something like that? Even food was used a lot at our house as an example -- pizza slices especially were helpful in connecting fractions to angles (1/4 of a circle is 90 degrees, etc).

If you need something visual, I'd search YouTube (if you're okay with using that). You might want to specify "geometry - angles" since geometry will cover other things such as volume and area.

Julie
Julie, married 29 yrs, finding our way without Shane
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cbollin

Re: Help with Geometry

Unread post by cbollin » Tue Nov 29, 2011 3:42 pm

maybe a few tips will help? I found that when I used the HIG for geometry it made it sooooooooooo much HARDER.

Are you struggling along the lines of "how do I read a compass" and use it to make angles and measure them?
If it is perimeter and area and figuring out "missing sides"......
I'm looking at the topics in 4A and that's the major geometry topics in that book.

Julie mention video for specific topics. One source that is becoming popular for video teaching on specific math topics is KhanAcademy.org

You might consider something like the "key to geometry" series?

I know for my middle gal, I used flowcharts - I never wrote them down, but I knew the steps and we'd go through it.

TriciaMR
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Re: Help with Geometry

Unread post by TriciaMR » Tue Nov 29, 2011 4:12 pm

Hmmm, trying to think of a way to explain...

Get a pencil, and tie a piece of yarn in the middle. Now, hold the yarn along side the pencil over by the eraser. Slowly pull the yarn around until it is straight up from the pencil while keeping the yarn taut. The path that the yarn went through is the arc that you want to measure. So, when you put your compass there, you want to start at the 0 by the eraser and go up to where the string is. We just finished angles in 5A, and I had to keep reminding my dd to start at the "0" and count from there when measuring the angles. It's a little confusing that they put a 0 and a 180 at the same point. But, you have to look at where you start and where that arc goes through to figure out where the "0" is.

Also, I have yet to find a compass small enough and that we can see clearly to get the "exact" measurements of the angles in the book. I figure if we get within a couple of degrees of the correct answer, we did pretty good. Especially when the diagram is within and inch of the center binding!

If an angle has a little box in the corner it is 90 degrees. If it is a straight line it is 180 degrees. If it went a full circle, it is 360 degrees.

Don't know if any of that will help you.

-Trish
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MelissaB
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math struggles

Unread post by MelissaB » Tue Apr 08, 2014 4:40 pm

hsm wrote:I am a bit frustrated with math right now. My oldest dd is currently working through Singapore 4B. She started in 2A last spring. Overall, she is doing okay with it. Our goal of course is to finish 5B this summer, so she can move on to Saxon as planned.

Here is the frustration. We have been working on fractions/decimals for what seems like forever. She loathes fractions and really struggles to work those problems. She understands what a fraction is and how a decimal is really a fraction, but working problems like reducing the fraction or finding a common denominator usually results in tears. We have been working hard on this and she just can't seem to move forward. I even printed free worksheets with fractions just to practice these skills.

Another big struggle for her is the word problems, usually ones that use the bar graph method, but any 2 step problem is often too challenging. We do the problems in the text together and I usually will work with her on the workbook problems. She seems to understand as I am showing/explaining, but if she is doing it on her own, she struggles and usually misses it or simply doesn't know what to do with it.

I use reviews as a test to see what she is retaining and understanding and she is often getting many answers incorrect. I am worried she will struggle in Saxon and whether she will be able to finish Singapore "in time". I know in homeschool, timing is somewhat irrelevant, but I would like to keep her on track if possible. I have no intention of switching math, but we could use some advice.
I don't know if this will be helpful.(?) I thought I might share this tidbit:

I went to public schools k-12, and strived to make good grades. My fifth grade year, though, our teacher introduced fractions. I don't know why, but I struggled desperately with fractions and decimals. My 9-wk. report card had a "D" in math &)... I just did not get fractions. The next year, though, it "clicked." I understood fractions easily, and did well.

So, based on my experience (which isn't worth very much! :) ), maybe consider moving on this year. Try again next year and see if she has more confidence in fractions/decimals.
Melissa B. (Arkansas)
Girls ages 16 & 13
Completed K, 1st, and Investigate {ECC; CTG; RTR; Expl.-1850; and 1850-Mod. Times}
"That they may teach the young women to be sober, to love their husbands, to love their children,.." Titus 2:4

bcleeper
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Re: math struggles

Unread post by bcleeper » Tue Apr 08, 2014 8:28 pm

Many kids struggle with fractions. In fact, I am teaching a fraction class at my homeschool enrichment group.

The biggest struggle I have seen has actually been a struggle with multiplication facts. The kids just do not see the common multiples between the two denominators. I don't know if this is your daughter's case, but it is just a thought.

Also, If she has progressed from 2A to 4B in the past year...she may just need a little time to "catch up" and let things settle in her brain. That is a lot of information to process in a year.

There have been times in my kids math learning we have had to take a break from our regular curriculum and work on something else for awhile. Sometimes it is just a developmental thing or a mind block that resolves with time and confidence.

I hope that helps!
Connie
ds-17, ds-14, ds-11, dd-9, dd-almost 9, ds-almost 9, dd-8

hsm
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Re: math struggles

Unread post by hsm » Wed Apr 09, 2014 11:38 am

These are some good thoughts and ideas. She seems to "kinda" get it but not completely so maybe a break will help rest the brain a bit. She has covered a lot of material in the last year. I know they will be covered again. She doesn't have trouble with her multiplication facts. She knows them well, but I do think she struggles coming up with a common multiple. Not sure why that is.
TriciaMR wrote:May I suggest Life of Fred Fractions book. It is funny and engaging, and it really helped my dd.
Tricia- I am hitting my forehead...duh. I have Life of Fred in a box in my basement. I had tried to have her use it a year and a half ago and she hated it but, that was before she had much fraction exposure so maybe it was just too soon. I am going to pull it out. Might be a nice change of pace for her. We will see what happens.
Lori-IL
K/ECC, CtG/Learning God's Story
dd-12, dd-9, ds-6

hsm
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Re: math struggles

Unread post by hsm » Sat Apr 12, 2014 7:55 am

Guess who is liking Life of Fred Fractions now? :-)

If you started late with Singapore and attempted to finish before 7th/saxon, how did you handle bumps in the road and still manage to get through it? Would it be detrimental if she doesn't finish 5B before Saxon?
Lori-IL
K/ECC, CtG/Learning God's Story
dd-12, dd-9, ds-6

Julie in MN
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Re: math struggles

Unread post by Julie in MN » Sat Apr 12, 2014 9:07 pm

hsm wrote:If you started late with Singapore and attempted to finish before 7th/saxon, how did you handle bumps in the road and still manage to get through it? Would it be detrimental if she doesn't finish 5B before Saxon?
I'm pretty sure that you just take the Saxon placement test and make sure she's ready for 8/7, or if she needs to take a level lower in Saxon for 7th grade. The math page says:
  • A 7th grader who has completed Singapore Level 5B or higher should begin Saxon Math at level 8/7.

    All other 7th - 12th graders who are new to Saxon Math should take the Saxon Placement Test and begin where placed.
I was an oddball and I had my son finish 6B Singapore in 7th and then go right into Algebra in 8th, but I had already taught a high schooler Algebra so I was able to evaluate based on what I knew from doing Algebra the first time.

Julie
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hsm
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Re: math struggles

Unread post by hsm » Mon Apr 14, 2014 7:27 am

Julie in MN wrote:My son did a lot of fractions math facts in 7th grade. I was tutoring at Kumon at the time, so that's what I used, but in any case I really encourage keeping up math drill up through fractions.
She is pretty good at basic math facts but more practice certainly wouldn't hurt and she could be a little faster with recall. How do you drill faction math facts? Sorry if that is obvious but I am not sure what you mean. Can you suggest a resource for that? Thanks Julie!
Lori-IL
K/ECC, CtG/Learning God's Story
dd-12, dd-9, ds-6

Julie in MN
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Re: math struggles

Unread post by Julie in MN » Mon Apr 14, 2014 9:26 am

My son did a lot of fractions math facts in 7th grade. I was tutoring at Kumon at the time, so that's what I used, but in any case I really encourage keeping up math drill up through fractions. It makes upper maths so much easier/faster.

Just the basic conversions of like 12.5% = 0.125 = 1/8. Students can be doing math lessons and math drill separately, they don't need to line up.
hsm wrote:She is pretty good at basic math facts but more practice certainly wouldn't hurt and she could be a little faster with recall.

How do you drill faction math facts? Sorry if that is obvious but I am not sure what you mean. Can you suggest a resource for that? Thanks Julie!
You can drill math facts like anything else, with flashcards and computer games and etc. Here is an old post of mine about drilling fractions: http://board.mfwbooks.com/viewtopic.php ... 166#p89166
I think someone else mentioned Key To Fractions on there; my older dd used that. It's a systematic way to step through the ideas, if needed.

But I wonder if you're asking what exactly is drilled? Well, I'll try to think of a few.

1. The main thing I remember was the conversions I mentioned, so things like 12.5% = 0.125 = 1/8, my son had those down well (memorized) when we were done. Even throughout high school, it helped that he knew some of those off the top of his head, to use with things like ratios and complex equations.

It seems like we went up to 1/12? Kumon had a nice way of basically saying a list out loud until you could say it fluently, then doing paper drills of each thing, then slowly mixing them up. Funny, but the info also came in handy when he started using tools in the garage LOL.

2. Also getting down some of the reducing facts, which are basically multiplication/division, but they look different on fraction drill pages. My son got to where he knew by heart some of the big numbers that reduced down to some of the small numbers (I think we went up to 12x12).

A quick google gave this page, which goes on forever, but seems to cover a lot (look for fractions, simplify & convert, and there are drill pages on simplifying fractions like 32/48):
http://www.math-drills.com/fractions.shtml

There are lots of ways to do drill besides worksheets, too, from Quarter Mile Math to Quizlet to flashcards to probably some apps. You eventually may need to search for "middle school" level materials, to avoid too much time on simple concepts.

3. It helps to have those rules of divisibility on hand, to make even big numbers reduce quickly.

For instance, when the last 2 digits are divisible by 4, the whole number is divisible by 4; and if the sum of all the digits is divisible by 9, then the whole number is divisible by 9: http://math.about.com/library/bldivide.htm

4. Practice the difference between +/- and x/: with fractions.

You need common denominators for +/- but not for x/: because you just go across for x and flip for :.

5. I think some of the hands-on games I mentioned in the link to my old post were to get it through my son's head that 1/5 is not good enough for 1/6 in real life, it won't fit, it doesn't work, these things need to be exact. Hands-on seemed to help him with accepting that he couldn't just do it his own way.

Does that help? I'm not meaning two complete math programs, just 10 minutes or so (20 minutes at the most) of drill each day as a separate subject.
Julie
Julie, married 29 yrs, finding our way without Shane
(http://www.CaringBridge.org/visit/ShaneHansell)
Reid (21) college student; used MFW 3rd-12th grades (2004-2014)
Alexandra (29) mother; hs from 10th grade (2002)
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Alicia42
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Re: math struggles

Unread post by Alicia42 » Tue Apr 22, 2014 2:09 am

Don't worry - fractions is something which invariably causes a lot of trouble to teachers and students alike (especially just after you have introduced the basics to the kids). Here's how you can make it simpler for both of you:

1. Try explaining what a fraction is by relating it to something they like, e.g. a pizza. This analogy is bound to be immediately recognized by your daughter. And then move on to simple fractional problems, using the same pizza analogy.

2. Denote fractions as pictures for better understanding. Remember, children are more of visual learners. Mere drawings on paper would also help.

3. You mentioned that working out problems like reducing a fraction to its most simplified problem reduces your daughter to tears. The way out? Don't simply make her do such exercises on paper; try fraction games like these: http://www.mathblaster.com/parents/math ... tion-games These have interactive visual representations of fractions which will keep your daughter interested and in the meantime, she will learn in the process while not realizing that she has actually mastered the basics.

Here's what I recently read somewhere online: The results of the third National Assessment of Educational Progress show an apparent lack of understanding of fractions by 9, 13 and 17 year-olds as well. "The performance on fractional computation was low, and students seem to have done their computation with little understanding," says the study. Meaning thereby that there is hardly any cause for you getting worked up on this front, since this is a universally known problem all along.

Kelly1730
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Re: math struggles

Unread post by Kelly1730 » Tue Apr 22, 2014 7:06 am

I appreciate this thread! I was looking for review ideas for the boys summer math. There are some great suggestions here. I think between Life of Fred, some worksheet drill and on-line math games, I've got it covered;)
Blessings,
Kelly
Mom to 6
Mimi to 8
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hsm
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Re: math struggles

Unread post by hsm » Tue Apr 22, 2014 8:20 am

This is great! Thank you so much for the encouragement and great ideas/links! She loves online games and this looks great!
Lori-IL
K/ECC, CtG/Learning God's Story
dd-12, dd-9, ds-6

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