## Connections and Extensions

6-8
1

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.

Students can answer on the following questions in pairs, or you may choose to have a class discussion about each of the questions.

1. On the 6 × 6 Product Game board, suppose your markers are on 16, 18, and 28, and your opponent's markers are on 14, 21, and 30. The paper clips are on 5 and 6. It is your turn to move a paper clip.
• List the possible moves you could make.
• Which move(s) would give you three squares in a row?
• Which move(s) would allow you to block your opponent?
• Which move would you make? Explain your strategy.
 1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 49 54 56 63 64 72 81

 1 2 3 4 5 6 7 8 9

2. What four factors were used to create the Product Game board below?  What number is missing from the grid?
 9 15 18 21 ? 30 35 36 42 49
3. Think about the following questions dealing with time:
• In developing ways to calculate time, astronomers divided an hour into 60 minutes. Why is 60 a good choice (better than 59 or 61)?
• If you were to select another number to represent the minutes in an hour, what would be a good choice? Why?

4. What is my number?
• Clue 1 When you divide my number by 5, the remainder is 4.
• Clue 2 My number has two digits, and both digits are even.
• Clue 3 The sum of the digits is 10.
References

This 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.

#### Applet Developer

• Richard Burgis, Connected Education Technology, burgisr@hotmail.com

#### Web Developer

• Daniel Harned, Michigan State University
• Brian Keller, Michigan State University

none

Questions for Students

Refer to the instructional guide.

### Classifying Numbers

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

### The Product Game: Making Your Own Product Game

 Students work in pairs to create their own game boards, a worthwhile challenge. They learn by experimenting and by making mistakes about what factors and products to include in a game.

### The Product Game: Playing the Product Game

6-8
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.)

### Learning Objectives

Students will:

• Make connections and expand on what they have learned
• Use clues to "Guess My Number"

### NCTM Standards and Expectations

• 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
• Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results.

### 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.
• CCSS.Math.Practice.MP6
Attend to precision.