Spaghetti and Meatballs For All [Paperback]

Instead of all those problems about two trains rushing towards one another, this book takes a practial problem and uses it to illuminate spatial problem-solving.

Mr. and Mrs. Comfort decide to invite their family and neighbors over for dinner. Pretty soon, 30 people have accepted so they will be feeding 32, including themselves. In a role reversal from the sexual stereotypes, Mr. Comfort is the cook and impractical one while Mrs. Comfort is the left-brained problem solver. She knows what needs to be done, but everyone else has to work it out for themselves by moving the furniture around.

Mrs. Comfort figures out that they don't have enough tables and chairs for this many people. So she rents some. She correctly figures out that 8 tables seating four people each will do the trick (8 times 4). She rents 8 tables and 32 chairs (but they deliver only 31, and she has to find an extra folding chair).

All is well, until the guests start to arrive. They don't want to sit at separate tables. They want to eat at one big table so they can be closer to everyone else.

That creates a problem. Each time two tables for four are put together, two places are lost (you now have only two ends, while you had four before with separate tables). That's not immediately obvious to the guests, because most of the chairs and tables are unused in the beginning and they don't know how many people are coming.

Mrs. Comfort tries to warn everyone that it won't work, but they ignore her. She finally gives up.

When most of the people arrive, there are not enough places for them at the table (even though there are enough chairs), so they begin pulling the tables apart from one another.

Sure enough, in the end, the guests are seated at 8 separate tables for four. Isn't logic wonderful?

Mrs. Comfort could have ordered more tables and had everyone sit closer to one other. But she wanted to save money. That makes sense, doesn't it?

There is an adult's guide in the end for how to work with your child to make this a problem that she or he can work on. The suggestion is to make 8 little cut-out squares, and to move them into different configurations to handle the various numbers of guests. From this, the child can see that the perimeter varies for the same area, depending on how the area is configured. That lesson will never need to be taught again.

You can also use some of the cooking quantities in here to do math as well. Assuming the children eat so much, and the adults so much, how much will be left over of the meat balls?

Having seen how such a problem can be constructed, I suggest that you develop your own story puzzles. I can guarantee that your child will remember you as a cross between Einstein and Diderot if you do. Here's a hint: How would you go about planning a trip for your family if you were going to have to use frequent flyer miles and the number of miles you had to use varied with when you flew? You can complicate that one for older children by introducing variables like the cost of hotel room nights and car rental days, and having a fixed number of frequent flyer miles to work with in order to find the solution that optimizes the trip and its cost.

But I'm sure you will have even better ideas!

Math teachers: This book will bring the gladness back into your heart, as well as create dedicated, happy students. Do yourself and your students a favor and use this book as a teaching aid.

Think carefully about the periphery to get to the heart of the matter!