Student Work Post #7

This task is called “The Raft Game”. The learning goal of this task is how to exchange 5 of something to get one of something. For example 5 planks to get a whole raft. This task is designed to elicit student thinking by providing them with different ways to think about getting to one plank, then to two planks and so on until they reach 5 planks and then they can exchange that for a raft. The students have to figure out how many beans they can exchange to get one plank. If the student has left over beans then they have to figure out how many more beans they have to get to get another plank.

Two possible ways that this task could be represented is by explaining it to the class in a group setting. This could be done for the first time so that everyone gets the instructions on how to play the game. The second way to represent this task is by having the children actually play the game in centers. In the picture above there are two boys that were playing the game during centers time. 

Two ways I would anticipate a student might solve this task would be if the student rolls a 4 and then a 5. They now have 9 beans. They may exchange all 9 beans for one plank, thinking this was correct.  Another anticipated student approach would be to “rig” the dice when it is their turn. I have seen some students do that, and that is taking away from their practice to add numbers or subtract numbers to get to 5.   

First, the student would roll the dice, then they would pull out the number of beans out of the bag.  For example, if the student rolled a 3, they would then pick up 3 beans out of the plastic baggie. Next, the partner goes; let’s say they roll a 4. The first partner now goes, and they roll a 2. 3+2= 5 so they now have 5 beans. Now they are able to exchange the beans for one plank. As soon has they get 5 planks then they exchange that for one raft. Whoever gets the most rafts is the winner.

If the student were to struggle with the exchange of the beans, I would help them to recognize certain amounts of objects that are in sets.  For example if you have 10 beans, how many planks get you get from 10 beans. The answer is 2!  I would have them count it out. If the student exchanged all of the beans, then I would explain to them they we are only suppose to exchange a certain amount. This type of thinking tells me that he struggle with knowing what 5 looks likes in different representative ways.

Two approaches that could advance student thinking on “The Raft Game” could be to add a second dice into the game. This way if the students get ten beans then they will have to figure out if they have 10 beans then how many planks can they grab. Another approach could be to turn this game in to a money game for example instead of beans we could have pennies and nickels to exchange for each other.

Three questions that I still have about the artifact:

1.     How can the students experiences this exchanging task in other ways?

2.     Is this task helpful to their practicing of exchanging 5 of something to 1 of something?

3.     What are some other ways we can extend this learning experience?

Answer:

1.     The students could experience this task through a penny and nickel exchange game. This game would entail the same ideas, but instead of beans there would be pennies and nickels. My next student work analysis will focus on this type of game.

2.     I think this task is helpful to their exchanging practice. The students are able to practice exchanging 5 beans for 1 plank and 5 planks for one raft.

3.     Some other ways to extend this game could be to add two dice, for Kindergarteners this may be tricky but I think for some it could be a nice extension.