# Multiple Turnover Game

## Curriculum Goal

#### Primary: Number Sense

• Represent and solve problems involving multiplication and division.

## Context

• Whole class introduction. Students then play in pairs or small groups.

## Materials

• One deck of numbered “multiple” cards per group (2 – 4 students), with magnitudes depending on skill level (Appendix A)
• 2 – 50: For students who are still learning basic multiplication facts with products to 50 (Grade 3 & 4 students at a basic level).
• 2 – 80: For most students in Grade 4; allows for review of multiples up to 50 and extends knowledge for determining factors up to 80.
• 2 – 113: For students who are confident with lower numbers and are ready for a challenge.
• Optional: for students to record their cards, the factors, and the cards that are turned over for each factor (Appendix B)
• Optional: calculators (to assist students in determining factors and multiples)

## Lesson

• Introduce the game by randomly choosing 10 cards from the 2- to 80-numbered deck. Draw these on the board and provide the students with a factor (whole number greater than one). Ask students if any of the numbers written on the board are a multiple of that factor and have them explain their strategy.
• Explain the objective and rules of the game:
• 10 cards are dealt to each player and placed face up; they remain visible to all players.
• The player with the smallest multiple card starts the game. They will choose a factor.
• All players look for multiples of that number in their card set, and turn those cards face down.
• Students take turns choosing factors, playing until one player has turned over all their cards.
• Model how the game is played to the whole class, selecting one student to play with you.
• Choose a factor and ask, are any of these numbers a multiple of (factor chosen)? How can we find out?
• Invite students to share how they determined multiples of the factor.
• Later in the demo, deliberately turn over a card that does not contain a multiple of the factor to see if students can catch the mistake. If students do not notice the error ask, what do you think, can I turn this card over?
• Allow students approximately 20 minutes to play one or two rounds of the game.
• How do you know the number is or isn’t a multiple of the factor? What do you notice about the multiples?
• Why did you choose to call out that factor?
• Look to see if students can recognize factors of multiples and strategically choose a number that is a factor of their multiple cards.
• If students use skip counting from zero to determine multiples of a factor (e.g., factor is four, multiple is 54), encourage them to start with a multiplication combination they know that will bring them closer to the target number. Ask the following: Can you multiply four by a factor that will get you closer to 54 instead of starting from zero? Do you know four times 10? Can you start with that product?
• This questioning encourages children to use multiplicative thinking rather than repeated addition (Kinzer & Stanford, 2014).

## Look Fors

• Do students accurately identify most products of multiplication combinations up to 7 x 7 in Grade 3 and 9 x 9 in Grade 4? To what extent do students use direct retrieval?
• What characteristics of multiples do students use to determine if a number is a multiple of another number? For example, do they know that multiples of five end in five or zero? Do students recognize they must name the number itself as a factor when they have a card with a prime number?
• What strategies do students use to determine factors of multiples that are more challenging? Are they able to reason from multiplication combinations they already know, or do they skip count?
• Skip counting from zero is a long and effortful process that is also prone to error. Conversely, the ability to break down complicated multiplication problems into simpler ones is an effective multiplication strategy that shows the student is using the distributive property and moving beyond an understanding of multiplication as repeated addition (Kinzer & Stanford, 2014).

## References

Kinzer, C., & Stanford, T. (2014). The distributive property: The core of multiplication. Teaching Children Mathematics, 20(5), 302-309.

Pearson Education (2012). Investigation two: multiplication combinations. Investigations in number, data and space: grade 4 (pp. 68-75). Glenview, IL: Scott Foresman.

## Related Lessons

Students represent and solve problems using multiplication to create a rectangle or square on a board before their competitor.