A Probability and Number Sense Math Game – Please contribute

Ontario educator Stepan Pruchnicky aka @stepanpruch sent out a request calling for math games (perhaps using cards or dice) that might be helpful for a grade 5 classroom learning about Numeracy / Probability topics.

If you know of any, then kindly leave a link or description in the comments section, or reply directly to Stepan using the twitter link above.

Here is my contribution which comes courtesy of Dr. Cathy Bruce and Louisa Chan.

River Crossing:

Here is the Twitter discussion I had with Dr. Bruce and Louisa.

Based on this brief Twitter discussion, I believe the River Crossing Game is played as follows.

Materials:  8.5 x 11 paper, 20 ‘counters’, and two 6-sided dice.

Prepare game board:

1)  Get a sheet of 8.5 x 11 paper and fold in half, lengthwise.

2)  Each player draws 10 ‘docks’ on their half of the page.

3)  Place one counter on each dock.

4)  Each player numbers their 10 docks by picking any number from 1 to 12.

river crossing

(Photo courtesy of @louisa_cee)

Goal of game:   To take turns rolling two 6-sided dice.  Add the value of your roll and if you have a dock with that number, then you can remove your boat (counter) from the dock. First one to have all their docks clear, wins.

The game, as described above, will likely lead to fierce competition, disagreements, and developing strategies for winning.  I am wondering, however, if this game might be more of a grade 6,7, or 8 type of ‘probability topic’, as it relates to the Ontario Curriculum.

Can it be revised to work with the grade 5 expectation of “…determine and represent all the possible outcomes in a simple probability experiment…”?  For sure.  In the end however, if you view curriculum expectations as a floor instead of a ceiling, then don’t worry.

How I would revise “River Crossing” to use 1 die (D) or 1 dice

Students could construct a D for each game of River Crossing they make.  Imagine multi-sided dice like:

Roll Your Color

(Photo courtesy of BEV Norton)

Students could construct the game D by selecting a plastic or wooden 3-D shape from your math work room.

Wooden Blocks
(Photo courtesy of MacAttck)

And, using post-it notes, put numbers on each side as it corresponds to the created River Crossing game board.

Want another level of probability gaming added to it?

Perhaps have each student role a 6-sided D, add them up, and then write the total on a post-it note, to be place on the selected D shape.  Imagine the ‘agony’ of your dock number not being rolled, even if the game hasn’t started.

Perhaps a revised rule needs to be created for this event.  For example, if your dock number is not represented on the D, then maybe you get to ‘change’ your dock number.  Is this fair?  Can a player disregard their undesirable dock number to only then select the number that shows up most frequently on the co-constructed game D?  Perhaps your opponent can pawn off one of their undesirable dock numbers to you so that they themselves can pick a new dock number? Either way, a good discussion will ensue because of this problem.

Want to up the number sense difficulty?  Use more 6 sided dice or have students multiply the two rolled numbers instead of adding.

How I would revise “River Crossing” to include a colour spinner

Instead of ‘numbering your docks’ you could ‘colour code your docks’.

Pull up your favourite colour spinner, web-tool.  A quick search brought me to http://www.mathplayground.com/probability.html


In the change spinner option you can construct your game spinner.  For example, before game is played, the two players can roll two 6-sided dice and add the rolled values together, to construct the size ‘value’ of each colour of the spinner.

For the spinner example above, I quickly constructed it like this:

spinner change

Maybe in this game, players can preselect what colours are permitted to colour your dock with. That way the event of a colour not being one of the possible events on the spinner, will not be an issue.

How I would revise “River Crossing” the concept

Maybe it is the Marvel Universe comic book collector kid, I used to be, talking right now.

But perhaps Spider-Man and Wolverine decide to practice together to hone their respective abilities.  Note that they aren’t fighting…

The player docks could then be replaced by “Spider-Man” and “Wolverine” specific moves.

Everything else stays the same.

Just ideas.

Don’t like this concept because you are uneasy with potential not appropriate for school arguments?  As with all things, adjust accordingly to suit your students’ needs.

In certain settings, the idea of students using cards or dice might even need to be a topic for discussion/permission.

Back to Stepan…

I am sure you have your own math game ideas, or math games you have played or borrowed from someone else.  If so, then kindly add a link or description in the comments section so that we can all benefit.

Thanks for reading.

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One Response to A Probability and Number Sense Math Game – Please contribute

  1. Paul,
    I’m speechless. Thanks for taking time to do this and the amazing game (with mods!!). I’m always impressed with the kindness of my friends on Twitter. The way that people give without thought of receiving is so touching.
    I’ve gotten some great stuff from a bunch of people. I promise I’ll compile, post, and send it your way. Also, I’ll keep you in the loop for our math night.
    THANK YOU!!!!

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