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Mathematics Grade 6
Strand: GEOMETRY (6.G) Standard 6.G.4
An activity creating boxes for candy helps students understand measuring volume and surface area.
Navigating through Measurement in Grades 3-5, by NCTM; ISBN 0-87353-544-8
Math on Call, A Mathematics Handbook, by Great Source Education Group; ISBN 0-669-45770-1
In this activity, students will be working with nets to determine the surface area of various boxes. A net is a two-dimensional pattern that can be folded to make a three-dimensional model of a solid, and is an excellent visualization for surface area. Surface area represents the number of squares that cover the surface of a prism. The formula for surface area of a rectangular prism is: SA = 2(l x w) + 2(l x h) + 2(w x h). Students should already know how to find the area of two- dimensional figures and the volume of three-dimensional figures.
4. Communicate mathematical ideas and arguments coherently to peers, teachers, and others using the precise language and notation of mathematics.
5. Connect mathematical ideas within mathematics, to other disciplines, and to everyday experiences.
Invitation to Learn
Give groups of students copies of Net 1 and Net 2. Show them how to make the nets into boxes. Ask your students how the boxes are alike (volume is the same). Ask them how the boxes are different (different shapes). Ask them what the dimensions are for each box. Have them cut the tape and unfold the boxes. Have the students find the surface area for each net. Point out that although the boxes had the same volume, the surface area is not the same.
Curriculum Extensions/Adaptations/ Integration
Reid, J. (1992). The effects of Cooperative Learning with Intergroup Competition on the Math Achievement of Seventh Grade Students. ERIC Source (ERIC # ED355106). Retrieved November 28, 2007, from www.eric.ed.gov.
This paper reports a study designed to determine the effect of cooperative learning strategies on mathematics achievement in seventh graders. Students were divided into two groups. One group participated in cooperative learning strategies, and the other group received individual/competitive instruction. Pre-tests indicated no differences existed in the groups prior to instruction, but that the cooperative learning groups performed significantly higher on the post- test. The paper concluded that cooperative learning strategies are more effective in promoting mathematics achievement.
Reineke, J.W. (1993). Making Connections: Talking and Learning in a Fourth-Grade Class. Elementary Subjects Center, Series No. 89. Eric Source (ERIC # ED365537). Retrieved December 10, 2007, from eric.ed.gov.
This report describes a fourth grade classroom where students thinking was made public through discussions in which students presented and justified their interpretations of, and solutions to, the problems presented in class. Results suggested that the teacher and her students learned to talk about mathematics in ways that made their thinking visible and indicated that they know mathematics in fresh, inventive ways.