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The idea for this activity came from two sources, both presented at Regional NCTM conferences. A presenter at the November 2000 conference in Omaha, NE, provided the actual dot cards we used to make overhead copies. I regret that I do not remember his name to give him credit. I saw similar ideas presented by Julie Howell at the February 2002 regional meeting in Oklahoma City, OK.
Description
Needed Materials: Overhead dot cards or cards large enough for the entire class to see, a piece of paper and writing utensil for each student. Sample dot cards
Directions:
1. Students work individually with paper and pencil to record their answers, but sit in small groups so collaboration is possible.
2. At the top of their papers, the students write “I saw…” on the left side and “I know this is right because…” on the right side.
3. Show a dot card for about 3-5 seconds, and then ask the students to record what they saw and how they know it is right.
4. After a minute or two, facilitate a discussion of responses by calling on students for their answers or have the small groups compare results. You may want to record various answers at the chalkboard.
The mathematical goals are for the student to think about numbers and how they are composed as well as to practice verifying mathematical ideas.
Comment on the overall effectiveness of this activity. Then use the form below to reflect on the activity from the perspective of both the teacher and the student. Give the lesson points based on how well it went--each question is worth up to 4 points.
Enlightening! As we expected, the activity was reasonably
easy for students in these two grade levels.
It did allow success for ALL the students, including special needs and at-risk
students. Because success was not
immediate for all students and all the students remained engaged throughout the
activity, the teacher and I decided dot cards could be used
appropriately at this level, particularly if used earlier in the school
year. We agreed that this activity and
related dot-card activities would ideally be utilized in the K-2
classrooms. (I believe a student’s
thorough understanding of “parts of numbers” would help eliminate the problem I
encountered with front-to-back subtraction earlier in the year.)
Of particular interest was the
difference in the way the 3rd and 4th graders justified
groups of dots. When a card with 3
groups of 4 dots was shown, the 4th graders wrote “12, because 3 X 4
= 12” while the 3rd graders wrote “12, because 4 + 4 + 4 = 12”. Students were eager to present their proofs.
The activity was a natural
discussion starter for the commutative and associative properties of addition
and multiplication.
Learning modalities were primarily visual in nature, but also oral as the students verbalized their proofs. For some students, I reinforced their answers by tapping once for each dot they saw (rhythmic). This was a team-taught activity with the classroom teacher facilitating whole-class discussion and both of us circulating during small-group dialogues.
_4_ Was the purpose of the activity clear to me?
_3_ Was the purpose of the activity clear to my students?
_3_ Did the activity support a range of learning styles?
_4_ Were the students engaged during this activity?
_14_ Total points (out of 16)
The purpose (objective) of the activity was…
I communicated to the students why we were doing the activity by…
…telling them at the beginning what we were doing and what I hoped they would be able to do. Then as the activity progressed, I reinforced the purpose by pointing out student examples that accomplished what we wanted. (E.g., “I wanted to see if you could recognize the same number in different ways--Mackenzie and Andy both saw 9, but Mackenzie saw it as 2 + 3 + 4 while Andy saw it as 4 + 5.”)
The part of the lesson that was student-centered was…
…the student discourse about what they saw, both in whole class and small-group discussions.
