The second quote, from the quasiorder link, said a《b could sometimes mean a comes before b, sometimes a is part of b, and sometimes a is a smaller version of b. Since we're talking about early elementary here I would think that a is usually part of b and b covers it.
For example, the turtlehead multiplication video I mentioned could be used to practice multi-digit multiplication even if the youngster needs to count on his fingers or draw out and count the dots for some of the digits, as long as they understand what multiplication means and can work with numbers to that place value. If they understand numbers to that place value, then it's hardly different than doing page after page of single digit multiplication. Why would they have to have their times table completely memorized before they see something new they can do with multiplication, multidigit multiplying larger numbers.
I think it's the same for long division. If they can do all the steps, divide, multiply, subtract, then it should be okay for them to do a few problems while you tell them what the next step in the problem is. They won't want to do a lot of problems before they memorize the times tables, because it's tedious. And even then they'll probably only want to do a lot of them if it's word problems that require long division. But I don't think it hurts to let them do a few problems now and then.
That's an example of when b covers a. Subtraction, multiplication, and division are all part of long division, and long division covers it.
Last edited by La Texican; 04/04/14 10:56 AM.
