602.4.12 Cardinality To 15
Task: 602.4.15-04, 38, 39 (Tk 1)
A. To help a group of 10 first-graders count rationally to 15 requires that the students be able to perform the 4 principles of counting:
1. Each object that is being counted is assigned only one number to represent it. This is called one-to-one correspondence.
2. When counting a group of objects there is a fixed order sequence of numbers. This is called stable-order rule.
3. The last number given to the last object counted represents the total number of objects. This is called the cardinality rule.
4. The order of the objects being counted doesn’t matter. This is called the order irrelevance rule. The students already understand how to rationally count to10 so I am going to build on this prior knowledge and take it to 15. The steps I would use would be to:
1. Using some magnetic manipulatives I would start with a group of 10 magnets in one group on a white board and 5 others in a different group on the board. I am using the magnets because they are easy to move around and the white board allows me to write and erase the name of the number down below the magnet. There is no pattern to the magnet placement in the large or small group. They are randomly placed inside the group.
2. I would start by …show more content…
randomly choosing and moving the magnets from the group of 10 to a random place in a box in a different place on the white board counting out loud the first 2 numbers and writing the number below the magnet and having the students repeat the number after me. I then have the students together count each successive piece on their own out loud till all ten are counted. I write the number of the piece below the magnet. Then I ask the students how many magnets are there in this box. The students have used the one-to-one rule by each piece being represented by a different number. It also uses the stable order rule because the objects are in a fixed order 1, 2, 3... 10. The students also use the cardinality rule in being able to determine the total number of pieces in the box. The students also used the irrelevance rule when the magnets are chosen randomly from the group of 10 and placed in a random spot within the new box and they correctly associate the representative number to the piece.
3. The next step is to draw their attention to the other group of 5 magnets and say “Oops we missed these. Let’s add these to our box.” I move the 1st piece from the small group to a place within the large group. I would then have the students count out loud again 1 through 10 pointing to the magnet and its number. When we get to 10 I point to the new piece and say out loud 11 while writing the number below the piece and I have the students repeat the number. Then I have the students count again the large group out loud all the way to eleven. We repeat this process of see-say-share till I am sure they now can count to 11. I ask the students to tell me how many magnets are now in the large group. This process is repeated till all the magnets from the small group are added to the large group and the students have reached 15. The students have used all 4 principles in this step, one-to-one correspondence using a different number for each piece, order irrelevance by having not set organization of the magnets within the large group, stable order by having an fixed order of numbers such as 1, 2, 3…15, and finally the use of cardinality by identifying the correct number of magnets in the large group.
B. I would assess the student’s mastery of rational counting to 15 by having the students demonstrate by having the students color smiley faces that match the number I ask the students to color. The students will each get a sheet with 4 rows of 15 smiley’s. I will ask the students to color in 10 faces in the 1st row, 11 in the 2nd row, 13 in the 3rd row, and 15 in the last row. Mastery will be demonstrated by the students successfully coloring in 3 out of the 4 rows correctly.
C. To help ELL students and students with memory disabilities would be to have them practice the counting sheet with a cross-age student.
This allows the student to practice with the help of an older student. The ELL or learning disability student getting the extra practice and help will give them the extra support they may need to meet the expectations of 3 out of 4 rows colored correctly. The supporting student will have the learning student color in random numbers of squares they call out. Practicing like this will help them through any possible confusion and strengthen their understanding so that when the take the assessment they are more comfortable with what is being asked of them. The reason for this is not to reduce expectations but to give the extra support so the student can meet the
expectations. The exceptional learners I would expect that they be able identify 4 out of 4. The level of difficulty remains the same; the expectations would be altered to meet their ability.
References
Friel, S., Curcio, F., and Bright, G. (2012). Developing counting and number sense in early grades. In R. Johnston (Ed.), Helping children learn Mathematics, 10th edition (pp130-153). Hoboken, NJ: Wiley
A. To help a group of 10 first-graders count rationally to 15 requires that the students be able to perform the 4 principles of counting:
1. Each object that is being counted is assigned only one number to represent it. This is called one-to-one correspondence.
2. When counting a group of objects there is a fixed order sequence of numbers. This is called stable-order rule.
3. The last number given to the last object counted represents the total number of objects. This is called the cardinality rule.
4. The order of the objects being counted doesn’t matter. This is called the order irrelevance rule. The students already understand how to rationally count to10 so I am going to build on this prior knowledge and take it to 15. The steps I would use would be to:
1. Using some magnetic manipulatives I would start with a group of 10 magnets in one group on a white board and 5 others in a different group on the board. I am using the magnets because they are easy to move around and the white board allows me to write and erase the name of the number down below the magnet. There is no pattern to the magnet placement in the large or small group. They are randomly placed inside the group.
2. I would start by …show more content…
randomly choosing and moving the magnets from the group of 10 to a random place in a box in a different place on the white board counting out loud the first 2 numbers and writing the number below the magnet and having the students repeat the number after me. I then have the students together count each successive piece on their own out loud till all ten are counted. I write the number of the piece below the magnet. Then I ask the students how many magnets are there in this box. The students have used the one-to-one rule by each piece being represented by a different number. It also uses the stable order rule because the objects are in a fixed order 1, 2, 3... 10. The students also use the cardinality rule in being able to determine the total number of pieces in the box. The students also used the irrelevance rule when the magnets are chosen randomly from the group of 10 and placed in a random spot within the new box and they correctly associate the representative number to the piece.
3. The next step is to draw their attention to the other group of 5 magnets and say “Oops we missed these. Let’s add these to our box.” I move the 1st piece from the small group to a place within the large group. I would then have the students count out loud again 1 through 10 pointing to the magnet and its number. When we get to 10 I point to the new piece and say out loud 11 while writing the number below the piece and I have the students repeat the number. Then I have the students count again the large group out loud all the way to eleven. We repeat this process of see-say-share till I am sure they now can count to 11. I ask the students to tell me how many magnets are now in the large group. This process is repeated till all the magnets from the small group are added to the large group and the students have reached 15. The students have used all 4 principles in this step, one-to-one correspondence using a different number for each piece, order irrelevance by having not set organization of the magnets within the large group, stable order by having an fixed order of numbers such as 1, 2, 3…15, and finally the use of cardinality by identifying the correct number of magnets in the large group.
B. I would assess the student’s mastery of rational counting to 15 by having the students demonstrate by having the students color smiley faces that match the number I ask the students to color. The students will each get a sheet with 4 rows of 15 smiley’s. I will ask the students to color in 10 faces in the 1st row, 11 in the 2nd row, 13 in the 3rd row, and 15 in the last row. Mastery will be demonstrated by the students successfully coloring in 3 out of the 4 rows correctly.
C. To help ELL students and students with memory disabilities would be to have them practice the counting sheet with a cross-age student.
This allows the student to practice with the help of an older student. The ELL or learning disability student getting the extra practice and help will give them the extra support they may need to meet the expectations of 3 out of 4 rows colored correctly. The supporting student will have the learning student color in random numbers of squares they call out. Practicing like this will help them through any possible confusion and strengthen their understanding so that when the take the assessment they are more comfortable with what is being asked of them. The reason for this is not to reduce expectations but to give the extra support so the student can meet the
expectations. The exceptional learners I would expect that they be able identify 4 out of 4. The level of difficulty remains the same; the expectations would be altered to meet their ability.
References
Friel, S., Curcio, F., and Bright, G. (2012). Developing counting and number sense in early grades. In R. Johnston (Ed.), Helping children learn Mathematics, 10th edition (pp130-153). Hoboken, NJ: Wiley