## Playing the Product Game

6-8
1

Students learn how to play the Product Game. As they play the game, students develop understanding of factors, multiples, and the relationships between them. Winning strategies are discussed. The Product Game was adapted from Prime Time: Factors and Multiples, part of the Connected Mathematics Project, and was written by G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips (Dale Seymour Publications, 1996, pp.17-25.)

## Launch

In the Product Game, students explore multiples. Before you introduce the game, make sure your students understand what a product is.

We are going to learn to play a new game called the Product Game. What does the word product mean?

In the Factor Game, you start with a number and find its factors. In the Product Game, you start with factors and find their product. The diagram shows the relationship between factors and their product.

When you are satisfied students can give examples of products with understanding, introduce the Product Game.

The best way to explain the rules is to play a game against the class. Project the Game Board overhead for students to see.

Distribute a copy of the Product Game Rules Activity Sheet to each pair of students.

The Product Game board consists of a list of factors and a grid of products. Two players compete to get four squares in a row—up and down, across, or diagonally.

Explain that the list of numbers at the bottom of the board are factors and that the numbers in the grid are the products that can be made by multiplying any two factors. When you play the game, use two colors to mark the products; one to mark the class's products and the other to mark your own.

### Product Game Rules (board)

1. Player 1 puts a paper clip on a number in the factor list. No square on the product grid is marked with Player 1’s color because only one factor has been marked; it takes two factors to make a product.
2. Player 2 puts the other paper clip on any number in the factor list (including the same number marked by Player 1) and then shades or covers the product of the two factors on the product grid.
3. Player 1 moves either one of the paper clips to another number and then shades or covers the new product.
4. Each player, in turn, moves a paper clip and marks a product. If a product is already marked, the player does not get a mark for that turn. The winner is the first player to mark four squares in a row -- up and down, across, or diagonally.

## Explore

Have students pair up to play the game. Students can mark products on the product grid with colored markers or pencils, or with colored game chips.

Alternatively, students may use the applet to play the game.

### Product Game Rules (applet)

1. Player 1 puts a marker on a number in the factor list. The markers are the green rectangles at the ends of the number line 1-2-3-4-5-6-7-8-9 at the bottom of the applet: a horizontal rectangle at the right and a vertical rectangle at the left. Click and drag a marker to a number in this number line. You can start with either marker. No space on the product grid fills in with Player 1's color because only one factor has been marked; it takes two factors to make a product. (You can fill in names for the players in the applet!)
2. Player 2 puts the other marker on any number in the factor list (including the same number marked by Player 1). The space on the product grid containing the product of the two factors marked is colored in with Player 2's color.
3. Player 1 moves either one of the markers to another number and the new product is filled in with Player 1's color.
4. Each player, in turn, moves a marker and the space with the product is marked with the proper color. If a product is already colored, the player does not get a mark for that turn. The winner is the first player to mark four spaces in a row -- up and down, across, or diagonally.

For either version (board or applet), distribute the Playing the Product Game Activity Sheet for students to complete in pairs.

## Summarize

Have a class discussion about whether it is better to go first or second. Have students share any strategies they discovered while playing the game. Here are some comments students have made:

• Diaco said it is better to go second, because if you go first, you do not get to make a move on the board.
• Betty said that when you get toward the end of the game, you have to avoid the factors of the numbers your opponent needs.
• Jabe said that if you had to go first, you should choose the number 1 because it gives your opponent fewer choices about where to go to get four in a row.

Go over the follow-up questions with your class. This is especially important, since the word multiple is introduced for the first time.

The Product Game Investigation was adapted with permission and guidance from:

Prime Time: Factors and Multiples, Connected Mathematics Project, G. Lappan, J. Fey, W. Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications, (1996) pp.17-25.

Assessment Options

1. Use the Playing the Product Game Activity Sheet as a form of assessment.
2. Use informal assessment by circulating the room and taking note of students who:
• Are proficient with their multiplication facts.
• Understand factors, multiples, and the relationships between them.
• Understand that some products are a result of more than one factor pair.
• Develop problem solving strategies.
3. Ask students to write down what sorts of interesting patterns and strategies they've fount while playing the game.

Extensions

1. Have students modify the rules of the game. For example, students may want to see how the play changes if the goal is to get three in a row.
2. Continue on to the second lesson in the unit, Making Your Own Product Game.

Questions for Students

1. Is it better to go first or second?
2. Why did you choose to place your marker there?
3. What do you think is the relationship between factors and multiples?
[Factors are multiplied to get the product; a number can have many factors. Multiples are a result of multiplying by an integer.]

Teacher Reflection

• How could the lesson be modified to increase math talk?
• What did students do to demonstrate engagement and perseverance?
• How should you pair up students to play the game?

### Making Your Own Product Game

6-8
In Part II, students make their own game boards. The task of creating a new game is challenging to most students. They learn a lot by experimenting and by making mistakes about what factors and products to include in a game.

### Classifying Numbers

6-8
Students use Venn diagrams to represent the relationships between the factors or products of two numbers.

### Connections and Extensions

6-8
Students make connections and expand on what they have learned in the first three lessons. Students explain the effects of different moves on the game board. Finally, students "Guess My Number" using various clues.

### Learning Objectives

Students will:

• Review multiplication facts.
• Develop understanding of factors, multiples, and of the relationships between them.
• Understand that some products are the result of more than one factor pair.
• Develop strategies for winning the Product Game.

### NCTM Standards and Expectations

• Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
• Use factors, multiples, prime factorization, and relatively prime numbers to solve problems.
• Develop and analyze algorithms for computing with fractions, decimals, and integers and develop flue

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP2
Reason abstractly and quantitatively.