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  1. 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.)
  2. I recommended a tangram app to him and his mother, but I don't think they ever downloaded it. 🤔
  3. 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.
  4. That is a really good question. I may try that tomorrow.
  5. 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.
  6. He has explained it to me, basically every time we go over it.
  7. Without question he does not have a good mental model of shape. 6 weeks ago he could not differentiate a square from a rectangle and I know that is something most kids learn as toddlers and spend years cementing. My big hurdle is how to spend some serious time on it without him thinking I'm treating him like a baby.
  8. I really don't think that will help. He can do a rectangle, and he can do a square. But he can not do a rectangle+square. I could have him count until he was blue in the face and it wouldn't get us any closer to the next step, because 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. I'm going to put my creative hat on and come up with some activities. Maybe even something like tangrams but much more basic. And I've been asking him for a month to measure a real life room and calculate its area and perimeter, but he hasn't, so maybe we will do that on Friday as well.
  9. This one was drawn on graph paper. 😬 It had the unit squares, and he knows he could find the area by counting them, but he also knows that after the first week of practice I didn't really want him just counting them anymore, because 1) there's more room for mistakes and 2) it doesn't help you when your dimensions are something like 17x252. He can not take for example an L shape and turn it into two rectangles to be able to calculate the area of both. I feel like what he really needs is more practice with shapes, rather than more practice with area - because he can do the area of a basic shape - just not one that is more complicated. I am a little stumped about how to bring that into lessons though. I tried with pencil and paper, but it didn't help.
  10. I do believe so. He understands the concept of multiplication, and we started, and spent a long time on area on graph paper, where you could see the square units. We talked about what area is (for example the square footage of a room - how much flooring one would need to buy) vs length or volume. We've talked about how (on the graph paper) you can see that the 5x3 rectangle has five groups of 3 sq units. And he can still get there on his own. It's just never intuitive. For example in the last set of problems it asked him to find the perimeter and area of a 5x7 rectangle. And he gave me perimeter written (5x2)+(7x2) and then "area" as 5+5+7+7. When I asked him how we find the area, he said, "length times width, Oh I did perimeter again." And then he did it correctly. Later gave him two review problems for area and perimeter, the first one was a regular rectangle, which he did correctly. The second one was a 7x2 rectangle attached to a 3x3 square. He got the perimeter (YAY! That was a huge issue for a while) but didn't know how to get started finding the area and needed help. And yes, we spent a ton of time on that when we originally did it. But breaking shapes apart into other shapes - even a rectangle or square into two triangles or this figure I drew that was clearly a square and rectangle sharing a 3 unit edge into its component parts is super, super hard for him. If you do something like draw a 10x2 rectangle and ask him to divide it into 2 rectangles he really struggles.
  11. Just to give a quick update - he's finished the MM 3B book and we're almost done with 4A. He does very well with arithmetic and seems to be catching on to most of the conceptual ways MM teaches. Order of operations was no problem and neither is multi-digit multiplication. I'm having him do all the review at the end of 4A because he's had less-than-ideal amounts of practice and I want him to have that review time. But in the week or so he's working though it, I've been teaching the first new lessons of 4B - namely long division and averages. No problems and with practice he will be fine. Geometry still a sticking point. My mom (who was an elem. teacher for decades) expressed a thought. What if the spatial reasoning part of the brain mostly closes at a certain point - much like language/learning foreign language. And a child who has had no exposure to basic spatial concepts may have a much harder time grasping them when introduced at a later age. It would certainly explain a lot about how a child who can grasp long division on the first go is still struggling with area of rectangles months after its introduction (though it's getting better - slowly.) But he's doing great - gets his work done. It's slowly getting neat enough to read (I don't know if I mentioned that earlier.) Cross your fingers for 4B - there's a decent amount of geometry in it!
  12. Mine was done at the fire station, and lots of fire fighters were working the clinic, but it was all overseen by their head of pandemic response (and that was his position before Covid even) who is an RN, and vaccines were administered by a medical person - I'm not sure if it was a nurse or paramedic.
  13. The parents in my circle who have given their children placement or standardized tests this year, only to find them 3+ grade levels behind certainly learned a lot about their kids' education that they hadn't known before. They were shocked at just how far behind their children were. And it was not a case of silly mistakes or testing anxiety. Those kids are truly that far behind. Now all but one of those parents has been kicked in the pants and are seeking solutions. If the state had required a test of any kind starting in 3rd grade or so - even if it never had to be reported to anyone, these parents would not be discovering their shortfalls for the first time in junior high. Because they just do care, but have executive function or other issues and let schooling get away from them until they were smacked in the face - by test scores.
  14. This has been an issue of late. That the education the Amish provide their children was enough, for hundreds of years, that if they left the community they could still find a decent place in the world. But with technology being woven into the fabric of everyday life, as well as the minimum education required to get most jobs that will support you, some Amish youth are finding they can't leave even if they want to. Or if they do, it is a terrible uphill battle.
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