Remediating math in older student

[MistyMountain]

My 4th grader is behind in math skills. She even thinks she is bad at math. I think a lot of it is curriculum related. She goes to a school that uses Saxon and she learned algorithms not conceptually what was happening. I did summer math with her but most of what I did still did not build that foundation and had things like counting strategies.

 

I thought about using Ronit Bird and using that to just teach things she is struggling with but

I heard it does not include fraction work and I really would like some fraction work too. I like that it uses games though. Gattegno looks interesting but I heard to start from the beginning and it would take quite a while to hit stuff that would help. The math in the beginning of Gattegno is easy for her but the algebraic way of writing things is hard. I am still undecided if something like that would help or not. Is there anything else out there that uses some Cuisenaire especially for remediation.

[mathmarm]

Remediation for what parts of math? WHY is she behind--which parts is she struggling on? What levels/components of Saxon and how are they using them in school? 

 

 

 

Are you home schooling her now or is she still in school? 

 

How familiar are you with cuisenaire rods? It may be that your best bet is to get the Annotated Lab Sheets for Miquon not the student pages and then use that to show you how to teach each concept.

 

 

[MistyMountain]

She is still in school. They are using 5/4 but she did the 1-3 version too. She is solid in substization, addition and subtraction facts, multiplication and division. She is not good at mental calculation of bigger numbers and uses the algorithm for that. 3 digit by 1 digit multiplication was tripping her up. There is a lot of little things she is missing but it seems they introduce stuff without much of a lesson and then they only do around 2 problems or so and then lots of problems of what they did in the past but very little for each concept.

 

I never used a curriculum with the rods. We just played around with them and did a few things from Education Unboxed. She did not really use them. I have been watching Education Unboxed recently and seeing things Ronit Bird wrote about them.

Edited January 6, 2017 by MistyMountain

[HomeAgain]

I would look at MUS dvds (used or borrowed if you can get them).  Gamma would be a good one to start with.  You can make paper blocks in Excel or Word to go with if you don't want to invest in a set right off.  I also made matching graph paper using the three colors repeated (Hundreds, Tens, Units) so there could be a seamless transition to doing work for students who needed the extra help between blocks and plain paper.

[mathmarm]

She is still in school. They are using 5/4 but she did the 1-3 version too. She is solid in substization, addition and subtraction facts, multiplication and division. She is not good at mental calculation of bigger numbers and uses the algorithm for that. 3 digit by 1 digit multiplication was tripping her up. There is a lot of little things she is missing but it seems they introduce stuff without much of a lesson and then they only do around 2 problems or so and then lots of problems of what they did in the past but very little for each concept.

 

I never used a curriculum with the rods. We just played around with them and did a few things from Education Unboxed. She did not really use them. I have been watching Education Unboxed recently and seeing things Ronit Bird wrote about them.

Is she's solid on subitization and has the 4 operations down, then what is she behind in? How are her problem solving skills? I wouldn't leap ahead to fractions until I was really happy with her understanding of operations on whole numbers--how and why they work and if she could reliably explain how to solve 2 and 3 step problems using whole numbers.

 

Regardless, the CORE concepts for all basic math is the idea of a unit, place value and the commutative/associative/distributive properties and the idea of an inverse.

 

We compose and decompose units. The "tens" and the "hundreds" are units in our number system, knowing when to compose or decompose from one unit to the next is important and critical to the idea of regrouping. Her fluency with the math facts is a big boon in this situation.

 

 

Teach her to use expanded form and to compose/decompose across units.

 

 

So, write 3-digit numbers and talk about what the hundreds, tens and ones mean, look at 2 and 3 digit numbers and write them in expanded form.

 

The amount "341" has 34 tens in it, or 341 ones in it, etc...

 

If you write out a few 3-digit numbers in expanded form for her to add, then she'll be able to easily see when to regroup to the next, thus practicing these orally and over a white board can boost her ability to add/subtract mentally. 

 

 

Practice writing out the problems, then working them through orally, several at a time.

For multiplication, I would teach her the distributive property and have her write the 3-digit number in expanded form. So if she is doing 314 * 7, she would write (300 + 10 + 4) * 7 and distribute the 7 to each part L->R and doing this will help her to not be dependent upon the rote algorithm and this is likely to help her see how to do these types of problems mentally as she says 

 

The answer is 21hundred....70....90....8.  2198! 

[MistyMountain]

She is not at grade level when I give her placement tests and her grades are not good right now. She gets basic place value like what is the thousands, hundreds, tens and ones but I do feel she is a little shaky when actually doing problems. That is how I showed her to solve the 3 digit multiplication but she had trouble with understanding multiplying the hundreds part and managing all the parts in her head. She was learning how to do that with multiplying 2 digit numbers by 1 digit though. She cannot add 2 digit numbers with regrouping mentally. She can do 2 and 3 digit addition and subtraction on paper but she is going through the motions not really understanding. She can solve 2 digit addition without any regrouping mentally. She was able doing multi digit left to right subtraction the Right Start way with the abacus sideways and I think doing things like that will help her see it better but maybe I should work on getting 2 digit mental skills and pairs to 100.

Edited January 7, 2017 by MistyMountain

[Rosie_0801]

 I wouldn't leap ahead to fractions until I was really happy with her understanding of operations on whole numbers--how and why they work and if she could reliably explain how to solve 2 and 3 step problems using whole numbers.

 

Oddly enough, neither my daughter nor my tutored student could learn multiplication and division until they'd worked quite a bit on fractions.

 

 

 

If number sense and place value are the problem, Paps Minicomputers are fantastic.

[mathmarm]

Give her placement tests using what? Different publishers do things differently. If you give her the Saxon Placement test, then where does she test? If you give her a standardized assessment test, then how is she testing? 

 

She is not at grade level when I give her placement tests and her grades are not good right now. She gets basic place value like what is the thousands, hundreds, tens and ones but I do feel she is a little shaky when actually doing problems. That is how I showed her to solve the 3 digit multiplication but she had trouble with understanding multiplying the hundreds part and managing all the parts in her head. She was learning how to do that with multiplying 2 digit numbers by 1 digit though. She cannot add 2 digit numbers with regrouping mentally. She can do 2 and 3 digit addition and subtraction on paper but she is going through the motions not really understanding. She can solve 2 digit addition without any regrouping mentally. She was able doing multi digit left to right subtraction the Right Start way with the abacus sideways and I think doing things like that will help her see it better but maybe I should work on getting 2 digit mental skills and pairs to 100.

 

Is there a reason that she needs to be able to do the work in her head right now? If not, I would work on mental math separately with an intensive focus on mental calculation during the summer, but I wouldn't make mental math a priority if she is struggling in her math class.

 

Earlier you said that she is "solid" in subitization, addition and subtraction facts and multiplication and division. What did you mean by that? The concept? The multiplication and division facts? Executing the algorithms?

 

Can she do these problems accurately with pencil and paper?

Can she explain/talk about the concepts for +,-,*,/ (even if she's not 100% correct in her explanation)?

 

If you show her a problem, such as 1234 / 6, can she tell you that it means "to start with 1234 of something, and split it into 6 equal groups, and if there are any left over that'd be a remainder?"

 

Can she look at 987 - 456 and make the connection to the whole = part + part example, so that she's able to confidently say "Oh, that means that 987 is the whole and 456 is one part, and we have to find the other part? and to so this, we seperate out 456 from the whole and find how many are left?" 

 

If you gave her a 3 or 4 digit number, could she draw it in base ten?

If you showed her base-10 models of numbers, then could she easily see what the number was?

 

You said that she knows place value, but if you call her over and ask her "how many tens are there in 987?" then would she answer 8 or 98? Would she understand why you can say that there are 98 tens?

 

In general, I prefer to teach all multi-digit operations left to right. Whether we are doing 912 + 789, 1389 - 590, 275 x 23 or 981 / 13,

I prefer that in the early stages students go left to right when working larger problems and that they show their work.

 

It's not as compact to put on paper, but it's clearer, emphasizes place-value, allows them to find errors more easily, reduces frustration from getting "stuck"  mid-problem and for many kids as they gain fluency on paper, they begin doing problems in their head.

[mathmarm]

If school performance is pressing, then since she is using Saxon 54 in school, you could look up her book online (its available as a PDF on many school websites) and introduce/teach the topics in advance and give her several problems to practice on--so that by the time she does it in class, then those are her 22nd, 23rd and 25th time completing that type of exercise, not her 1st, 2nd and 3rd.

 

For some lessons Saxon has additional exercises in the back of the book, but in general it's easy to just make up more exercises for her to do also.

 

[MistyMountain]

She never took a standard assessment test. Last year during testing the computers went down and our state scrapped the test altogether. I mean the multiplication and division facts. I not sure of the answers to all the things you asked. I will ask her those things tomorrow. I just started explaining problems to her left to right very recently. I do think that will help but they do not do things that way in class so I am not sure what she can do in school. It will take a while before I can get ahead of her book.

[MistyMountain]

She was able to describe what was happening in that kind of division problem. She knows what numbers are if shown in base ten. She could draw in base ten up to the hundreds but could not draw thousands. She did not describe subtraction like that but could be led into calling it a whole and parts without giving her the answer. The one thing she could not do was say there was 98 tens in 987. She said 8 and when I asked if there could be more she could not accurately describe how many.

Edited January 8, 2017 by MistyMountain

[readinmom]

We used this with some success...

Edited January 8, 2017 by readinmom

[Rosie_0801]

She was able to describe what was happening in that kind of division problem. She knows what numbers are if shown in base ten. She could draw in base ten up to the hundreds but could not draw thousands. She did not describe subtraction like that but could be led into calling it a whole and parts without giving her the answer. The one thing she could not do was say there was 98 tens in 987. She said 8 and when I asked if there could be more she could not accurately describe how many.

 

The minicomputers really help with this. 

[mathmarm]

From lesson 1, Saxon Math 5/4 uses the idea of "some" and "some more" = "total". This is the same as other curriculums that teach  "part" + "part" = "whole" just worded differently, but you can spell it out for her.

 

They even use a bare bones model of this on pg 3 of the student text.

 

I would show her this on a white board. 

 

<-------whole------->

<--part--><--part-->

 

And talk about how it can be more than just two parts that make up the whole. For example:

 

<-------------7-----------> is

<-----5--------><---2---> or 

<----3----><------4-----> or 

<-1-> <-2-> <-2-><-2-> etc

 

Talk about how this relates to addition and subtraction of numbers of any size, not just small numbers. Find a list of generic word problems online and draw models for them. Talk about how if you change the words, you change the model.

 

ie

Mary has 5 apples and Bob has some apples. Combined, Bob and Mary have 14 apples, how many apples does Bob have?

 

<------------14----------->

<--M:5--><-----B:?---->

 

versus

 

Mary has 5 apples, and Bob has 4 more than Mary. How many apples do they have combined?

 

<---------------?------------->

<---M:5:---><----B:(5+4)->

 

For this example, ask how many steps it takes to find the ?. (2-steps)

Why? Because we have to find all the parts first, and secondly we can find the whole. etc...

etc...

 

Once she's grasped this with smaller numbers and can explain, and teach it with smaller numbers 5 days in a row then you can make up word problems with 2-digit and 3-digit problems and draw out bar models for them. DO NOT PRESSURE HER TO SOLVE THEM MENTALLY. You want her to be able to first and foremost correctly understand, visualize and model the problems. Then she can compute the answer on paper. Do not make this about mental math. Do not. Do not. Do not.

 

 

If her understanding is lacking and her grades are suffering, then you want to address the skills that will make her successful, not add yet another skill to over whelm her. Using 1st and 2nd level word problems will make it easier to focus on the problem solving process so that she's not drowning in arithmetic.

 

You can do the same thing for multiplication and division as "Sharing" problems".

 

Personally, I prefer to introduce the idea of fractions as taking one portion of another number. You can use c-rods or ten-frames so you can build various numbers and ask (what is half of 12? What is 1/4th of 20? etc.).And you do exercises of making a group twice, thrice, and quadruple the size it was. I have a thing against the whole "multiplication as repeated addition" practice and dislike that early association. It's okay for kids to find that connection, but I don't teach it.

 

If she knows her skip-counting and multiplication facts really well and understands how to find 1/2 or 1/10 of a number, then maybe you can challenge her, instead of saying "what is 6 * 8" ask her what is 5/6ths of 48, etc.

 

I would read over the first several lessons of Saxon that teach Fractions ( Lessons 22, 26, 36, 37,, 56 and 61) to get an idea of how she's already been taught fractions and begin formulating ways that are going to mesh with what's already rolling around in her head.

 

She was able to describe what was happening in that kind of division problem. She knows what numbers are if shown in base ten. She could draw in base ten up to the hundreds but could not draw thousands. Was that a drawing problem, or she didn't know what thousands could/should look like? If you have some similiarly sized books around, such as a set of encyclopedias or anything you can talk about how a thousand is 10-hundreds stacked on top of one another (then show her a book "hundred" and stack them atop of one another to show how it changes shape from flat to a 3-dimensional cube. Then her some printed base-10 blocks the thousands cube will make more sense. She did not describe subtraction like that but could be led into calling it a whole and parts without giving her the answer. The one thing she could not do was say there was 98 tens in 987. She said 8 and when I asked if there could be more she could not accurately describe how many. Help her practice turning 1-hundred into 10-tens, and talk about how if you have 130, but re-structure the hundreds to tens, then you have 0-hundreds and 13-tens. Maybe cutting some hundreds flats into ten sticks will make this "click" for her.

 

Once she's cut some printed hundreds along the lines to make tens enough, then she can also draw this as [ h ] = ||||||||||

 

You want to create a routine of doing about 5 examples and exercises of hundreds --> tens, and 5 examples of tens --> ones each day. After the restructuring for the sake of restructuring we take practice on various subtraction that require regrouping and starting LEFT to RIGHT.

 

135 - 87 we restructure to 13-tens, and subtract the 8-tens from 13-tens and we have 5-tens left.

Now we have 5-tens and 5-ones, but we restructure this to 4-tens and 15-ones and subtract the 7-ones to get 8-ones so that our final answer is 4-tens 8-ones or 48.

 

The restructuring exercises are a warm up. Then you immediately do the subtraction with restructuring, left-to-right.  Do some of these every day

6-restructuring problems, 4 subtraction with regrouping. 

 

Later change it to 6-restructuring, 3 subtraction with regrouping, 1-addition

Then, by the end of January you can do 5-restructuring, 3-subtraction, 2-addition.

This will be easy enough to begin doing, without spending any money and will give you guys a chance to question and probe for her level of understanding and clarify the things that are cloudy and firm-up the things that are shaky

 

You can print base ten blocks off the internet and it won't cost you much.

 

At her age, she may also appreciate examples with pennies, dimes and dollars.

 

Of course you can expand this to converting thousands to tens and ones, as well as hundreds, and ones to tenths and hundredths. 

You can level up the arithmetic exercises so that she's working with larger numbers, but you want her to build understanding and fluency at a lower level, then 

 

Edited January 8, 2017 by mathmarm

[Farrar]

I love the way Miquon has fractions as part of the foundation. Some of the activities with fractions for the rods are really great - I honestly think that's what the rods are best at - the thing that demonstrates their versatility and ability to inspire understanding best.

 

Honestly, I know you're concerned and that because she's in school there's a pressing need for her to be able to catch up, but it doesn't sound like she's in dire straits or dramatically behind. The thing that's probably harming her the most right now is the need to rush ahead to keep up with her peers. She sounds like she just needs more practice and more time with these concepts and for you to push the conceptual understanding in a different way from how Saxon is presenting it.

[shinyhappypeople]

FWIW, Ronit Bird would be way overkill in your case.  

[mathmarm]

Honestly, I know you're concerned and that because she's in school there's a pressing need for her to be able to catch up, but it doesn't sound like she's in dire straits or dramatically behind. The thing that's probably harming her the most right now is the need to rush ahead to keep up with her peers. She sounds like she just needs more practice and more time with these concepts and for you to push the conceptual understanding in a different way from how Saxon is presenting it.

:iagree:

 

OP, I encourage you to take the long-term view on this thing. Don't think of it as getting her grades up by the end of 3rd, but preparing her to make a strong start in 4th, and to thrive in 5th grade math and to have the confidence to tackle whatever math she may need or want in highschool and college.

 

I really want to encouarge you to back-up, and take deep, steady breaths as you work through the basics from a more conversational, conceptual level. Often times, no matter what is happening in class kids will benefit from extra one-on-one attention to boost them from "struggling" to "okay" and "okay" to "good" and "good" to "excelling".

 

Go through the concepts together, repeatedly. Guide her and then direct her through examples, then let her walk you through examples several times, then give her some to practice from and coach her along.

 

Emphasize the left to right methods--but this isn't for her to do them in her head, this is for her to see the base-10 system at work over and over again. Writing and saying the problems as she goes, she'll begin to see how to do them in her head---and later, over the summer when you guys are working through a mental math program, she'll pick all of it up really quickly and focus on building speed, but this is not the time to press mental math.

 

It's okay for one problem to take up multiple lines on the notebook paper.At home, don't allow her to do problems right to left, do them left to right and have her show her work each time.

 

You are NOT saving paper, you are teaching arithmetic.

 

 Write out the problems the "long way" each time. Every time. 

  239

+578

  700

  100

    17

  817

 

 

[MistyMountain]

She is in 4th. Thank you! Your advice is really helpful and is helping me sort out the best approach to take. I think your plan does sounds really good. It good to hear that she not in too bad of a place. I do think that just a little bit more time and showing things more conceptually and using the left to right approach should help. I would be happy with just a small bit of an improvement this year and a good understanding of what is happening in things we work on. I do feel a lot of it is she is not clicking with the way it is being taught and she just needs a little bit more time with things.

Edited January 8, 2017 by MistyMountain

[MistyMountain]

The minicomputers really help with this.

I have been looking over the getting a 3rd grader used to the minicomputer lessons and it seems like it would take a while for her to get used to that system and get confident. Looking over the studies on CSMP it seems that is true. The studies are mostly positive but there were a lot of teacher comments about needing to supplement with other stuff and teachers felt that it was not the best fit for the lower kids. I guess in a classroom you have less one on one time and you cannot drop levels a little for the kids that need it and the lowest quarter did actually test better then the control. It is very interesting the approach they take and I can see how it can lead to good understanding but I do not think it would be the best course to take for her at this point.

[Rosie_0801]

I have been looking over the getting a 3rd grader used to the minicomputer lessons and it seems like it would take a while for her to get used to that system and get confident. Looking over the studies on CSMP it seems that is true. The studies are mostly positive but there were a lot of teacher comments about needing to supplement with other stuff and teachers felt that it was not the best fit for the lower kids. I guess in a classroom you have less one on one time and you cannot drop levels a little for the kids that need it and the lowest quarter did actually test better then the control. It is very interesting the approach they take and I can see how it can lead to good understanding but I do not think it would be the best course to take for her at this point.

 

I credit them for busting my dd's dyscalculia. She jumped 50 percentile points in the last 9 months. I was suggesting them as a supplement, not the be all and end all. My daughter's non-verbal intelligence is much higher than her verbal intelligence, so I teach her using non-verbal methods first, then we work on translating them into standard algorithms.

 

But that's a sample size of one, which ain't scientific!

 

I have shown them to a few adults with dyscalculia, and they've picked them up quicker than adults without dyscalculia, which I thought was interesting.

[shinyhappypeople]

I credit them for busting my dd's dyscalculia. She jumped 50 percentile points in the last 9 months. I was suggesting them as a supplement, not the be all and end all. My daughter's non-verbal intelligence is much higher than her verbal intelligence, so I teach her using non-verbal methods first, then we work on translating them into standard algorithms.

 

But that's a sample size of one, which ain't scientific!

 

I have shown them to a few adults with dyscalculia, and they've picked them up quicker than adults without dyscalculia, which I thought was interesting.

Nevermind, here and games here  :)

 

I am *so* interested in trying this with my older DD (dyscalculic-lite).  Where do I even begin to look on the csmp web site for instructions about the mini-computer. It's overwhelming.

Edited January 8, 2017 by shinyhappypeople

[Rosie_0801]

I am *so* interested in trying this with my older DD (dyscalculic-lite).  Where do I even begin to look on the csmp web site for instructions about the mini-computer. It's overwhelming.

 

Have a look at the grade three entry supplement.

http://stern.buffalostate.edu/CSMPProgram/Primary%20Disk/PrimarySupplment.pdf

[letsplaymath]

You've gotten some good ideas here, but I'd like to throw out something else for you to consider. JUMP Math is written especially for kids like your daughter who have trouble with a traditional approach and need a confidence booster. It's an excellent program, and the free teacher materials provide all you need to use it as an afterschooling supplement.

 

You would start with the Confidence Building Unit, which is a special series of lessons on fraction math.

• Teacher's Manual -- Do read all of this. The notes are very important.
• Student Pages

If those links won't open for you, go to the main website and create a free account, then look at the Confidence Building Unit page. You want the Level C fractions unit.

 

Then go to the 4th grade lessons here. Download the teacher's guides and blackline masters. That should give you plenty to start with, though if you really like the program, they do have books you can buy in the future.

 

Work through the lessons in order. Don't worry about whether they match up with what your daughter is doing in school. The lessons start deceptively easy and build step by step to a deep understanding of math concepts, creating a strong foundation for future learning.