How does Singapore teach...

[Doodle]

...4+5, 5+6, 6+7, 7+8 ? These were part of our math lesson today. I'm considering switching to Singapore and am curious as to Singapore's approach to these equations.

[johnandtinagilbert]

parts make a whole...at some point, they encourage making 10's.although I can't remember where. We're in 2B and adding 3-digits to 3-digits mentally, by making tens.

[MDMom]

parts make a whole...at some point, they encourage making 10's.although I can't remember where. We're in 2B and adding 3-digits to 3-digits mentally, by making tens.

 

Yep, we are in 1B right now and covered this introduced in 1A.

[Tress]

4+5, would be either just memorised or as double 4 plus 1 or double 5 minus 1.

 

5+6, 6+7, 7+8 , making tens (you could also do doubles plus/minus one, but making tens is the most important).

 

This is all in Singapore Primary Math 1A.

 

HTH.

[Doodle]

4+5, would be either just memorised or as double 4 plus 1 or double 5 minus 1.

 

5+6, 6+7, 7+8 , making tens (you could also do doubles plus/minus one, but making tens is the most important).

 

This is all in Singapore Primary Math 1A.

 

HTH.

 

Our math program instructed the 'doubles plus one' method, which make perfect sense to me. The 'make ten' method seems to be more convoluted, but I guess it is better for more advanced calculations? So in Singapore the 'make ten' for 6+7 would translate into 3+(3+7). Does that illustrate the method of thinking correctly?

[Spy Car]

Oops

Edited February 25, 2010 by Spy Car

[Spy Car]

Singapore lays a ground work of re-grouping numbers from "wholes" to "parts" by a variety of methods including "number bonds" that look (roughly) like this:

 

...9

].^

4....5

 

So a student gets facility in this re-grouping skill and it is not making 10s in absentia (if that makes sense). It does take some time, relative to simply memorizing, but it pays off at promoting mental math skills.

 

Bill

[Tress]

What Bill said :D

 

For 6+7, you would know that 7 is made up of 3 and 4, so you give the 4 to the 6 to make 10, you still have 3, so 10 + 3 is 13.

6 + 7 = 6 + 4 + 3 = 10 + 3 =13

 

 

Other way around, 6 is made up of 3 and 3, so you would give 3 to 7 to make 10, you still have 3 left, 10 + 3 is 13.

6 + 7 = 3 + 3 + 7 = 3 + 10 = 13

 

I know it sounds quiet convoluted :001_smile:, but it is very necessary for calculations with larger numbers and if your child understands this well, adding and subtracting larger numbers is a breeze.

[Aubrey]

What Bill said :D

 

For 6+7, you would know that 7 is made up of 3 and 4, so you give the 4 to the 6 to make 10, you still have 3, so 10 + 3 is 13.

6 + 7 = 6 + 4 + 3 = 10 + 3 =13

 

 

Other way around, 6 is made up of 3 and 3, so you would give 3 to 7 to make 10, you still have 3 left, 10 + 3 is 13.

6 + 7 = 3 + 3 + 7 = 3 + 10 = 13

 

I know it sounds quiet convoluted :001_smile:, but it is very necessary for calculations with larger numbers and if your child understands this well, adding and subtracting larger numbers is a breeze.

 

It *does* sound convoluted to explain it, but this is the way I always did math in my head as a child, & I was absolutely delighted to find a prog that teaches it that way on purpose.

 

Whether or not it's the best way, it's familiar to me, & it's entertaining in a boring grammar class, lol. As if the numbers were matryoshka dolls. Or however you spell that.

[Spy Car]

This week we hit subtraction of numbers such as 13 by 7.

 

And here you subtract 7 from the 10 "part" of 13, and thus have 3 + 3.

 

Which is 6 :D

 

The little-man didn't bat an eye-lash.

 

Bill

[Tress]

It *does* sound convoluted to explain it, but this is the way I always did math in my head as a child, & I was absolutely delighted to find a prog that teaches it that way on purpose.

 

Me too! Me too!

It is just that writing it all down makes it look very cumbersome.

 

This week we hit subtraction of numbers such as 13 by 7.

 

And here you subtract 7 from the 10 "part" of 13, and thus have 3 + 3.

 

Which is 6 :D

 

The little-man didn't bat an eye-lash.

 

Wait untill you come to double digit addition or subtraction. My dd had no problem what so ever, except that she wanted to tell me every little small step.....:tongue_smilie:

 

Then you get something like this:

23 + 18

well, mum, you have 20 and 3 and 10 and 8.

The 8 is 7 and 1, so you give the 7 to the 3 to make 10,

but remember, mum, you still have a 1...

bla

bla

bla

bla

 

For every sum. Every. Sum.:lol:

[ElizabethB]

Number bonds:

 

http://letsplaymath.wordpress.com/2007/01/13/number-bonds-better-understanding/

[The Governess]

Yes, learning the number bonds for numbers 1-10 is so helpful. Singapore really focuses on mastering number bonds before doing any "real" addition or subtraction.

 

When you get to numbers 11-20, you add primarily by "making a 10." So, if you are adding 6+7, you could take 4 from the 7 to make a 10 with the six and then add the three leftover ones to get to 13. Alternatively, you could do doubles plus one: 6+6 is twelve, seven is one more than six so there is an extra one, one more than 12 is 13. Or, you can "count on" so if you are adding 9+3 you could just count three more than 9 to get to 12.

 

There are also some exercises that go like this: 6+7 = 10+?

 

One of the exercises is to draw two rectangles and divide each into 10 squares. If you are adding 6+7, you would put six cubes (or beans, or pennies, etc.) into the squares of one of the rectangles and seven into the squares of the other rectangle. Then your dc would move 4 cubes from the rectangle that has 7 over to the rectangle that has six, so that that rectangle now has 10. Then it's easy to see that there are three cubes left in the other rectangle, which make 13 when you add them to the 10.

 

FYI: A lot of this stuff is only in the teacher's manual, and you'll miss out if you just buy the text & workbook. :001_smile:

[Spy Car]

Wait untill you come to double digit addition or subtraction. My dd had no problem what so ever, except that she wanted to tell me every little small step.....:tongue_smilie:

 

Then you get something like this:

23 + 18

well, mum, you have 20 and 3 and 10 and 8.

The 8 is 7 and 1, so you give the 7 to the 3 to make 10,

but remember, mum, you still have a 1...

bla

bla

bla

bla

 

For every sum. Every. Sum.:lol:

 

:lol:

 

Can I relate!

 

Plus I once made the mistake (when trying to get my son to sleep) of responding to an after lights-out plea for "one more story", thinking I'd sneak a little math in by making up a little story:

 

So once a 7 was walking though the forest when he spotted a 5. The 7 desperately wanted to become a Ten so he asked the 5, "oh please 5, won't you give me 3 so I can be a Ten. The 5 graciously agreed, and became a 2.

 

So there was One Ten and Two Units, which makes 12.

 

So after many months, I'm still saying, "forget about the woods" when asking him to "explain" how he's doing his additions :lol:

 

Bill

Edited February 26, 2010 by Spy Car

[Aubrey]

This week we hit subtraction of numbers such as 13 by 7.

 

And here you subtract 7 from the 10 "part" of 13, and thus have 3 + 3.

 

Which is 6 :D

 

The little-man didn't bat an eye-lash.

 

Bill

 

Mine get wide-eyed, but I think that's my fault, not Singapore's. I just get so. excited. about math. And when I get excited, I talk REALLY FAST. And when I realize I'm talking really fast, I add more words. You know, to help the student understand. :lol:

 

I taught ESL, so I really know better. Lucky for them, I was teaching English! :D

[Tress]

So after many months, I'm still saying, "forget about the woods" when asking him to "explain" how he's doing his additions :lol:

 

Forget about the woods! :lol: That's hilarious!

 

I taught ESL, so I really know better. Lucky for them, I was teaching English! :D

 

Totally hijacking this thread, Aubrey can I pm you about ESL? I could use some advice.

[cajunrose]

We are doing MUS..kinda. It sounds like it teaches adding similar to what we are doing. My problem is that my 6...going on 7 year old doesn't seem capable of doing math like that in her head. I have tried everything. She's just not getting it. I don't know what to do or how to handle it. We are just working on facts right now and moving on. She still doesn't have them memorized, but we are working on it. I have started trying to teach her time, money, measuring also. I think MUS is lacking in these things.

 

I KNOW it's necessary for them to learn these facts the way that these problems teach them for the higher order addition problem but what do I do to get us there? I'm stuck!

 

Sorry to hijack...it just seams like there are a lot of people on this thread that can help me (us).

 

Thanks

Stephenie

[Doodle]

Thanks to all! I feel more comfortable now with making the switch to Singapore. I believe it will be better in the long run. I was not taught math this way and am not good with adding in my head. I must add 2 digit number on paper and with an equation like 6+7, I have to 'count on' (with my finger :blush5:).

 

I love using c-rods for our math lessons. A special thanks to you Bill. It was your posts I read last year about them and the Miquon program that convinced me to start that program. :thumbup: Yesterday we used them for our 'double plus one' math facts. I put out a 6 and a 7 rod. Then place a 6 and a 1 rod on top of the 7 to show it was the same. Then Doodle did his double 6 math fact and added on 1! Last week we used them with the book Math-terpeices by Greg Tang. Doodle loved it!

[2squared]

RightStart provides another way - The Fives Strategy - if that would help.

 

6+7=5+5+1+2

 

I think this way is a little more cumbersome than The Ten Strategy, but my dd sometimes finds this way easier with +6 and +7 numbers.

[Spy Car]

Thanks to all! I feel more comfortable now with making the switch to Singapore. I believe it will be better in the long run. I was not taught math this way and am not good with adding in my head. I must add 2 digit number on paper and with an equation like 6+7, I have to 'count on' (with my finger :blush5:).

 

I love using c-rods for our math lessons. A special thanks to you Bill. It was your posts I read last year about them and the Miquon program that convinced me to start that program. :thumbup: Yesterday we used them for our 'double plus one' math facts. I put out a 6 and a 7 rod. Then place a 6 and a 1 rod on top of the 7 to show it was the same. Then Doodle did his double 6 math fact and added on 1! Last week we used them with the book Math-terpeices by Greg Tang. Doodle loved it!

 

Thank you so much, this post makes my day :001_smile:

 

Bill

[mcconnellboys]

I believe it's doubles, plus or minus one....

[Kennic]

It's mostly by making a ten, since that concept is very important, in the textbook. The Home Instructor's Guide does include a lesson on doubles and doubles + 1 as an alternative method for quick recall. More than one method is given on lots of things.

[StephanieZ]

I don't think the "doubles" method is EVER taught in any Singapore text or workbook or IP. I am pretty sure I would recall if it were ever taught.

 

The "counting on" method is taught early on.

 

The make ten method is taught next and is a fundamental method. Others have explained it very well. It comes in very handy time and again at later stages.

 

The "doubles" method could be in the HIG or TMs, as I haven't seen those.

 

IME, the text and workbooks teach all the concepts that are important to learn -- and produce a very well educated math student. The only think you NEED to add is drill on basic facts. I am not sure if the HIG/TM stuff would add benefit to you or might even detract from the program if it is teaching substitute methods that may or may not be beneficial . . .

[The Governess]

I don't think the "doubles" method is EVER taught in any Singapore text or workbook or IP. I am pretty sure I would recall if it were ever taught.

 

The "counting on" method is taught early on.

 

The make ten method is taught next and is a fundamental method. Others have explained it very well. It comes in very handy time and again at later stages.

 

The "doubles" method could be in the HIG or TMs, as I haven't seen those.

 

IME, the text and workbooks teach all the concepts that are important to learn -- and produce a very well educated math student. The only think you NEED to add is drill on basic facts. I am not sure if the HIG/TM stuff would add benefit to you or might even detract from the program if it is teaching substitute methods that may or may not be beneficial . . .

 

Yes, the doubles method is in the HIG as an alternate method. The HIG gives a few alternate methods to help with learning a concept if the student is having a hard time with the main method, or to use as a supplement to the main method.

 

After reading Liping Ma's book on teaching elementary math, I am seeing the benefit of teaching multiple methods. If a child learns how to solve a problem in multiple ways, they are developing a deeper understanding of the math and are making more connections, seeing how separate methods and concepts are related. I think learning how to approach a problem from many angles is a great tool for a child to have, and teaching them to do this from the very beginning will come in very handy down the road when problems become more difficult. I would guess this is a main reason why many parents choose to use two or more math programs simultaneously.

 

I think that the inclusion of alternate strategies (as well as detailed instructions on how to present the main strategy in concrete ways) in the HIG is one of the many reasons why it is an essential part of the program and can't imagine not using it. So I guess we'll have to disagree on this one. :D

 

I also like the Right Start method that was mentioned of breaking the numbers down into 5+extra ones and then adding. I think I will add some problems of this type into our lessons.

[StephanieZ]

Yes, the doubles method is in the HIG as an alternate method. The HIG gives a few alternate methods to help with learning a concept if the student is having a hard time with the main method, or to use as a supplement to the main method.

 

After reading Liping Ma's book on teaching elementary math, I am seeing the benefit of teaching multiple methods. If a child learns how to solve a problem in multiple ways, they are developing a deeper understanding of the math and are making more connections, seeing how separate methods and concepts are related. I think learning how to approach a problem from many angles is a great tool for a child to have, and teaching them to do this from the very beginning will come in very handy down the road when problems become more difficult. I would guess this is a main reason why many parents choose to use two or more math programs simultaneously.

 

I think that the inclusion of alternate strategies (as well as detailed instructions on how to present the main strategy in concrete ways) in the HIG is one of the many reasons why it is an essential part of the program and can't imagine not using it. So I guess we'll have to disagree on this one. :D

 

I also like the Right Start method that was mentioned of breaking the numbers down into 5+extra ones and then adding. I think I will add some problems of this type into our lessons.

 

Interestingly enough, my dc each come up with infinite ways to solve problems. . . I think that a well educated math student is able to deduce a variety of methods from the fundamental ones once they are truly learned. It is always interesting listening to my 7yo explain how she solves a particular problem. . . as she might approach it in many different ways. FWIW, we do use Miquon as well, and have a very mathy home, so the "alternate" approaches in the HIG (or other places) may already be explored here. . .

 

Anyway, I agree that having alternate ways to solve a problem is important. . . I just have not found that we needed any additional teaching materials to achieve that goal. . . As, for us, mastery of the concepts in the Text/Wkbk have resulted in fertile math minds that are able to develop infinite ways to solve problems. . .

[Jen in PA]

I never explicitly taught the doubles method, but dd started using it on her own. She was used to shifting the values around in her head after plenty of number bonds practice, and the doubles thing just sort of happened. So she often sees 6 + 7 as 12 +1 almost instantaneously.

[johnandtinagilbert]

:lol:

 

Can I relate!

 

Plus I once made the mistake (when trying to get my son to sleep) of responding to an after lights-out plea for "one more story", thinking I'd sneak a little math in by making up a little story:

 

So once a 7 was walking though the forest when he spotted a 5. The 7 desperately wanted to become a Ten so he asked the 5, "oh please 5, won't you give me 3 so I can be a Ten. The 5 graciously agreed, and became a 2.

 

So there was One Ten and Two Units, which makes 12.

 

So after many months, I'm still saying, "forget about the woods" when asking him to "explain" how he's doing his additions :lol:

 

Bill

:lol: Dgs tells the story from MUS each time....you can only have nine in the house, then they have to move into the tens house...I like the woods better though...I might be telling that story at bedtime tonight.

 

We are doing MUS..kinda. It sounds like it teaches adding similar to what we are doing. My problem is that my 6...going on 7 year old doesn't seem capable of doing math like that in her head. I have tried everything. She's just not getting it. I don't know what to do or how to handle it. We are just working on facts right now and moving on. She still doesn't have them memorized, but we are working on it. I have started trying to teach her time, money, measuring also. I think MUS is lacking in these things.

 

I KNOW it's necessary for them to learn these facts the way that these problems teach them for the higher order addition problem but what do I do to get us there? I'm stuck!

 

Sorry to hijack...it just seams like there are a lot of people on this thread that can help me (us).

 

Thanks

Stephenie

talk it through with manips first. then you talk, she builds. then you build and write several times on a board. Then drill, baby, drill!

 

For drills, I choose 5 facts per week and make signs to hang up. (This week were all making tens) I write the number in coordinating colors (to go with MUS) so they'll use the page when they're working. They can memorize them this way. We also use Holey Cards every day, and MUS online drills every day. It's practice, practice, practice. You might also enjoy hopscotch where you put answers in the boxes, call out problems (6+7) and she has to leap onto 13...

[Spy Car]

:lol: Dgs tells the story from MUS each time....you can only have nine in the house, then they have to move into the tens house...I like the woods better though...I might be telling that story at bedtime tonight.

 

 

Just be sure you'll really, really like hearing this story :D

 

Bill