Division: Cut an actual pie.
Square: lay out tiles/blocks/whatever.
Cube: build a 3x3x3 cube using cube-shaped items (like blocks or six-sided die).
The school treated math in an abstract manner. Whenever my son with dyscalculia got very lost, I made it as concrete, hands on, real world and literal as possible.
By literal, I mean I tried to show him that terms like "cubed" or "squared" were literal descriptors of physical phenomenon, not just made up keywords.
If you draw up an old-fashioned times table, you can show that multiplication uses the word "times" because you have this number that many times and show why it makes absolutely no difference what order the numbers are listed for multiplication. You can do the same thing with coins or piles of anything (sticks, pebbles, whatever). Five piles of six items or six piles of five items both add up to thirty.
I helped my math-challenged son get over his baggage in part by teaching him "Adding is qick and easy counting. Multiplying is just quick and easy adding. If you make 10 piles of 30, you've got 300 items and don't have to spend forever manually counting them and hoping you don't get confused and lose count along the way. Exponents are just easy multiplication. Math is your friend and makes those tasks easy."
So you can show that for addition and multiplication, the written number order does not matter because in real life the order doesn't matter. But for subtraction and division, it does matter how you write it because the written math represents something real and it matters in reality.
When my son found it confusing and nonsensical that a bigger number on the bottom of a fraction makes a smaller number, I pulled a pie out of the refrigerator and cut the pie into two pieces and we talked about how you write that (1/2) and then I cut it again making it 4 pieces (1/4) and then I cut it again making it 8 pieces (1/8) so he could see that dividing one whole pie into halves, quarters and eighths made for steadily smaller pieces.
For basic math, many of the words used are rooted in real world observations. "Square" numbers form a physical square on the times tables. "Cubing" a number can build an actual cube.
Square: lay out tiles/blocks/whatever.
Cube: build a 3x3x3 cube using cube-shaped items (like blocks or six-sided die).
The school treated math in an abstract manner. Whenever my son with dyscalculia got very lost, I made it as concrete, hands on, real world and literal as possible.
By literal, I mean I tried to show him that terms like "cubed" or "squared" were literal descriptors of physical phenomenon, not just made up keywords.
If you draw up an old-fashioned times table, you can show that multiplication uses the word "times" because you have this number that many times and show why it makes absolutely no difference what order the numbers are listed for multiplication. You can do the same thing with coins or piles of anything (sticks, pebbles, whatever). Five piles of six items or six piles of five items both add up to thirty.
I helped my math-challenged son get over his baggage in part by teaching him "Adding is qick and easy counting. Multiplying is just quick and easy adding. If you make 10 piles of 30, you've got 300 items and don't have to spend forever manually counting them and hoping you don't get confused and lose count along the way. Exponents are just easy multiplication. Math is your friend and makes those tasks easy."
So you can show that for addition and multiplication, the written number order does not matter because in real life the order doesn't matter. But for subtraction and division, it does matter how you write it because the written math represents something real and it matters in reality.
When my son found it confusing and nonsensical that a bigger number on the bottom of a fraction makes a smaller number, I pulled a pie out of the refrigerator and cut the pie into two pieces and we talked about how you write that (1/2) and then I cut it again making it 4 pieces (1/4) and then I cut it again making it 8 pieces (1/8) so he could see that dividing one whole pie into halves, quarters and eighths made for steadily smaller pieces.
For basic math, many of the words used are rooted in real world observations. "Square" numbers form a physical square on the times tables. "Cubing" a number can build an actual cube.