# Playing Shifting Stones in Class

Shifting Stones is a tile-manipulating game where you move or flip tiles to match patterns in your hand of cards. It is suitable for 1-5 players and takes 20-30 minutes to play. The strategy for Shifting Stones requires an economy of cards scored vs. cards expended to move tiles. Drawing on Davis et al.’s (2015) spatial reasoning wheel, the game’s mathematical strategizing primarily engages situating as players orient the patterns of the cards, investigate the possible paths (pathfinding) to change the location of the tiles to match their hand. Although this game would be appropriate for Grades 3 to 12, we have played this game several times with students in Grades 5 and 6. This page provides our tips and ideas for playing this game in your classroom.

Here are some images of Grade 6 students’ notions of how they engaged with different spatial reasoning elements when playing Shifting Stones. Notice the intertwining spatial reasoning and strategizing.

Considerations for getting started
• Prepare games: Label and number your games. It is easier to keep track of the games and make sure that your students are taking care of the games.
• Plan Groups: Decide how you want to group students for game play.
• Good Sportsmanship: Create a supportive environment by providing some guidelines for good sportsmanship. You may need a reminder of sportsmanship as time progresses. Here are some suggestions.
• How to win and lose graciously. If you win, don’t boast. If you lose, try to be happy for the winner. Be kind to yourself. Learning a game takes time. Often the winners have more experience.
• Don’t give up in the middle of a game if you are feeling like you are not winning. Ask your team-mates for help to make a good play.
• Be gentle when you see a team-mate make a mistake. Don’t get defensive when someone reminds you of the rules.
• Don’t bully. Playing is no fun if you have no one to play with.
• At the end of every game, thank your team-mates for playing with you.
• Cooperative play can help create a supportive environment and encourage communication. Below are a couple ideas for cooperative play
• Team with highest score in class wins
• Pair students. Eg in groups of 4 have two students support each other.
• Print out handouts: Quick ‘how to play’ guides, scoresheets, and reflection sheets. And if you would like a hardcopy of this page, click here.
Week 1: Introduction of the game

Focus

• Mathematical & Logical Reasoning: Exploring and comparing the possibilities for matching patterns in the cards by moving the positions of the tiles.
• Spatial Reasoning: Orienting the patterns in the cards to the positioning of the tiles.
• Noticings: Do student know that the tiles can only move one space (vertically and horizontally) or flip for one card move? Can they match the moves accurately to their cards?

Suggestions for classroom game play

First, Introduce the game by watching this video in class

Then, play a game against one student, with the rest of the class gathered around. Deliberately make a couple of mistakes to clarify rules, such as switch the corner tiles and count that was on move, move the tiles diagonally and count that as one move.

Organize the students into numbered groups. Give each group the same numbered game and a quick Shifting Stones guide. Give each student a scoresheet and a pen or pencil. We have noticed many scoring errors. One way to address this is to have each student in the group fill out the scoresheet for all players. Then have them compare their scores and analyze discrepancies.

After Game Play

Organize the students to clean up their games.

Give each student the Week 1 reflection sheet to assess students’ strategies and understanding of the game. Once the sheets are complete, assess them as a class. You could have them assess their own as you complete it on a whiteboard or screen. REMEMBER: The assessments are not to assign a mark, they are just to assess and further understandings of the games and strategies.

Student Journal Prompts:

• What does orienting your the patterns found in the cards to the North position of the tiles mean?
• When you are not facing the North position of the tiles, how do you imagine the direction of the patterns in the cards?
Week 2: Clarification of the rules and scoring

Focus

• Mathematical & Logical Reasoning: Analyzing the direction and number of moves for necessary to the tiles to match the patterns found in the hand of cards.
• Spatial Reasoning: Visualizing the predicted path the tiles will move.
• Noticings: Are students able to see which way is North in the game? How do they compensate for differences when the are sitting facing not the East, West or South of the tiles?

Suggestions for classroom game play

Start to play a game against one student. Make some mistakes. For instance, move a tile one space and flip it. Then count it as one move. Switch tiles in the corners and count it as one move. See the Misconceptions below.

Organize the students to play the game. Give each Group the same numbered game and a ‘how to play’ guide. Give each student a scoresheet and a pen or pencil.

Organize the students to clean up their games.

Give each student Reflection sheet 2. Reflection sheet 2 enables assessment of students’ strategies and understanding of the game.

Student Journal Prompts:

• How do you decide which cards to score and which cards to discard?
• How do you evaluate which tile placement score the most points?
• What do you find challenging about comparing attributes for situating tiles?
Week 3: Balancing the ratio of cards spent to points gained

Focus

• Mathematical & Logical Reasoning: Conjecturing and predicting which cards will score and which cards you will discard to move the tiles for the best possible location.
• Spatial Reasoning: Visualizing the predicted path and the number of necessary tile moves.
• Noticings: Are students able to evaluate whether they have enough cards for the number of moves necessary?

The strategy for Shifting Stones requires an economy of cards scored vs. cards expended to move tiles. While there may be some questionable counting going on near the end, in the conversation below (see the conversation in this video) Blair, Grade 5, explains this concept of balancing expenditures for points gained.

Abbey: I don’t know what I should do. Should I do this one or should I do this one (she pointing to the 3 point and 5 point card)?

Blair: See, here’s the thing. If you go for that one (pointing to the 5 point card), then you basically are going to have to move both of these down (pointing to the two orange fish) and then flip them over. That is already 4 cards. Then you need to move this up (pointing to the moon tile) four spaces and turn it over. In total that is 9 uses of points and if you use these two that is 18 points lost. And if you use the ones that is still 9 points lost.

Suggestions for classroom game play

Start with a whole class discussion, to evaluate the costs of moving cards. Which cards are best to spend? Which cards are best to score? Why?

• Organize the students to play the game. Give to:
• Organize the students to clean up their games.
• Give each student Reflection Sheet 3. Reflection Sheet 3 enables assessment of students’ use of each of the three possibilities for placing tiles. Are they able to use place their tiles to form a grid? Are they able to score a grid accurately?

Student Journal Prompts:

• How does shifting stones tie into math?
Week 4: More game experiences

Focus

• Mathematical & Logical Reasoning: Analyzing the direction and number of moves for necessary to the tiles to match the patterns found in the hand of cards, and Justifying the expenditure of cards for points scored.
• Spatial Reasoning: Visualizing the predicted path the tiles will move.
• Noticings: How many steps ahead are students able to predict?

Keep playing the game as many times as your students enjoy.

Student Journal Prompts:

• How do you choose your tile moves for each turn?
• Summarize the game in a one-pager
Acknowledgements

Gratitude and credits to the students of Westmount Charter, Heather Lai, Pam Mah, Mischa Simpson, Munesah Rahman, & Dr. Janelle McFeetors at the University of Alberta for the creation of this resource.

This website draws on research supported by the Social Sciences and Humanities Research Council.

References

Davis, B., Okamoto, Y., & Whiteley, W. (2015). Spatializing school mathematics. In Spatial reasoning in the early years: Principles, assertions, and speculations (pp. 139-150). Routledge.