I am one of those that needs concrete examples to understand mathematics beyond arithmetic. You need to remember that I am STILL the kid who got an A+ in Astrophysics and a D- in Calculus during my senior year of boarding school! 
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My main learning this week is.
‘The Online Infrastructure of the UK is still woefully unprepared for online learning.’
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You are not alone. In my state the new system for online learning crashed horribly on the first day after vacation … haven’t heard anything since (I have no kids).
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It’s Showbie they are using for my daughters primary school. It works OK.
The only downside is worksheets get posted at 9 and throughout the day while I’m working.
We’re very lucky as we’ve got a very dynamic head of school who has no idea about ICT, which means he listens to parents.
So in theory, all work is uploaded the night before so we can work out what it actually means. 
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Need help. Our six year old daughter does not understand numbers. At all.
She can count.
Her homework is stuff like, there’s an 8, and that can be split into two numbers. If one is a 2, what’s the other? She does not get this at all. If we give her some tokens to count up and split, she might end up with a number she can write down, but she really doesn’t understand why. When asked why she wrote it, she’ll say it’s because that’s the answer we told her, or similar.
I’m writing this after an hour spent on two such questions and I’m frazzled, so maybe not making much sense.
Is there any way out? The Japanese school system does nothing for kids behind the curve.
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First question.
If you give them 4 coins, could they tell you how many coins they have?
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I had a little bit of practice at this when home teaching at the start of the year. I found the easiest way to try and get the concept across was by grabbing a set of objects (doesn’t really matter what - I used some small pads of ink). Using your example:
If 8 is the target number, I would put out 8 items, and let my daughter finger count, touching each one to get to 8. Then we would put 2 to one side (trying to get her to count out the two and separate them from the rest). Finally, count out what remains. Rinse and repeat with a huge amount of patience.
I tried to get my daughter to finger print the target number (hence the ink pads) and then draw boxes around the component numbers, but honestly just using a set of objects was more effective.
Eventually they will start to be able to eyeball the number of items.
It sounds like this is what you are pretty much doing. It might be a case of grabbing items that make it more engaging. 6 dolls at a tea party, 2 leave to catch a bus - how many are left? 10 grapes, if we eat 4, what’s left? etc.
An edit - what might be a wrinkle is the writing of numbers on top of the activity. Try it all purely verbal and see how you get on.
Yeah, I guess I need to give up on the why and the numerals for now. As long as she has tokens and can count the answers, we’ll stick with that for now.
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We definitely had to separate out the writing part from the activity to start with, as that was engaging a different skill set - remembering what each number looks like, and mastering the motor skills to write it etc.
We could do a counting activity verbally, and then if I asked my daughter to write the number 6 down, she would do it. But if challenged why she wrote a 6, she would likely answer ‘because you told me to’, and not necessarily link the answer back to the activity.
I’m just frustrated and sad. I have a feeling school is going to be very hard for her. She’s already saying she hates learning and wants to be stupid and go back to daycare. It’s not going to get any easier.
Sorry, had to vent. I’ll be back if I have more questions.
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Is this diagram familiar to you?
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(It wasn’t until the start of this year…)
No. I’m guessing it’s the equivalent of the Japanese box above two boxes.
Yep. A part part whole model.
Good for these type of problems, physically building 8 in the top, dragging down 6 and then dragging the 2 down to the other circle. With anything like this concrete objects is key.
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Pandemic cubes were a godsend for this during the last lockdown.
We also played shop with it to make it a bit more fun. “If you give me 6 cubes I will give you this t-Rex”. Have the wee man check how many cubes he gives me. “That’s too many I only wanted six” so I would give him some back till I’m left with six and then have him check how many he was left with and how many I have.
Helped him stay engaged with it but they are all different little monsters. Sounds like your doing great. They all have bad days.
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Is there anything that she’s super into that you could use to disguise the learning?
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