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Can someone explain how Rightstart math teaches addition with carying?


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Going by the RS Activities for the Al Abacus, here's the progression:

 

*Addition without using place value. E.g. to add 9+9, you'd enter 9 beads and then another 9 beads, so you'd end with one row of 10 beads and one row of 8 beads.

 

*Lots and lots of place value work.

 

*Introduction to the idea of "bead trading" - exchanging a ten for 10 ones, etc.

 

*Then addition with place value - first w/out regrouping, then with. It's rather anticlimatic, actually - just a natural extension of addition and place value.

 

Is this what you were looking for? (I know it's not exactly a "few words" :tongue_smilie:.)

 

ETA: I think there is some implicit/basic adding with place value when learning the facts above 10 (before the bead trading).

Edited by forty-two
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Hahaha, I taught my dd with RS A-D, owned E, still have G, and so those responses were pretty funny! In a nutshell? You form a 4-digit quantity with the abacus (side 2), the place value cards, the base-10 picture cards, and write it on the chalkboard. Repeat with a second 4 digit quantity. Now shove them together and add. You do it with the base-10 picture cards first, so they SEE the trades. Then you do it on the abacus where they SEE the trades. Then you do it with the place value cards where you are translating the answer from the abacus. And finally you do it with that written form on the chalkboard, beginning to see the written algorithm of carrying. You never actually tell them how to carry. They just figure out that carrying is the shortcut for showing trades from the manipulatives. All that was led up to with shorter stints using those manipulatives, building up to the day when they do all 4 of those activities in a circle, round-robin style.

 

Clear? :)

 

And yes, I used to rep for them. :)

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36 + 28

 

Add 36 + 20 to get 56 (3 tens plus 2 tens = 5 tens). Then add 8 to get 64 (my kids would do this by noticing that 8 = 4 + 4, and knowing that 6 + 4 = 10 gives them 60 + 4 more = 64). It sounds complicated but it's actually very simple and efficient.

 

Tara

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Agreeing with OhElizabeth regarding how trades are taught, and how that work supports an intuitive understanding of the carrying algorithm.

 

However, I want to take it back a step, and mention what came before seeing and doing trades: place value. RightStart does an excellent job of helping children truly understand place value, with the use of base ten cards, place value cards, and the abacus. In my opinion, a solid understanding of place value makes trading/regrouping/carrying much easier to grasp.

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Agreeing with OhElizabeth regarding how trades are taught, and how that work supports an intuitive understanding of the carrying algorithm.

 

However, I want to take it back a step, and mention what came before seeing and doing trades: place value. RightStart does an excellent job of helping children truly understand place value, with the use of base ten cards, place value cards, and the abacus. In my opinion, a solid understanding of place value makes trading/regrouping/carrying much easier to grasp.

 

Yes. :iagree:

It's more than just how the trading/carrying is taught. RightStart spends a lot of time teaching a solid understanding of place value prior to introducing trading. By the time trading is introduced, it's really a non-event; it's just the next logical step.

I love RightStart for those early grades.

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Ok , thanks girls . Now I get it . I did not know that I was using a similar way to explain my child about place value , without ever doing Rightstart !

I use a base ten blocks manipulatives instead of cards , but it's the same... and I use the RS abacus too but he prefers the base ten for carrying. Thanks for mentioning "trade" I like that much better than carying .

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However, I want to take it back a step, and mention what came before seeing and doing trades: place value. RightStart does an excellent job of helping children truly understand place value, with the use of base ten cards, place value cards, and the abacus. In my opinion, a solid understanding of place value makes trading/regrouping/carrying much easier to grasp.

 

:iagree:

 

While we only "cherry-pick" on elements of Right Start (as opposed to doing the full program) this emphasis on teaching place value first, and the means they use to teach it, makes so much sense. It is absolutely fundamental IMO as a precursor skill, and I've not encountered another program that does it as well or as purposefully early as the Right Start materials we've encountered.

 

Bill

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:iagree:

 

While we only "cherry-pick" on elements of Right Start (as opposed to doing the full program) this emphasis on teaching place value first, and the means they use to teach it, makes so much sense. It is absolutely fundamental IMO as a precursor skill, and I've not encountered another program that does it as well or as purposefully early as the Right Start materials we've encountered.

 

Bill

 

Bill, how many math programs are you using anyway? You are as bad as I am when I really love something; I tend to go a little overboard with curricula. :D

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Ok , thanks girls . Now I get it . I did not know that I was using a similar way to explain my child about place value , without ever doing Rightstart !

I use a base ten blocks manipulatives instead of cards , but it's the same... and I use the RS abacus too but he prefers the base ten for carrying. Thanks for mentioning "trade" I like that much better than carying .

 

I've done a lot of this type of activity with both the Right Start base-10 cards and place value cards with the AL abacus, but also used actual base-10 "flats" and C. Rods (Orange as "10s" the rest as units).

 

I really think it is vitally important for children to get this from the start. And even some great math programs (such as "Singapore") seem woefully deficient in this regard.

 

Bill

Edited by Spy Car
spell-check victim :D
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..this emphasis on teaching place value first, and the means they use to teach it, makes so much sense. It is absolutely fundamental IMO as a precursor skill, and I've not encountered another program that does it as well or as purposefully early as the Right Start materials we've encountered.

 

Montessori does, and with real thousand cubes as opposed to picture cards.

 

And even some great math programs (such as "Singapore") seem woefully diffident in this regard.

 

I agree.

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Montessori does, and with real thousand cubes as opposed to picture cards.

 

.

 

We use real thousands cubes as well. I have unit cubes, 10 rods, hundred flats and thousand cube - all physical materials rather than the pictures. I much prefer real materials because for many kids the concept is abstract enough that the pictures really don't solidify the place value concept or let them see and feel how 10 10s are 100 or that 10 100s are 1000. With the blocks and flats she can stack up 10 100 flats and lay them next to the 1000 cube and see how they are identical so when I ask her to trade them in - she sees that she's getting the same thing.

 

Heather

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I have used an abacus, rods, cubes, counters, cards etc. as well. But another method I love is simply using legos. I donĂ¢â‚¬â„¢t know what it is; something about them is very easy to visualize. Maybe itĂ¢â‚¬â„¢s because they are so familiar? :D

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Montessori does, and with real thousand cubes as opposed to picture cards.
Yes, there are definitely parallels between Montessori math and RightStart Math!

RightStart borrows from and builds on both the Japanese and Montessori math pedagogies.

You can read more about the connections between RightStart and Montessori here. :)

 

(And actually, RS Math does use 100s blocks to build 1000s blocks. But once the concept is grasped, the child moves to picture cards instead, for ease of manipulation.)

Edited by jplain
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Yes, there are definitely parallels between Montessori math and RightStart Math!

RightStart borrows from and builds on both the Japanese and Montessori math pedagogies.

You can read more about the connections between RightStart and Montessori here. :)

 

(And actually, RS Math does use 100s blocks to build 1000s blocks. But once the concept is grasped, the child moves to picture cards instead, for ease of manipulation.)

 

As someone who has had two children in Montessori school each for 3 years and used RS, I think the parallels are very much stretched by RS. It really ins't much like how math is taught in Montessori classrooms at all - aside from a shared emphasis on place value. The beads she refers to in this article are much closer to rods than the abacus. I had some Montessori teaching training and I think that's part of what made RS so frustrating for me to teach. That doesn't make RS bad - but the Montessori comparison isn't really that accurate.

 

Heather

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As someone who has had two children in Montessori school each for 3 years and used RS, I think the parallels are very much stretched by RS. It really ins't much like how math is taught in Montessori classrooms at all - aside from a shared emphasis on place value. The beads she refers to in this article are much closer to rods than the abacus. I had some Montessori teaching training and I think that's part of what made RS so frustrating for me to teach. That doesn't make RS bad - but the Montessori comparison isn't really that accurate.

:001_huh: Heather, I'm not trying to say they're identical.

 

As I mentioned in a previous post, I believe the emphasis on place value is probably the most important part of the early RS Math curriculum. That, in my opinion, is something that both Montessori and RightStart emphasize more heavily than other well-known math curricula.

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Oh, so you do not use the program? Sorry to be nosey. Ignore me if you will. ;)

 

The short answer is, because we started early and I was determined to make mathematics exposure fun, and as "concrete and comprehensible as I could possibly make it, I drew on many sources and spent of good deal of my own brain-power into creating my own hybrid/fusion approach.

 

I wanted a 3rd way between "delaying" math until my son was ready for a "formal" program, and doing *nothing*.

 

So I begged, borrowed and stole ideas from many sources, including Right Start author Dr Cotter. I developed a lot of "independent" ideas along the way, but I think she is spot on in developing place value awareness in her program form virtually the outset. My expropriation of her ideas may have looked a little different, but they share a common core.

 

Here is an old sig. How many Hundreds? Tens? Units?

 

What's not to understand?

 

Bill

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The short answer is, because we started early and I was determined to make mathematics exposure fun, and as "concrete and comprehensible as I could possibly make it, I drew on many sources and spent of good deal of my own brain-power into creating my own hybrid/fusion approach.

 

I wanted a 3rd way between "delaying" math until my son was ready for a "formal" program, and doing *nothing*.

 

So I begged, borrowed and stole ideas from many sources, including Right Start author Dr Cotter. I developed a lot of "independent" ideas along the way, but I think she is spot on in developing place value awareness in her program form virtually the outset. My expropriation of her ideas may have looked a little different, but they share a common core.

 

Here is an old sig. How many Hundreds? Tens? Units?

 

What's not to understand?

 

Bill

 

In all honestly, I think you lost me with the questions. Perhaps itĂ¢â‚¬â„¢s one of those days and IĂ¢â‚¬â„¢m a little daft. :)

Thanks for the explanation, yes, I see your need to beg, borrow or steal. LOL.

I have used plenty of manipulatives, and there really is a lot of common ground and similarity when it comes to explaining math concepts in various ways. And thatĂ¢â‚¬â„¢s whether it is Montessori, Miquon, RS, or whatever. Not that I am any kind of an expert, but thatĂ¢â‚¬â„¢s my humble observation.

You should publish your hard work, Bill, if you can ever find the time. I know a few ladies here would probably love to see what youĂ¢â‚¬â„¢ve come up with.

:tongue_smilie:

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Montessori does, and with real thousand cubes as opposed to picture cards.

 

 

I wanted "real" thousand cubes rather badly at one point, but didn't want to pony up $60 to purchase (10) base-10 "cubes".

 

What I really hoped to find was (10) 10 X 10 X 10 cm blocks made out of that very dense foam play-blocks are sometime made from. No luck.

 

I even thought about square boxes, but could only find 4 X 4 X 4 inch boxes (which are close in size).

 

But I settled for "pictorial" means (via the Right Start cards) for place values over 100. You do what you can do :D

 

Bill

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In all honestly, I think you lost me with the questions. Perhaps it’s one of those days and I’m a little daft. :)

 

Well that would be 4-Hundreds, 7-Tens, and 5-Units.

 

The last might throw a person unaccustomed to C Rods and their (normal) values, but the yellow rod is "half" of an Orange rod...and anyway the kids get it :D

 

 

You should publish your hard work, Bill, if you can ever find the time. I know a few ladies here would probably love to see what you’ve come up with. [/font]

:tongue_smilie:

 

Yea, and then anyone who was unconvinced that I was a nut before-hand, surely would after-wards :tongue_smilie:

 

Bill (who does have a certain method to his madness :lol:)

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Ah! Right, right, I see doh. You were asking questions about the link you provided. Gotcha.

Yes, the kids do get it. IsnĂ¢â‚¬â„¢t that nice? And itĂ¢â‚¬â„¢s all in the name of fun and games to them. ItĂ¢â‚¬â„¢s great. I just need to make an effort to guide them in math play more often.

 

Miquon should help. :D

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It's more than just how the trading/carrying is taught. RightStart spends a lot of time teaching a solid understanding of place value prior to introducing trading. By the time trading is introduced, it's really a non-event; it's just the next logical step.

I love RightStart for those early grades.

 

:iagree: I think learning place value starts with the numbering system and then the next step is just natural. Using one-ten-one for eleven, two-ten for twenty, etc is just brilliant. My Ker easily understands the numbering concept and he logically progressed to adding two-ten-five plus two-ten-five to get five-ten without any help from me.

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:iagree: I think learning place value starts with the numbering system and then the next step is just natural. Using one-ten-one for eleven, two-ten for twenty, etc is just brilliant. My Ker easily understands the numbering concept and he logically progressed to adding two-ten-five plus two-ten-five to get five-ten without any help from me.

 

I ended up with a slightly different "naming system" than RS, so "twenty-five" here was 2-Tens 5-Units.

 

I do think it is better for the "Unit" values to have their own "place name" attached, so 5-Units, as opposed to just 5. And that "Units" is a better name than "Ones", as 5-Ones or 1-Ones are names that could create some of the same confusion one seeks to avoid.

 

But the bottom line is introducing place value in this sort of "modified" naming convention (so 1-Ten 2-Units, rather than twelve) is a great way to help achieve clarity without having to deal with the idiosyncrasies of the English language.

 

It really works wonders!

 

Bill

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We use 'units' too. Probably left over from our Montessori days. I prefer that to 'ones' as well.

 

Heather

 

MEP and Miquon also use "Units" (while Singapore uses "Ones").

 

Even though my kindergartner fully understands "twelve" and "twenty-five" I still find it helpful at times to continue to speak of these as 1-Ten 2-Units, or 2-Tens 5-Units.

 

We just finished some "before school" subtraction problems such as: 25 - 9, where the Singapore method is to subtract the 9 Units/Ones from one of the 2-Tens in 25. And I think keeping the nomenclature clear helps facilitate that kind of mental math.

 

Bill

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1-Ten 2-Units, or 2-Tens 5-Units.

 

 

I would think that this would be more confusing than using the terms 2-ones or 5-ones because, it seems to me, that the child would just have to relearn the terminology when moving on in math, since no higher math curriculum I have seen speaks of place value in terms of units. I have always seen it referred to as the "ones place," not the "units place."

 

Tara

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I would think that this would be more confusing than using the terms 2-ones or 5-ones because, it seems to me, that the child would just have to relearn the terminology when moving on in math, since no higher math curriculum I have seen speaks of place value in terms of units. I have always seen it referred to as the "ones place," not the "units place."

 

Tara

 

It's a false-concern. After a certain age children have no difficulty knowing what we may call the "Units" place some people call the the "Ones" place, or vice-versa.

 

Just as their is no concern about 1-Ten 2-Units (or Ones) vs twelve.

 

It in the younger children where the semantic confusion is likely to occur. Some would say wait until the children are old enough to not have any semantic confusion, and I'd say use means to teach for clarity in age-appropriate ways.

 

"Ones" or "Units" is not the end of the world. My son (kindergarten) has zero difficulty having his school text and Singapore use "One", and us speaking of "Units." People will have their preferences, I have mine.

 

Bill

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  • 5 months later...
Agreeing with OhElizabeth regarding how trades are taught, and how that work supports an intuitive understanding of the carrying algorithm.

 

However, I want to take it back a step, and mention what came before seeing and doing trades: place value. RightStart does an excellent job of helping children truly understand place value, with the use of base ten cards, place value cards, and the abacus. In my opinion, a solid understanding of place value makes trading/regrouping/carrying much easier to grasp.

 

bumping with a new question....

 

We have arrived to this spot in RS B and my dd 6 will 'park' here for some time, I imagine. I just introduced the concept of trading 10 ones for 1 ten (with the abacus turned longways with the 1, 10, 100, 1000 across the top).

This is so different from the way I learned math -- and taught my other dc. I'm even invite dd7 to join us for these RS lessons so she can 'see' place value in this clever way.

 

I feel like Super-Teacher with my abacus, pv cards, base-10 cards, etc. I almost look like I know what I'm doing (or at least I have my dds convinced I do.) :) I follow the script fairly closely. I am so thankful for RS!

 

I'm curious...How long did place value take to 'set in' for the average math student? Not just recognizing the different places (dd knows that already) but intuitively grasping how place value works.

 

Does that make sense? Thanks in advance!

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You know, that's along the same lines as what I've been wondering, except I have the opposite problem. My DD totally gets place value as far as the whole base ten thing goes. Her problem is that she's having an absolutely terrible time remembering which number is which. She'll read a number - let's say 24 - correctly, but then tell me there are 4 tens and 2 ones. The fact that she reads the numbers correctly tells me that she isn't having any reversal issue, and if she is asked to enter the number on the abacus, she does it right and that solves the problem. She just can't look at the number and remember which is which. So if anyone could also answer my question (how long should it take a kid to remember which number is which?) I'd really appreciate it. :)

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I would suggest using a Montessori place value mat (or a large place value chart) and making 2/3/4 digit numbers using the base-10 manipulatives or the RS cards.

 

There is an icecream scoop place value game on filefolderfun.com that my dd enjoyed. That may help too.

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Yes. :iagree:

It's more than just how the trading/carrying is taught. RightStart spends a lot of time teaching a solid understanding of place value prior to introducing trading. By the time trading is introduced, it's really a non-event; it's just the next logical step.

I love RightStart for those early grades.

 

While I did not choose RS as our math program, the Right Start way of teaching place value and doing it early is something I "stole" from the Activities book. It totally make sence to me work on this sort of "big picture" understanding from early on (the way RS does).

 

Bill

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I ended up with a slightly different "naming system" than RS, so "twenty-five" here was 2-Tens 5-Units.

 

I do think it is better for the "Unit" values to have their own "place name" attached, so 5-Units, as opposed to just 5. And that "Units" is a better name than "Ones", as 5-Ones or 1-Ones are names that could create some of the same confusion one seeks to avoid.

 

But the bottom line is introducing place value in this sort of "modified" naming convention (so 1-Ten 2-Units, rather than twelve) is a great way to help achieve clarity without having to deal with the idiosyncrasies of the English language.

 

It really works wonders!

 

Bill

 

I think our kids are about the same age and I just love all your math posts. So, I discovered quickly last year when teaching DD to add double digits that she had a hard time understanding place value with English but no trouble when I switched to another language. I was hesitant using a foreign language to teach math because I don't know how this will affect her math skills in the future but it was the only way for me to get her to understand place value and do mental math quickly. I thought about using English, but it would require one extra word and relearning the numbering system. Math is still about the only subject that I teach using a foreign language. In any case, I really think young kids should be taught, at least initially, the RS numbering system because helps not only with place value and regrouping.

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I think our kids are about the same age and I just love all your math posts. So, I discovered quickly last year when teaching DD to add double digits that she had a hard time understanding place value with English but no trouble when I switched to another language. I was hesitant using a foreign language to teach math because I don't know how this will affect her math skills in the future but it was the only way for me to get her to understand place value and do mental math quickly. I thought about using English, but it would require one extra word and relearning the numbering system. Math is still about the only subject that I teach using a foreign language. In any case, I really think young kids should be taught, at least initially, the RS numbering system because helps not only with place value and regrouping.

 

 

As you are no doubt aware, math educatiors believe some of the reason other countries childen seem to take naturally to math, where ours may not, is our "strange" and idiosyncratic naming conventions. "Twelve" or "twenty-four" where may languages use the equivalent of 1-Ten 2-units or 2-Tens 4-Units.

 

I do know using a "math way" to name numbers on top of learning "English" made (and ontinues to make) a big differencing in understanding. When anything feels slightly wobbly we go back to the "math way" and it seems to clarify the points a rather quickly.

 

Bill

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I worked with Aly on some MM blue place value worksheets today. They will be perfect filler and bridge during our RS pauses. I love how multiple resources round out a concept and show different ways of approaching a topic.

 

Snowfall, have you seen the MM blue place value supplements? That might do the trick for your dd. Even though my dc know what place value is, MM comes at it a bit differently. I also have the blue base-10 blocks which are a great visual, in addition to the RS base-10 picture cards.

 

Bill, Is your son also doing math at school with a typical procedural method? I read somewhere that CA public schools are implementing Singapore. Are you in a lucky school district?

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Bill, Is your son also doing math at school with a typical procedural method? I read somewhere that CA public schools are implementing Singapore. Are you in a lucky school district?

 

Beth, our district (and therefore the school) has chosen a new program called enVision Math. Not the choice I would have made, but not horrible.

 

I wish they used Singapore, but also realize Singapore can be taught as mere "procedure" too, so there are limits to just switching programs without good teacher educate (re-eduction).

 

In a way it makes it "easier" for me to be using something wholly apart from what the school is using. Plus we are one year ahead by grade level at home and the school math is serving as "review" as we march forward with our own combination.

 

I did speak to our principal Thursday night to see how a parent might affect textbook choices. It turns out it is a 7 year process (the last cycle recently finished) so no chance changing things in time for my child. Although schools can purchase their own books from those which meet State standards, as PM SE does. I suggested we switch next year and just buy the books. But the suggestion did not elicit great enthusiasm.

 

EnVision, at least, has adopted the "pictorial" style in demonstrating math procedures that is similar in style to those found in "Asian" math books. So things could be better, and they could be worse.

 

Bill

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I worked with Aly on some MM blue place value worksheets today. They will be perfect filler and bridge during our RS pauses. I love how multiple resources round out a concept and show different ways of approaching a topic.

 

Snowfall, have you seen the MM blue place value supplements? That might do the trick for your dd. Even though my dc know what place value is, MM comes at it a bit differently. I also have the blue base-10 blocks which are a great visual, in addition to the RS base-10 picture cards.

 

I agree about using multiple resources! I have considered the MM place value book. I have the measurement book, so maybe I'll just grab that one, too. I also use the base 10 blocks with DD - she much, much prefers them over the abacus, although we only have one thousand cube, so when doing multiple thousands we have to use the abacus.

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I agree about using multiple resources! I have considered the MM place value book. I have the measurement book, so maybe I'll just grab that one, too. I also use the base 10 blocks with DD - she much, much prefers them over the abacus, although we only have one thousand cube, so when doing multiple thousands we have to use the abacus.

 

Do you have the RS base-10 pic cards? They are ideal. I'd love 10 thousand-blocks but the cards are great.

 

Yes, the MM blue Place Value 1, 2, 3 are a bargain. Nothing is better than touching the manips but MM provides nice pictorials, similar to Singapore.

 

Bill, sounds like you have the best of many worlds. Your son is blessed. :)

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Do you have the RS base-10 pic cards? They are ideal. I'd love 10 thousand-blocks but the cards are great.

 

I like these RS base-10 cards (and place value cards) too. Building this knowledge early, as RS does, makes complete sense. I looked for a suitable 1000 value cube alternative (other than paying $60 for 10 base-10 "cubes) but never found any. But the cards served the bill.

 

Bill, sounds like you have the best of many worlds. Your son is blessed. :)

 

I feel very fortunate indeed.

 

Bill

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Do you have the RS base-10 pic cards? They are ideal. I'd love 10 thousand-blocks but the cards are great.

 

Yes, the MM blue Place Value 1, 2, 3 are a bargain. Nothing is better than touching the manips but MM provides nice pictorials, similar to Singapore.

 

Bill, sounds like you have the best of many worlds. Your son is blessed. :)

 

We have the cards, but she doesn't really like those either. She is very, very, very particular and persnickety. I've never actually been able to nail down what makes her like or dislike something - I don't know if she even knows. lol

 

I agree, Bill. Your son is very lucky. :)

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Montessori does, and with real thousand cubes as opposed to picture cards.

 

 

 

My understanding is that Dr. Cotter, the creator of RS, has Montessori influence.

 

I own a set of interlocking cubes, so we sit down with ones and build a 10, then with the 10's we build a 100 flat, then we take 100's and build a 1000's cube. From there I use the real blocks as much as I can but generally by the time RS is dealing with multiple 1000's my kids find the pictures easier to work with (take less space), so they have all easily switched over. But I think building the quantities with a physical object was important to being able to use the pictures without skipping a beat.

 

Heather

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Beth,

 

I slow it down by getting it all and doing just one of those 4 digit problems a day. By the time we get through that and the 9 digit problems (the 9 digit I have both broken down and done in one day, depends on the child) they have all gotten it.

 

Heather

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You know, that's along the same lines as what I've been wondering, except I have the opposite problem. My DD totally gets place value as far as the whole base ten thing goes. Her problem is that she's having an absolutely terrible time remembering which number is which. She'll read a number - let's say 24 - correctly, but then tell me there are 4 tens and 2 ones. The fact that she reads the numbers correctly tells me that she isn't having any reversal issue, and if she is asked to enter the number on the abacus, she does it right and that solves the problem. She just can't look at the number and remember which is which. So if anyone could also answer my question (how long should it take a kid to remember which number is which?) I'd really appreciate it. :)

 

Reversing what they are saying that way can totally be a maturity thing. It can also be a sign of dyslexia/dyscalculia, but it would have to be in combination with other symptoms and it would continue beyond the age of 7 and 8.

 

My kids wrong numbers backwards, but are dyslexic. My 3rd dd in particular (9yo) still does it, though she is better at self correcting. Then she has a bad day, like the other day where she wrote all of the letter c of cm in a whole page of centimeter measurements backwards. :blink: At things stay interesting...

 

Heather

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