Gifted Issues Discussion homepage Forums Age or Ability Specific Forums Elementary School Math questions: support/ enrichment

If Topic X is a prerequisite for Topic Y, then you should cover Topic X before Topic Y.

If Topic Y is a prerequisite for Topic X, then you should cover Topic Y before Topic X.

If neither topic is a prerequisite for the other then you may do the topics in either order, or do them at the same time.

But how much proficiency should be required in Topic X before moving to Topic Y? Understanding of the topic? Being able to do the arithmetic without using fingers/calculator?

It's a bit like that classic yes/no question: how long is a piece of string?

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.

The first quote, from the partial order link, said some parts have one thing that preceeds the other (and some parts don't ). An example is that my kid has done the first few pages of an algebra book. He had to skip the problems that had fractions and decimals. He's barely worked with those. For those problems knowing fractions and decimals preceeded doing the math. For the other problems, it didn't.

I (think) it's okay to show kids things they're not going to "get" it all the first time. I think learning new things means looking at stuff that some of it you know and some of it you don't know.

On the subject of mastering arithmetic, , I waiting until DD completes her pre algebra class before I let her have a calculator because the AoPS class really emphasizes mastery of how to solve the problem first, I.e, get optimal algorithm for tackling the problem decided first before actually tackling the routine exercise of performing the calculations that I feel that if she demonstrates competence here that the mastery of arithmetic will thus be implicitly present.

A test. Even if it is just for fun.