Activities
Before starting the unit, I will give pre-assessments to my students. This will allow me to measure comprehension as well as how to identify and address the misconceptions and weaknesses of my students. By utilizing pre-assessments I will have the opportunity to determine my students’ level of understanding of measurement. At the unit’s completion I will use post-assessments to determine the growth of student learning. Both assessments will be similar in the use of questions, material, and prompts from the entire unit. Students will be asked to respond in written form, using a sequential method of description. On a daily basis, I will use a variety of brief activities to gauge understanding and growth. At the beginning of each day, I will have students reflect and write a brief journal entry on previous lessons. At the end of the class, I will administer a short exit ticket. My students will answer an explicit prompt, so I can check for understanding. Throughout the unit on measurement, I will include time for student engagement in the practices described in the Common Core State Standards. Students will make approximate measurements, then form calculations. Next, students will use tools appropriately, i.e., how to read and use a ruler correctly. Finally, students will attend to precision in using and understanding measurement.
I will show how the following activities are related to each other with the goal of understanding measurement. An interesting feature is that these activities will be inter-mingled with the goals so that the actual participation will help promote a clearer understanding of our set of goals. Students will start the unit on determining the area of various shapes. Students will use Thinking Maps including Circle Maps and Multi-Flow maps to organize and define key vocabulary words used in the unit. Students will draw the shapes of rectangular arrays on chart paper. Students will then write key facts and details of measurement on the side of the drawing.
I will begin by developing the definition of area on a poster/anchor chart: the number of unit areas that it takes to fill a space. I will make sure that students also understand that a unit area need not be a square. For example, a right triangle with legs of length 1 and 2 is half of a 1 by 2 rectangle, so it has an area 1. But no unit square will fit inside it. Then, I will announce that in this unit, we will only study figures that can be decomposed into unit squares. I will demonstrate to my students the formula for an area of a rectangle: A (area) = (l ∙ w). For my students to understand the composition and decomposition of rectangular arrays, I will develop this idea by having my students use grid paper to create different arrays using colored foam unit squares.
Students will also understand that arrays with specified area can have different combinations of length and width. For example, an activity would be for students to rearrange sixteen chairs five different ways (see figure 11). These different shapes all have the same area, but have different perimeters. I will give my students a number (18, 36, 200), and challenge them to find all the rectangles with whole number side lengths and the given area, and to find the perimeter of each.
Figure 11: Arrays with the same product
I will explain to my students that the surface area of 3D objects is measured in square units and is the sum of the usual plane areas of all the 3D object’s surfaces. I will demonstrate this by asking students what the surface area be of the shape they have drawn. Students will draw rectangular arrays on grid paper which can be formed into nets for cubes. I will explain to my students that now that they’ve mastered measuring the surface area of 3D shapes, they can move on to measuring volume, which is the amount of space inside a 3D shape, measured in cubic units. I can refer to the poster which provides essential formulas.
Towards the conclusion of the unit, I will work with my students in determining the surface area and volume of prisms and boxes that represent original structures of buildings by using formulas for surface area and volume (figure 12).
Figure 12: The formula for the surface area:
SA= 2LW+2LH+2WH
The formula for volume:
V= L∙W∙H
My students will create different types of boxes/prisms: long, large short and tall. To challenge my students, we conclude the unit in complexity and rigor with the activities. Using cardboard in the form of nets folded into long rectangular prisms, I will develop my student’s understanding of area, surface area and volume. My students will begin with building a replica model of the Aon Center in downtown Chicago. Using cardboard and sectioned into nets, students will fold the nets into a long rectangular prism, (see figure 13). The Aon Center has the shape of a long rectangular prism. Next, I will have students work with a variety of different prisms in height to build a replica of the Willis Tower. These prisms will be by organized side by side of each other to form the model of the building.
The students will use their understanding of area, surface area and volume to measure rectangular arrays into nets which will then be folded into a series of rectangular prisms. They will then be tasked to build their own original structure/building from rectangular prisms. The students will research number of floors, surface area and volume of both buildings. I will have students use formulas to determine this data. By using area and volume, I will have my students apply understanding of rectangular arrays, surface area, nets and rectangular prisms to real life applications in the form of the building we have in our city of Chicago.
Figure 13: Understanding a basic rectangular prism and comparing the prism with similar real world applications such as the Aon Center in Chicago
The summative task is to design a building for an architectural company. Students will understand that architects and engineers take into consideration the amount of limited resources needed to compose original structures. The volume amount of the rectangular prisms will be given as a condition, and the students will come up with an original design of a building. Students will determine the surface area of their original design and be responsible for drawing a net of their rectangular prisms. Students will conduct a presentation to the class showing their structures and explain the details of area, surface area and volume.
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