Ratio Fill Up (Ratio/Fraction Equivalences)

Here is another game from TMC14.  This is the game that my group worked on so I can take some credit in it's creation.  My group's goal was to create a game about ratios/proportions.  We were thinking of ratio tables and wanting students to see that each ratio was equal to the other.  There are quite a few rules to this game as you can see.  I took the rules straight off of the TMC14 wiki.

Objective: To earn three points [counters] by filling ratio tables with congruent ratios.

Materials: Gameboard with 4 ratios tables with room for 5 ratios in each table,  ratio cards, point counters, calculator.

Set-up: Shuffle ratio cards and deal 5 to each player.

Game play:
1) The first player plays any ratio card from their hand in the blank first space in a ratio table and then draws a card to end his/her turn.
2) The second player can either play an equivalent ratio in the same table as the first player or play a different ratio in one of the empty tables.
3) Play continues with each player playing equivalent ratios to fill up the ratio tables and drawing cards to replace the ratios just played.
4) When a ratio table gets full, whoever played the last ratio into that table gets 1 point, as long as they can identify operations to get from the first ratio played to the last (ie, if the first ratio is 2/8 and the last is 4/16, they could say multiply by 2/2 or divide by 2/2 and multiply by 4/4).
5) The player to the right of the player that played the last ratio will take the calculator and divide out the ratios in order to check to make sure the ratios are all equivalent.
6) Cards from the completed ratio table are put into the discard pile, and the cleared ratio table is open for any player to play in.
7) The first player to 3 points (counters) is the winner.

Other rules:
1) If the draw pile ever runs out, reshuffle the discard pile to create a new draw pile.
2) If a card is played incorrectly the player that noticed the error draws an extra card and the incorrect card is put into the discard pile.
3) Skips, reverses and wilds:

• Skips automatically skip the next player, 
• Reverses switch which order the players play (so, if play is going left at first, it instead goes right), and 
• wilds can be played in any ratio table that already has a ratio in it, but the player who plays it must name an equivalent ratio that isn't already in the table.  

4) If none of the cards from a player's hand can be played on their turn, that player discards one card and draws one card and their turn ends.

OK, this is a lot of rules!  Our group did agree that the game still needed some tweaking, but we just ran out of time.  Also, I am not so sure about the 4th rule.  I'm having trouble seeing the value in doing that.  Maybe when I play it with students I will, but right now I am struggling.  I would rather have my students identify the pattern in the ratio table and figure out how to do that considering that the ratios are not placed in any specific order during play.  What strategy would they use to figure out that there is a scale factor of 2/2?  What discussions or debates would come out of this?  Sometimes the first and last ratios played don't display an easily identifiable pattern and for the lower students, this could cause frustration.  I'll just have to play it and see.

Another thing that I did to modify this was to add labels to the ratio table.  I just felt like if students saw the labels they would not be thinking fractions.  The Power Point below is completely editable, so if you would like to remove those or change them, it is possible. 

Below you will find the gameboard and cards that I made up to use with my students.  The cards are ment to be cut out like fractions.  A more challenging option would be to cut the individual numbers apart and have the students work together to make ratio tables that are true and to explain how they know they are correct.  There is definitely room for tweaking and developing spin-offs of the basic game.

If you play this with students and make modifications, I would love to hear what you did and how it worked for you!

Finding the best deal is harder than it looks...

I had another reminder this week about how different my childhood was from the students that I teach in my classroom today.  I realized it this week while studying unit rates and watching my students try and find information in advertisements.  I began to be very thankful that my parents taught me a lot about unit rates through very authentic and natural experiences.

My mom is a huge bargain hunter.  When I was younger, she would scour the grocery store ads and compare prices.  She had the calculator out and would go down to the unit prices to get the best deal.  Even standing in the grocery store, she would estimate the unit cost of the generic peanut butter and the big brand name on sale.  I remember whining many times about what was taking so long and my mother, ever so patiently each time, explained that you have to figure out the best deal to make your money go farther.  She explained how she was figuring out the unit cost and often times asked me or my brother to get the next item on her list, but to get the best deal.  Sometimes she even handed us a coupon and asked us to figure out if it was a better deal with the coupon or not.  So much great mathematical conversation and mental math work was going on during those trips to the grocery store.  I guess now I am thankful for always being dragged along with my mom.  She taught lifelong skills that I still use every time I stand in the grocery store aisle trying to save a few pennies.

My kiddos aren't growing up like this today.  This week, after defining unit rates, discussing them, giving practice problems, and my kiddos appearing ready to take on the world of unit rates, I was so wrong.  The application of this skill is trickier than I anticipated.  I gave my students free reign to find three products to compare by finding the unit rate and determining the best deal.  I thought that this would be a great real world experience for them.  I realized that they have a lot of trouble just reading a grocery store advertisement (which can be a completely separate lesson on ratios).  The ad was 4 boxes of cereal for $8 and the kiddos were comparing ounces to $8, not $2.  The kiddos also brought up items that were on sale for 25% off, but no price for the specific item was given.  They wanted to know how to figure out the price.  There were also lots of questions about how to calculate the unit rate, too!  I thought that they were so prepared to handle this!!

So, it is regrouping from here.  I have learned that this is not a life experience for them as it was for me.  I assumed when I shouldn't have and I am regretting not building more background for my activity.  My first plan is to reteach and practice again.  I made a scavenger hunt for them to do.  The Powerpoint is embedded below for you to use.  I used free clip art from a Google search and I did use names from kiddos in the class.  You can totally change that up. 



Each student will will in the answer sheet and I can buzz around to answer questions and just listen to their thinking.



After they finish the scavenger hunt, they can return to finding products to do their comparisons.  I am hoping that it is just a matter of some more practice and experience.