Task that Lead to Argument Writing

Pumpkin Problem

A nice problem to help facilitate problem solving; ideal to use as an opener.


Number Theory Problem:
A peddler is taking eggs to the market to sell. The eggs are in a cart that holds up to 500 eggs. If the eggs are removed from the cart 2, 3, 4, 5, or 6 at a time, one egg is always left over. If the eggs are removed 7 at a time, no eggs are left over. How many eggs are in the cart?
(Problem taken from McLoughlin, John Grant. (2002). Calendar Problems from the Mathematics Teacher. Reston, VA: National Council of Teachers of Mathematics.)
The Marbles Problem:
Karen has a bag of marbles. She gives 1/3 of the marbles to Jenny, then gives 1/4 of the remaining marbles to Jon. Karen has 24 marbles remaining. How many marbles were in the bag?


Linear Systems



Cats, Dogs and Mice - Oh My!
RAY:I happened to find this puzzler the other day in my puzzler folder. It's from Barry Lawber. And it's from July '96. Here's his puzzler: You're given a hundred dollars and told to spend it all purchasing exactly a hundred animals at the pet store. Dogs cost $15. Cats cost a buck, and mice are 25 cents each.
TOM: Let me get this straight. You have to spend exactly a hundred bucks and you end up with exactly a hundred animals?
RAY: Right. The other only other criterion is that you have to purchase at least one of each animal.
The question is, how many of each animal do you have to purchase to equal a hundred animals purchased at exactly a hundred dollars?