Sequencing Mathematics Lessons
Sequencing Mathematics Lessons
Sequencing Mathematics Lessons
Introduction & Background
The main aim of this lesson is to teach students how to determine the surface area and volume of right prisms using a variety of mathematical tools and through investigation. Students will carry out investigations using concrete materials and use the angles between the faces of prisms to identify right prisms. This lesson will also help the student solve a variety of problems that require conversions between measuring units of area, such as square meters and square centimeters. They will also be in a position to solve problems that involve volume and surface area of right prisms which may require conversions between the metric measures of volume and capacity. In the end, students will also be in a position to explain the relationship that exists between the measurement of area and exponential notation CITATION Mah15 l 1033 (Sharma & Stanton, 2015).
During the three lessons, students will develop and also apply the standard formula for finding the volume of right prisms using area of base and height. They will also investigate the volume of different cylinders and right prisms. Eventually, they will make conversions between the metric units of capacity and volume, and sketch the different prisms that have equal volumes. The students will also determine the key characteristics of right prims, the surface area of right prisms and solve mathematical problems that involve the surface area of cylinders and right prisms CITATION EDU15 l 1033 (EDUGAINS, 2015).
The lesson will start with an introduction of measurement and an explanation of what right prisms are and the difference between right prisms and cylinders. Students will then get a chance to build models of prisms using cubes. After making the models, students will have a chance to discuss what they think about the models and the differences discussed in class between right prisms and cylinders. Students will also have a chance to ask questions regarding the lesson and any other thing that they might not understand regarding right prisms and cylinders CITATION Sur15 l 1033 (Surface Area of Right Prisms and Cylinders, 2015).
Students will then determine the volume of the right prisms by simply counting the number of cubes used to make the structure. This will then lead to the nest step of developing and applying the formula used to calculate the volume of a prism CITATION Vol15 l 1033 (Volume of Right Prisms and Cylinders, 2015).
Students will also explore the cubes to determine the number of cubic centimeters that would be needed to fill a cubic decimeter entirely. They will first start by determining the number of cubic centimeters that would be needed to cover the base and then the number of layers that would be needed to fill the entire decimeter CITATION Mar131 l 1033 (McAteer, 2013).
Next, students will also determine the number of cubic decimeters that would be required to fill a cubic meter. This knowledge will help in determining the number of cubic centimeters that would be required to fill one cubic meter. Students will also solve the problems that require the conversion of metric units of volume (Tyminski, Weilbacher, Lenburg, & Brown, 2008).
The main aim of this lesson will be to determine the characteristics of rectangular prisms and cylinders and solve mathematical problems involving the surface area of cylinders and rectangular prisms. Students will start by developing and applying the formula used to calculate the surface area of rectangular prisms CITATION Boo14 l 1033 (Booker, Bond, Sparrow, & Swan, 2014). Students will also investigate the relationship that exists between the number of edges, faces, and vertices of different forms of rectangular prisms. Students will also do the same for triangular prisms, and learn how to solve problems requiring the conversion of metric units of area.
Next, students will investigate the historical study and definition of polyhedral. They will construct five platonic solids and develop the formula for calculating the surface area of cylinders using concrete materials. They will also determine the surface area of right prisms that have parallelogram bases and use concrete materials to build the same CITATION Jor11 l 1033 (Jorgensen & Dole, 2011).
In this lesson, students will take the time to sharpen the skills learned in the first two lessons. They will start by building prisms with bases made of composite figures including circles and calculate the surface area of the same. The students will then solve mathematical problems requiring the conversion of the metric units of area. Students will then apply knowledge and their understanding of surface area thus far in calculating mathematical problems of the surface area of prisms that have polygon bases.
Students will work in pairs to create one right prism out of nets or polydron materials. In the end, students will have to make at least one cube triangular prism, pentagonal prism, and rectangular prism. Octagonal prism, parallelogram-based prism, trapezoidal-based prism and a hexagonal prism. After constructing the models, students will then investigate the edges, faces and angles of the models and fill in their investigations in a chart. Students will exchange the different models and do the same for each shape. Students will then work together to analyze the information they have gathered in their charts and make not of all the patterns that appeared in the charts. In their notebooks, students will make a list of all the characteristics of the right prisms that they noted in their observations. They will then determine any relationships between the different shapes.
Students will then present their findings, and the teacher will check that they have completed the charts accurately. Emphasis should be stresses on the characteristics of right prisms, and the faces or rectangular faces keeping in mind the fact that the base is always 90 degrees and that the number of faces on the base of the prism is equal to the number of the total lateral faces of the right prism. Students should also note that the angles at the vertices of the base of the polygon are also similar to the angles found between the lateral faces of the polygon CITATION Low14 l 1033 (Low & Wood, 2014).
The teacher will give the students assignments and tasks to complete the lessons, and these will be assessed through discussions and observations. Students will work in pairs to create models of different polygons or shapes and take down the characteristics of the models in charts. Students will then study these characteristics of the different shapes with the help of their teacher CITATION Sur15 l 1033 (Surface Area of Right Prisms and Cylinders, 2015).
The teacher will also ask the entire class to collect familiar items with right prisms that they can find in their homes. Students will then describe these solids using the mathematical vocabulary learned thus far. They will hold up the right prisms and count the number of edges, faces and vertices orally. Students will then describe the contents of their charts orally to the rest of the class, and explain the characteristics they noted of the shapes using the mathematical vocabulary learned in class.
The teacher will keep on observing the same skills that students have gathered in class during other activities in the unit. This will also allow the teacher to focus on a small number of students in the class every day to ascertain their understanding of the content CITATION Umb03 l 1033 (Zagami, 2003).
The teacher will go through the students’ charts and check that the characteristics of the shapes that they listed are accurate. Students will also be given take-away assignments to do at home and to be marked at an agreed date by the teacher. This will also enable the teacher to gauge the students’ understanding of the lesson (Muir, 2007).
Aims of the report
Development of formula for the calculation of the surface area of right prisms. Solving mathematical problems that involve the surface area of right prisms and cylinders, and require the conversion of metric measures of the area (Tyminski, Weilbacher, Lenburg, & Brown, 2008).
Development of formula for the calculation of the volume of rectangular prisms. Solving of problems that involve the volume of rectangular prisms and conversion of metric measures of capacity and volume.
Investigation and application of the formula of the surface area and volume of right and rectangular prisms, as well as, cylinders. Solving problems that involve the volume of triangular prisms and conversion of the metric measures of area, capacity and volume CITATION Vol15 l 1033 (Volume of Right Prisms and Cylinders, 2015).
Calculation of the volume of parallelogram-based prisms, and the investigation of the volume of cylinders through comparisons with a capacity of the cylinders to volume CITATION Car13 l 1033 (Rickard, 2013).
At the end of the three lessons, students were able to determine the volume and surface area of right prisms and cylinders. Students were also able to determine the volume and surface area of trapezoidal-based prisms by decomposing the prism into two separate prisms; one triangular and the other rectangular. Students were also able to determine the volume of right prisms that had bases made up of different figures. Students also applied the formulas they had learned in class to determine the relationships that exist between cylinders and triangular prisms and the surface areas of the same. Students were also able to apply the area formulas and volume in exploring the relationships between cylinders and rectangular prisms with the same volume.
In the future lessons, students should work together in larger groups of between three to five members in order to share more ideas and gain more understanding than they did working in pairs. In addition, students will also have to prepare early enough by making or looking for models and shapes before the lessons begin to avoid wasting too much time creating the models. This will ensure that students understand what they are doing and what is expected of them in class as they will have enough time to experiment and gain a deep understanding of the shapes and their characteristics.
BIBLIOGRAPHY l 1033 Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching Primary Mathematics. New York: Pearson Higher Education.
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Jorgensen, R., & Dole, S. (2011). Teaching Mathematics in Primary Schools. New Jersey: Allen & Unwin.
Low, E., & Wood, M. (2014). Cambridge Primary Mathematics Stage 5 Teacher’s Resource with CD-ROM. Cambridge: Cambridge University Press.
McAteer, M. (2013). Improving Primary Mathematics Teaching And Learning. New York: McGraw-Hill Education.
Muir, T. (2007). Developing an understanding of the concept of area. Australian Primary Mathematics Classroom, 12(4), pp. 4-9.
Rickard, C. (2013). Essential Primary Mathematics. New York: McGraw-Hill Education.
Sharma, M. C., & Stanton, B. (2015, June 10). Math Curriculum Planning, Implementation & Support. Retrieved from Lamoille Area Professional Development Academy: http://lapdavt.org/services/math-curriculum-planning/
Surface Area of Right Prisms and Cylinders. (2015, June 10). Retrieved from TIPS: Combined Grade 7 and 8: http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade7and8/UnitB_SurfaceArea.pdf
Tyminski, A.M., Weilbacher, M., Lenburg, N., & Brown, C. (2008). Ladybug lengths: Beginning measurement. Teaching Children Mathematics, 15(1), 34-37.
The volume of Right Prisms and Cylinders. (2015, June 10). Retrieved from TIPS; Combined Grades 7 and 8: http://www.edugains.ca/resources/LearningMaterials/TIPS/tips4rm/grade7and8/UnitC_Volume.pdf
Zagami, U. S. (2003). Exploring Primary Mathematics: Metric Measurements, Stage 7. Pupils Workbook. Sidney: William Brooks & Company.
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