Demonstrate the Train Game.
This is a game for two players. Choose a student to be your opponent and demonstrate a round of the game.
At the start of each game, separate all the cubes so
that each player has ten cubes of only one color.
Opponents must have different colors. Two players
will work together to build one train until their train
has a total of ten cubes. Player 1 starts by choosing
1, 2, or 3 cubes. Players take turns choosing to add
1, 2, or 3 cubes at a time to the train. Students must
say the number of cubes in the train after their turn.
Whoever places the tenth cube and finishes the train
is the winner.
During the sample game, clearly demonstrate how to
use a counting-on strategy. Show students how to
count on from the number of cubes that is on the
train instead of counting from one. See Sample Dialog.
Play the Train Game.
Distribute 10 connecting
cubes of one color to each student. Have student
pairs play a round of the game. The game can be
played throughout the year on several levels. Most
students will simply enjoy playing it to see who
wins. As they choose the best number to add, they
are practicing mental computation and logical thinking. As students play more games, encourage them
to look for strategies to win the game. This develops
their problem-solving skills.
Circulate about the room to note how students count
and what strategy they use to win the game. Select
some students to share winning strategies later in the
lesson. See the Content Note for information on a
strategy for winning the game. However, the object
of playing the game at this time is to give students
practice counting and counting on in a motivational
context.
Students using a counting-on strategy during the Train Game:
Nila: I am going to start with three cubes.
Teacher: I am going to add on two cubes. How many are in our train now?
Nila: Five.
Teacher: John, do you agree with Nila? Are there five cubes? How can you count them?
John: I start with 3 and count on 4, 5. It's faster than starting from 1 and counting all of the cubes up to 5.
Teacher: Great. Now it is Nila's turn. How many cubes are you going to add to the train?
Nila: Three.
Teacher: Let's let Shannon tell us how many cubes are in
the whole train now. Shannon, can you use the same
strategy that John used to count? How many cubes
were in the train at the beginning of Nila's turn?
Teacher: Let's let Shannon tell us how many cubes are in
the whole train now. Shannon, can you use the same
strategy that John used to count? How many cubes
were in the train at the beginning of Nila's turn?
Teacher: That's right. Now, the way to win the game is to
place the tenth cube onto the train. I wonder how
many more cubes we need to make ten on this train.
Shannon: 8 is very close to 10. How about 1?
Teacher: Will that win the game?
John: No. You should put 2 more cubes on to make 9 and then 10 to win the game!
Shannon: He's right because 8 plus 2 more is 10.
Train Game is an adaptation of a Nim game. Nim games are
believed to have been derived from the ancient Chinese game
Tsyanshidzi or "picking stones." There are countless
variations of the game. For example, it can be played with
different numbers of cubes in the final train or by having
players remove cubes from a train instead of adding them to
it. In the form being played here, there is a simple strategy
for winning: whoever places the sixth cube on the train will
be able to win because he or she will leave the opponent with
four cubes. The opponent cannot add all four cubes to the
train at once, but adding any of them gives the other player
an opportunity to win.
Observe students playing the Train Game to assess their
progress toward the following Expectations:
- Identify the quantity of a small collection of objects without counting [E2].
- Count on from a given number [E4].
While students are working, keep the following questions in mind:
- Can students identify a small quantity of cubes without counting?
- Do students count all the cubes from the beginning of the train or count on from a certain number?
Sets of connecting cubes can be placed in a center so that
the Train Game can be used as a targeted practice activity
throughout the unit.
Introduce Math Practices and Share Strategies.
Reconvene as a group. Display and direct students'
attention to the Math Practices page in the Student
Activity Book Reference section. Tell them that the
Math Practices page will help them think about
things they do when they are solving and talking
about problems. Very briefly introduce the different
Math Practices displayed on the page, but focus on Finding a strategy, MPE2.
Tell students you are going to talk about some of the counting and game-playing strategies they used during the first round of the game.
- Show how you counted the cubes.
- Did anyone count the cubes differently?
- Which counting method is easier and quicker, more efficient?
- Did anyone have a strategy for winning? Show or tell us how.
- Are there other winning strategies?
- Did you try a strategy that did not work? Explain it to us.
Allow students to talk and begin thinking about strategies. They will have a chance to test the strate-gies in the next round.
- Does the player who goes first always win?
- If you put the cubes on one-by-one, who will win?
- In order to win, is there a certain cube that you would like to place on the train? What number cube is it?
Test Strategies.
Ask students to play the game again
but with a different partner. Encourage them to
choose and test one of the strategies discussed.
Continue to circulate about the room observing stu-dents' counting abilities.
To make this a successful cooperative experience, discuss
ways to decide who goes first. Since the game will be played
more than once, players can take turns. Note constructive
things that students say to one another. To foster better
group dynamics, share some of these comments with the class.
Variations of the Train Game include making the player who
finishes the train the loser instead of the winner, and playing
the game with larger trains, such as 15 or 20 cubes.
