Need Math Help

[school4princesses]

I can't answer about Singapore as I don't use it. But Khan Academy is a great place to go for explanations on any math topic you can imagine. There are videos to watch and, if you so choose, exercises you can do online to see if you understand what's being taught. Certainly worth checking out when the curriculum either doesn't explain or explain in a way that makes sense to our kids (or usually in my case - to me. )

Blessings.

[my3sons]

Hi Jessica! I would love to be able to pull out my 3A/3B Textbooks and Workbooks from past years and take a look at this too. Could you please share the Textbook and Workbook pages for this assignment? Then, I'll find my old books and take a look at them with you, and maybe be able to help better.

...In today's lesson the textbook asks you to find the equivalent fractions of 6/12, and then wants you to give the simplest equivalent fraction of 6/12. I know that it's 1/2, but there was no explanation of what the simplest equivalent fraction is, or what makes it the simplest, or how to find out if it's the simplest. It then goes on to ask you to "express each one of the following (8) fractions in its simplest form."

In Christ,
Julie

[Nealewill]

Julie - it is on page 70-73 in the 3b textbook.

Here is how I taught equivalent fractions to my kids. I would do the strip of paper like the did on page 70. I would have a strip and have them fold it. Then I would have them color half of the strip. Then we would fold it again. You could still see that 1/2 of it was folded but we now have 4 pieces so only 2 pieces are colored and 2 aren't. That is still 1/2. Then I would fold it again. Now we have 8 parts and 4 are colored. Same thing. I would also point out what we did. We split each piece in 2. So by doing that, we created twice as many pieces. (x2 for each part of the fraction). And then I would have them work the text book problems by drawing the picture listed on page 71. So they would have to draw (on a separate piece of paper or the dry erase board) the 2/3 bar. Then I would have them physically put the lines on it to show how each portion was affected. So they would physically have to turn each 1/3 into 2/6. Then they could see what portion was colored. So they would see the 3s turned in 6s and that the 2 would then turn into a 4. I would do the same for the 9ths. I would have them physically transform the 2/3s in the 6/9ths on paper. Then they could see the pattern that is taking place. My oldest is extremely hands on. This is how she learns. My other two can see from the picture but not my oldest. So I would do each of these items this way. This way she could experience what is happening. Yes, the lesson takes a little bit longer. But honestly, if I don't do this, my oldest won't get it. So I have to do this. I would do the same thing with the circles on page 72. I would have her work through "transforming" them into the new fraction. I found this type of activity worked wonders for me. And then on the worksheet, you could have them draw it. I would let my dd pick if she wanted to draw it but if she missed it, then she had to redo that problem and she had to draw it.

[Mom4Him]

Hi Jessica! I would love to be able to pull out my 3A/3B Textbooks and Workbooks from past years and take a look at this too. Could you please share the Textbook and Workbook pages for this assignment? Then, I'll find my old books and take a look at them with you, and maybe be able to help better.

Thanks, Julie! Yesterday's assignment was Textbook 3B number 6 on p. 73 - number 7 on p. 74; Workbook 3B p. 99-100

They're getting what equivalent fractions are (I think), but it was the *simplest* equivalent fraction that I was having trouble explaining. I get that it's the *simple* form, but how do you explain what makes it the *simple* form? In a round about way I told them it was when you couldn't divide the numbers anymore. The rest of p. 73 has them finding either the numerator or the denominator of the simplest equivalent fractions throughout the page, but there's nothing actually indicating that 2/3 or 1/2 are the simplest fraction - or what makes it so. Does that make sense?

In a way I was thankful we came to this "tricky part" - as we'd had some really great math days, and I was beginning to wonder if I'd made up the whole struggling thing in my mind.

As I've been thinking about it, I've realized that this really hasn't been a problem at all with my second grader. She is much better at math, but I think once I've gone through it with my older girls - it's been easier and I've felt much more confident to teach my next one in line. Although I often can't tell it's a tricky part until we're actually working on it, maybe it would help if I would take some extra time to look through the pages carefully before doing the lesson with the girls, so that I could look up (or ask about) any areas that aren't explained well (although I don't want to explain everything to death either).

I can't answer about Singapore as I don't use it. But Khan Academy is a great place to go for explanations on any math topic you can imagine. There are videos to watch and, if you so choose, exercises you can do online to see if you understand what's being taught. Certainly worth checking out when the curriculum either doesn't explain or explain in a way that makes sense to our kids (or usually in my case - to me. )

Jennifer, Thank you for the great idea. I'll have to check it out! I appreciate you, dear friend!

Here is how I taught equivalent fractions to my kids...

Daneale, Thank you for your sweet help! I really liked the hands-on activity on the first page of equivalent fractions, because that helped my girls get off to a great start. They like hands-on too.

Thank you, everyone! I think at this point I mostly am looking for reassurance in continuing with Singapore. But would love honest feedback about future levels and their explanations of more difficult math concepts.
Blessings,
Jessica

[StephanieU]

To work on the simplest form "graphically" you can use graph paper. If the denominator is 12 for example, have them draw a rectangle that is 1x12 with black marker or pen. Draw the lines for each square with pencil. Then color the squares for the numerator. Now ask them if there is a way to erase some lines and still leave equal pieces (and only whole pieces are colored). If so, erase those. Then write that fraction. Then try again. If you get to the point you can't erase any more, then it is in simplest form.

[MomtoJGJE]

Honestly it sounds like you did a great job? I also explain that they are saying to get it as low as it can go when they say simplest form. If I'm remembering correctly, and I might not be, that's when fractions are really just being introduced for the first time. Working with them I mean, not just knowing what makes a fraction. So think of this as the introduction to reducing fractions. They will get a lot of practice through the years.

[TrueGRIT]

What a great thread - this should be one to remember and refer to often! Such wise words here! One comment as far as the 'do they have to work it out or not?' In the Textbook portion, I make them work it out the way Singapore guides them to (often noted by Singapore in thinking word bubbles). In the Workbook portion, if they want to do it more mentally and they are able to get it right, I'm all good with that, until they miss several problems. Then, I just point out they need to go back to doing it the way I just taught them in the textbook, as their way (for now) isn't working, but I always stress I like that they are trying to do math mentally and that this is a great way to continue to build that skill over time, though maybe it's just not the best way to work problems with skills they JUST learned. Oh, and I do make them draw out the 'bars' for word problems that the Textbook examples showed them to do that for - as this is a WONDERFUL way to solve future, more difficult problems. (Solve for the 'unit' and you can figure out the answer to almost anything! It's pre algebra made easy, really.) That is just what we do though, so those are just some thoughts to ponder as you decide how you want to approach this.

In Christ,
Julie

Thanks for this. I think I have been making math more difficult for my oldest. He is normally good with math and has been struggling lately. I have never been good with math. He can look at a problem and know the answer but not how to work it out. I suppose I should let him do it that way more often unless it says differently?

Thanks for the thread Jessica, you certainly are not alone. I am trying to learn as well.

[amysconfections]

It was about level 3 when I got really frustrated with Singapore. I bought the Home Instructor guides and they helped a lot. I did not use them to teach out of. But, if I wasn't sure how to start off teaching a concept or I got hung up on something I used it.
I think this is what you may be missing. Some of us are just not as up and fresh on our math as others.
HOD does recommend that you drill math facts if they don't get them through the program and are struggling. I'm not sure when they would say drill. I start around 3b. I mostly do multiplication. If they struggle too much with addition and subtraction I drill a bit on that. But not nearly as much as multiplication. I have used websites such as xtramath.com, flashcards, timed drill sheets, etc.
The timed drill sheets seemed to work the best in my house. I just spent 5 min. They competed against themselves to see if they could improve on their own each day.

[Mom4Him]

Thanks (again) everyone.
Honestly the reason I posted about what happened last week was in order to help explain the struggle we're having. In my mind it showed the lack of explanation in Singapore, as well as the extra struggle caused by my girls not knowing many of the very basic math facts yet. We just did the best we could, and have happily moved on. From what I've seen, Singapore has such a unique way of teaching math concepts, that if you're not careful, you can miss them - which may have been what happened on that particular day, but I still think it was a good example of what I was talking about.

Yet, more than wanting specific help with that particular day, I'm wanting to know if Singapore continues in this way. As I'm praying about and deciding how to proceed from here, I'm looking for reassurance in continuing with Singapore, but also honest feedback about future levels and their explanations of more difficult math concepts. There really is so much I really appreciate about Singapore, and I know it takes time to really see the "fruit", but I'm wondering at what point in the frustration and tears do you realize that it's just not working and you need to try something else!?

Thank you so much!
Jessica

[mmschool]

I don't post often, but I thought I would add 2 cents here because I have looked into some of the research that has been done about math learning and it might apply here for your decision.

A brief explanation: your working memory is all of the stuff that you are actively thinking about just this second. And it only has so much space. Think about trying to remember a phone number, it is easier if you already know the area code, because then there is less stuff to try to hold onto. Sometimes your working memory gets over taxed. Think about a time that you are trying to cook a new recipe and suddenly four small people have questions that need to be asked NOW. It isn't that the recipe is too hard, or the questions unanswerable, sometimes you want to scream because your brain overloads handling them all at the same time. There are ways to handle that, though. You ask the kids to wait or make a line for questions. But, a neat trick you brain can do - it can outsource to memory. Think about a time that you were reading a board book, some short story that you have read dozens of times, but really you were thinking about your to do list. You didn't actually think about both, instead you thought about your list while reciting the book from memory! No overload.

The math application is this: it is hard to learn a new concept, especially a multistep process if each step includes tons that you have to think about. For example, long division: you break it into the first part and guess how many times the number goes in. Then you stop and multiply, maybe needing carrying so you have to remember what to add back in. Then you remember what step is next. Then you subtract, maybe with borrowing...and you are only part way through the problem. That is a ton to think about, especially when the calculation at each step needs thinking. On the other hand the process for equivalent fractions is a little more simple with a single calculation involved. Conversion charts are difficult because you are trying to remember half a dozen details - was it four or two quarts in a gallon? plus trying to calculate the actual problems. The long and the short is, that without the facts memorized their brains can overload from too much information to think about for each and every problem.

Perhaps you could spend the next month or so working on the most painless way to memorize some facts, be it falshcards or computer games. I think that Singapore makes a lot of extra practice books, because over there they expect that the parents are helping education at home. I think that they would expect the students to have extra practice on facts or word problems. It may not be super CM, but I don't think it is going against Singapore's "intentions." All the Chinese mothers I know have all kinds of flashcards for their kids to work on! I know that lots of kids are able to make mental models for themselves and they can memorize the facts pretty painlessly, but for some kids their brains don't work that way and it takes more practice. Some kids certainly take longer to work through studied dictation than others! Then, if they get smoother on facts and are able to outsource some of that math to their memories, they might have more space for each new conept and there may be less tears that come from brain overload. I think that if they get pretty good with their facts, but the explanations still leave them hanging, THEN maybe it is the time to consider that you need help explaining the concepts (maybe the home educators guides? I don't know how useful they are) or maybe you all need a program that is presented differently. But right now, with fact stuggles, that could be the root of all the tears. I know when my brain hits overload, too much to deal with right now, I usually burst into tears, so it makes sense as a coping mechanism! You wouldn't necessarily stop other math, or make it as dry as possible, but ten minutes per day, seperated from other math time, drilling facts in some way, could do a lot to make new math come more easily in the future, and allow you to stick with the benefits that you see in Singapore without all of the frustration.

Hope that helps you think through somewhat.
Lena

[Mom4Him]

Lena - that is so, so very helpful!
I love the illustration you provided! Oh, how I can relate. And it makes complete sense for what has been happening during math time.

I've read many times (here on the boards) that eventually kids just pick up these math facts as they go throughout their time in Singapore. And maybe most children do, but mine simply haven't. And from what you've written I can see that not having many of the "simple" math facts in their memories, may very well be the root of our frustrations. I think once we are able to get these math facts engrained in little minds, it will make new math concepts much easier, and will also allow me to more clearly assess our time with Singapore.

Thank you! Thank you! Thank you! I feel I can breathe a bit easier.
~Jessica