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Rapidly catching up in math (advice?)


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1 minute ago, Sk8ermaiden said:

I feel like I'm a bit of a broken record at this point. He can't figure out how two shapes form a new shape. Once you take a marker and draw a single line for him that separates a strange shape into a square and rectangle, he can do the area with no issues or prompting. Understanding shapes is what's not working. 

Do you think he might benefit from some play with things like tangrams or pentominos? 

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It's just that you drawing the LINE is a big hint, you know? Like, he now knows he's supposed to add. It's psychologically a serious hint. 

I'm arguing because the situation feels familiar to me. It feels like other situations I've seen, although mostly not in area. 

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24 minutes ago, Sk8ermaiden said:

the breakdown is not with what area is or how to calculate it - it comes when he has to recognize how two shapes come together to make a new one.

If you draw a handful of rectilinear shapes in one column, and the same rectilinear shapes in a second column but subdivided into rectangles, can he match them up correctly?

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Which Saxon book will he use? Can you look at a copy? Saxon Algebra 1 had one nastly geometry problem a day. If he gets only one geometry problem and only gets that one problem wrong a day, that is no big deal. 

I would focus on the arithmetic problems, because he will have far more arithemetic problems, and problems that build on that arithmetic.

It is not the end the world if the he is behind the first few months of 7th grade. I moved out of the country after Christmas of 7th grade. I took French in the USA, and was thrown into Spanish in the other country. I failed the class. If I had been tutored I would not have failed. And I would have been caught up by the end of the year, because the lessons were not sequential.  And if I had been tutored over the summer, even better.

Latin would have been far worse to have jumped into. Thankfully I was spared that because the Latin-teaching school told my father that I become "too American" and they didn't want such a "flippant" child on their campus. LOL. 

Just focus on the arithmetic and he will pass and eventually catch up if he has the aptitude to do math at the level the school teaches. Saxon has a lot of review at the beginning of the book. He will be fine.

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When I needed to teach my preeteen to do math faster and more accurately, I used to put a pile of skittles on the table between us and race him problem for problem. First person with the CORRECT answer got a Skittle.

He got faster and more accurate very quickly.

When I needed to wean him off that crutch, I made sure his best friend knew how math got done. His friend mocked him until he promised that he just did his math without mommy and candy.

But that is how the Saxon geometry problems were finally correct.

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I would suggest you that that L shape and tell him he has to draw a vertical line through it to cut it into 2 shapes.  So just half of the hint.  When he does it wrong, ask him if he has simplified the problem?  No?  You still have an L and now a little box?  Well, try again. It must be vertical. Show him how to slide the vertical line back a forth until he has 2 simple shapes.  And make a reference card of just 3 simple shapes he is allowed to make - square, rectangle, and triangle. Basically you need to get him to learn how to cut the shape without you telling him how to, but the job is just too big, so you need to simplify the parameters -- vertical line, must be cut into 2 shapes on the card. 

Once he has that down, then you say he can now cut either vertically or horizontally. No diagonals allowed yet. Once again, the 2 new shapes must match the 3 options on the card. 

Once he has that down, then do the diagonals. But now drop the vertical and horizontal, and only do diagonals. First only up diagonals, then up and down diagonals. Still only matching 3 shapes.

Once he has that down, you say vertical line and up diagonal only as the options. 

Rinse and repeat. Give him more and more options over the period of a month or 2 until it is any line you want to draw to make any shape you want to make. But right now, you are starting with this rather than ending with it.

Hope that helps. 

Edited by lewelma
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Just wanted to chime in... breaking a composite shape down into 2 shapes is harder than building a composite shape.  You might want to try giving him some paper shapes and having him work on combining them together.  So for example- adding the triangle to the square and making a house,  adding some shapes together to make a car.   I also want to suggest that he might have some sort of spatial disability.  These  shape issues you are talking about are very basic grade 1 type stuff... Most kids just "see" it without needing a lot of instruction.  You can get some pattern block pictures on TPT to use that involves using pattern blocks to create composite pictures.  You may need to do some very basic work on developing his spatial sense.  You could probably show him how to do it once, then have him experiment with it on his own time. 

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16 minutes ago, NorthernBeth said:

Just wanted to chime in... breaking a composite shape down into 2 shapes is harder than building a composite shape.  You might want to try giving him some paper shapes and having him work on combining them together.  So for example- adding the triangle to the square and making a house,  adding some shapes together to make a car.

That's a really excellent idea. Working forwards is supposed to come before working backwards. 

 

16 minutes ago, NorthernBeth said:

 I also want to suggest that he might have some sort of spatial disability.  These  shape issues you are talking about are very basic grade 1 type stuff... Most kids just "see" it without needing a lot of instruction. 

It does rather sound like it, if he really can't figure out how to split figures. 

 

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14 hours ago, HomeAgain said:

Do you think he might benefit from some play with things like tangrams or pentominos? 

This gave me the idea of making paper or cardboard unit squares, at least 1 sq.in.in size, and then drawing shape outlines that could be perfectly tiled (rectangles to start, then moving to more complex shapes gradually) that he could fill in with the unit squares.  I’m wondering if  drawing shapes on graph paper could feel like a special case of “graph paper rectangles” being countable by squares rather than having to build up your own tiling pattern tangram-puzzle style, for someone who doesn’t find area intuitive.  

Perimeter is a bit more obvious because the lengths just stay lengths, whereas with area, the lengths change into areas which have a whole different dimension, look, feel and meaning. 

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On 6/16/2021 at 8:00 PM, UHP said:

If you draw a handful of rectilinear shapes in one column, and the same rectilinear shapes in a second column but subdivided into rectangles, can he match them up correctly?

That is a really good question. I may try that tomorrow. 

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On 6/16/2021 at 8:08 PM, Hunter said:

Which Saxon book will he use? Can you look at a copy? Saxon Algebra 1 had one nastly geometry problem a day. If he gets only one geometry problem and only gets that one problem wrong a day, that is no big deal. 

I would focus on the arithmetic problems, because he will have far more arithemetic problems, and problems that build on that arithmetic.

It is not the end the world if the he is behind the first few months of 7th grade. I moved out of the country after Christmas of 7th grade. I took French in the USA, and was thrown into Spanish in the other country. I failed the class. If I had been tutored I would not have failed. And I would have been caught up by the end of the year, because the lessons were not sequential.  And if I had been tutored over the summer, even better.

Latin would have been far worse to have jumped into. Thankfully I was spared that because the Latin-teaching school told my father that I become "too American" and they didn't want such a "flippant" child on their campus. LOL. 

Just focus on the arithmetic and he will pass and eventually catch up if he has the aptitude to do math at the level the school teaches. Saxon has a lot of review at the beginning of the book. He will be fine.

The goal is to get him into Saxon 7/6. We ended up choosing a different  hybrid school, and they don't placement test until early September, so I definitely think he can do it if things keep going like they are. Because (where we are right now) the end of 4A and Beginning of 4B in MM are things he knows or review, our in person sessions have been reinforcing weaknesses and vocabulary while he does the reviews in the book on his own. 

I am glad to hear you say what you are saying about the arithmetic. That aspect seems to come much more easily to him. I suspect the first year will be challenging for him, because so much will not really be ingrained, long-term memory yet, but once he's gotten to slow down and get past it I think it will be much smoother sailing.

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On 6/16/2021 at 7:46 PM, HomeAgain said:

Do you think he might benefit from some play with things like tangrams or pentominos? 

I recommended a tangram app to him and his mother, but I don't think they ever downloaded it. 🤔

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On 6/17/2021 at 9:13 AM, NorthernBeth said:

Just wanted to chime in... breaking a composite shape down into 2 shapes is harder than building a composite shape.  You might want to try giving him some paper shapes and having him work on combining them together.  So for example- adding the triangle to the square and making a house,  adding some shapes together to make a car.   I also want to suggest that he might have some sort of spatial disability.  These  shape issues you are talking about are very basic grade 1 type stuff... Most kids just "see" it without needing a lot of instruction.  You can get some pattern block pictures on TPT to use that involves using pattern blocks to create composite pictures.  You may need to do some very basic work on developing his spatial sense.  You could probably show him how to do it once, then have him experiment with it on his own time. 

This is actually exactly what I was planning to do. I do wonder if some of his inability to "see it" comes from having no exposure to shapes as a kid. I mean it. No math apps or games, no blocks, no legos, no tangrams, no preschool workbooks, as far as I know, no preschool TV shows. 

We have spent some of the last three in person sessions on this and he is getting much better at it and can now independently subdivide shapes to calculate area, including ones that have to be cut into three different squares/rectangles. I am going to keep throwing in a couple a week, just for the practice, but I think we can stop focusing on it. 😀

He can also now correctly identify all the basic shapes and tell me the rules for them. (He couldn't at the beginning and I did teach it, but didn't know if it stuck - it did.) 

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I changed schools mid-year almost every year. Usually within the USA, but a couple times mid-year to another country. If I could just complete 75% of an assignment, I stayed calm. Aiming to prepare a student to be able to do 75% of the math problems is much easier than covering all the non-arithmetic strands that will each be a very small percentage of daily work. Saxon includes a full presentation of the non-arithmetic math problems, and for maybe one or two days gives several problems of that type, and them relegates them to a single problem a day, or even drops them. Personally, I would leave it to the teacher to deal with everything beyond the arithmetic.

His strength is the arithmetic. You could actually get him ahead in the arithmetic or at least rock-solid.

There is that 80/20 principle. It takes 20% effort to teach 80%, and 80% effort to teach the last 20%. Catch-up is about the 20% effort for 80% scores.

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A good follow on to what you're doing for review of everything is Lial's Basic college math, they have a geometry section now in the 9th edition. As a bonus, it says "college" in the title so they feel smart while doing the basics!! A used paperback copy is fine, there are several for cheap right now.

https://www.amazon.com/gp/product/0321825535/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1&asin=B00AEFU3RQ&revisionId=&format=4&depth=1

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On 4/13/2021 at 7:48 AM, Not_a_Number said:

Also, I personally hate the idea of remainders 😛 . 

I always used to picture people just throwing the remainders away.  3 lots of 12 puppies and stick this left over one in the shredder.  But then you can't have 12 1/3 puppies.

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4 hours ago, kiwik said:

I always used to picture people just throwing the remainders away.  3 lots of 12 puppies and stick this left over one in the shredder.  But then you can't have 12 1/3 puppies.

Right, which is why that problem isn’t pure division 🙂 

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  • 2 months later...

Just thought I'd give a final update. We completed Math Mammoth 3B and then 4A&B. He took the Saxon placement test and easily tested into 6th grade math. 🥰 So he's doing Saxon 7/6 at the school and finding it very manageable. He was telling his mom the other day that he got all the problems in class right, and then the teacher put two "challenge" problems on the board and he got them both right too. He said, "Maybe I am not actually bad at math." Which of course WE knew and I had told him many times, but it's different seeing for yourself in a classroom setting, I guess. 

My daughter ended up in Saxon Algebra I, which scared me a bit, but she is also finding it pretty easy. 

Next week I take over my friend's 3rd grader's math education, and I think I will stick with MM for him, though it is tempting to switch him to Primary Mathematics so I could do lessons for him together with my son. And just because I like it better. Hmm. I'll have to think. 😀

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1 hour ago, Sk8ermaiden said:

Just thought I'd give a final update. We completed Math Mammoth 3B and then 4A&B. He took the Saxon placement test and easily tested into 6th grade math. 🥰 So he's doing Saxon 7/6 at the school and finding it very manageable. He was telling his mom the other day that he got all the problems in class right, and then the teacher put two "challenge" problems on the board and he got them both right too. He said, "Maybe I am not actually bad at math." Which of course WE knew and I had told him many times, but it's different seeing for yourself in a classroom setting, I guess. 

My daughter ended up in Saxon Algebra I, which scared me a bit, but she is also finding it pretty easy. 

Next week I take over my friend's 3rd grader's math education, and I think I will stick with MM for him, though it is tempting to switch him to Primary Mathematics so I could do lessons for him together with my son. And just because I like it better. Hmm. I'll have to think. 😀

Yay!! That's great 🙂

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13 hours ago, Sk8ermaiden said:

He took the Saxon placement test and easily tested into 6th grade math. 🥰 So he's doing Saxon 7/6 at the school and finding it very manageable. He was telling his mom the other day that he got all the problems in class right, and then the teacher put two "challenge" problems on the board and he got them both right too. He said, "Maybe I am not actually bad at math."

That’s wonderful, so glad it worked out!

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