At an after-school center, students play a strategy game that also provides practice with two-digit multiplication. Try the game yourself and consider our questions, noticing the connections between any ideas that come to your mind.

Take four number cards from a deck of zero to nine cards. Make up a two-digit multiplication problem as shown on the game board below. Your goal is to find the highest possible product. Variation 1: Play for the lowest possible product. Variation 2: Allow the use of a one-digit number and a three-digit number. Here's a possible turn:

Using those cards, answer the following questions:

• What problem do you want to make?
• What is your product?
• Why do you think your product is the largest possible product?
• Compare your problem to our examples. Which one of our problems do you think will have a higher product? Look for clues as to what helps a product be very high.

• Was your product higher or lower than our examples?
• Were you surprised by the results?
• Why isn't the product of 97 and 86 the largest product?

In your mind, make up two word problems that go with your two-digit numbers. Have one involve area and the other involve something else.

  Reflect on The Products Game