Guess-and-Check vs. Algebra

I have a 5th and 7th grader.  At the dinner table last night, I asked:  If Tom takes 2 years from his age and gives it to Mary, Mary’s new age is twice Tom’s new age.  If Tom takes 3 years from his age and gives it to Mary, Mary’s new age is three times Tom’s new age.  How old are they?

My husband immediately said, ‘classic algebra’.  The 5th grader went, ‘I don’t know Algebra, I’m going to use Guess and Check’.  My 7th grader has started algebra so he started setting it up with variables T and M.

I just sat there and continued eating my dessert.

Would you know it, the guess-and-checker got the answer first.  The algebra solver plodded along, got a negative answer, changed his setup, rechecked the negative and positive signs and eventually arrived at same answer.

Start doing ‘algebra’-type problems with your kids before they learn algebra.  Simple problems like: Tom has $10 more than Joe.  Together they have $120.  How much does Tom have?  Problems like that prompt non-algebra students to use their number sense.  Ok, $10 is not a lot, so they have close to the same.  Half of $120 is $60.  Let me try $50 for Joe.  Tom has $10 more, that would make it $60.  Total’s only $110.  So Joe must have a little more to  total up to $120.  That kind of mental exercise for your child’s ind is like what going to the gym is for your body.

Here’s another algebra problem a 3rd grader should be able to do: The sum of 2 numbers is 20.  The difference of those same 2 numbers is 10.  What are those 2 numbers?

When your child starts algebra, his math muscles will be primed and ready to use unknown variable to help him do what he has been doing, just a lot more efficiently.  x, the Unknown, will be a very good friend indeed, instead of an intimidating stranger.