My son is in the fifth grade and doing well for the most part but constantly backslides when it comes to decimals and fractions. It seems like it comes down to a basic misunderstanding of what a decimal or a fraction is. He can look at a decimal or a fraction and plug in a formula but he can't answer basic questions about them and has a distinct lack of understanding about what these numbers represent.
As an example, if I were to show him 1.5 and I explain to him that the 1 represents 1 whole, complete, number or object and the .5 represents half of an object he seems like he gets it but then when I ask him how much he has he answers 6.
"So you have 1 whole pizza here, and then you have 1/2 of a pizzas. That 1/2 of a pizza is .5 pizza - it's less than one. How many whole pizzas are there?"
"1"
"Ok, good. So you have 1 whole pizza and we still have .5 of a pizza. If we add another .5 of a pizza how many do you have?"
With a question like that he'll answer 3, 11, 6, 5, or 1 but won't ever land on 2. He's so fixated on "5" in "0.5" that his ability to comprehend it as less than one is completely missing.
Here is what I have tried so far:
Pizzas (whole pizzas and slices).
Money - I thought this would be good because it's got the system backed in already. A dollar is a dollar, a dime is .10, a penny is .01 but for whatever reason this seems to barely work at all. I think he sees "a dollar" and "a penny" as two separate things instead of 1 of them being "1 dollar" and the other being ".01 dollar."
Lego - We're building a wall that is 10 studs wide - a 1x2 brick is .2 or 2/10s of the wall, a 1x3 is .3 or 3/10s of the wall, etc. How tall can you build a wall with these Lego. Basically giving him a pile of bricks and explaining how each of them is a 'part' of a wall. I really thought this was going to work but he was completely lost and asked to stop doing it this way.
I was able to get some success with fractions by giving him a handout that correlated fractions to Pokémon - Diglett is 1/3 of a Dugtrio. If you have 8 Digglet you can make 2 Dugtrio and would have 2/3 left.
Last night I tried a different approach when discussing decimals because he was having trouble understanding where 'tenths' and 'thousandths' were. I drew a bucket and said "If I gave you a spoon that holds '.001' of the water needed to fill this bucket how many times would you have to pour out the spoon to fill the bucket?" Then I had to walk him through it step by step - ten pours of ".001" to get it to ".01". So every ten pours of ".001" raises the ".01" by ".01" to "0.02" then "0.03" until eventually it gets to ".1". He then realized that it took 100 pours of ".001" to get the bucket ".1" of the way filled and that he would have to do that 10 times - so 10 x 100 is a thousand, the spoon holds 1/1000 - he got it. Then I asked him, "OK, if I give you a cup for the next bucket and each pour fills the bucket up "0.1" how many pours would it take and he was completely lost again.
I tried finding some videos to explain this but everything I watched bypasses teaching what a decimal is and jumps straight into their structure - they show "this is the tenth space" but don't explain what that means or how a "tenth" is different from the whole number.
Does anyone have any recommendations for videos or methods I could use to approach this from a different angle? It's like he's hit a wall - he can multiple and divide decimals and fractions when he remembers the 'rules' for doing so but the numbers are so devoid of meaning for him that his comprehension is shot.
Thanks for any assistance.