Numbers at the Concept Level: Application and Extension: The Three Games (Pre K-2)
The Hand Game
Lift the Bowl Game
This game requires the same counters and a small bowl. This is basically the same game as the hand game except the one division is put under a bowl instead of in the hand. It can be done as a pair or as an individual with self-checking the answer by lifting the bowl and counting.
Individualizing the Three Games
The nice thing about this game is that it requires hardly any materials: some sort of counter and your hand! Take out 10 counters of any type and separate the into two piles: one goes on the table and the other in your hand. It doesn't matter how you divide them. Have your students now figure out how many are in your hand. The answer is then verified by counting. Repeat with different divisions over and over. This was a good game for older children to run, practicing teaching younger siblings.
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This game requires the same counters and a small bowl. This is basically the same game as the hand game except the one division is put under a bowl instead of in the hand. It can be done as a pair or as an individual with self-checking the answer by lifting the bowl and counting.
Peek Through the Wall
This game again uses the same concept of dividing 10 counters into two piles, but this time they are separated by a "wall" made of an index card in which the middle has been cut out. This is the easiest version of the game because you can see both piles at the same time, so the answer is asked to be given very fast. This is the last transition before the student is asked to give the answers to problems such as 4 + __ = 10 on paper. By playing all these games many times, the student should be able to visualize the answer 6 in his head, so that these concepts are not memorized but really known.
This game again uses the same concept of dividing 10 counters into two piles, but this time they are separated by a "wall" made of an index card in which the middle has been cut out. This is the easiest version of the game because you can see both piles at the same time, so the answer is asked to be given very fast. This is the last transition before the student is asked to give the answers to problems such as 4 + __ = 10 on paper. By playing all these games many times, the student should be able to visualize the answer 6 in his head, so that these concepts are not memorized but really known.
Individualizing the Three Games
Once they understand the form of the games, they are ready to begin working at different levels, depending upon what is appropriate for them as individuals. Since you are working with your students all the time, you probably know where their level is, but if you don't you can find out by having him count various amount of objects and seeing if he is able to count them. If he is not able, then you know he needs more work with this amount before using this amount for these games. Is he able to tell you how many without counting them individually? If he is not, then he may need more experience with the activities on invariance and counting totals in number stations. If he can do that, hide a number of the blocks in one hand and showing the others still on the table, ask him how many you are hiding. If he is unable to do this, then he does not have a real understanding of this number.
source: Mathematics Their Way, Mary Baratta-Lorton
source: Mathematics Their Way, Mary Baratta-Lorton
