UTeach Dallas 5E Lesson Plan Template
Surface Area and Volume: A Lesson in Wrapping Presents
Author: Ryan Monaghan Team Members: Emily Wagoner Date and Time of Lesson: April 14, 2010 8:30 AM Grade Level: 8th grade Math, Pre-Algebra, non-honors Lesson Source: Texas Essential Knowledge and Skills (Process and Concept TEKS):
(8.8) Measurement. The student uses procedures to determine measures of threedimensional figures. The student is expected to: (B) connect models of prisms, cylinders, pyramids, spheres and cones to formulas for volume of these objects (C) estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. (8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to: (B) describe the resulting effect on volume when dimensions of a solid are changed proportionally. (8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve everyday experiences, investigation in other disciplines, and activities in and outside of school. The student is expect to: (A) Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines , and with other mathematical topics; (B) Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluation the solution for reasonableness; (C) Select or develop an appropriate problem solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acing it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) Select tools such as real objects, manipulative, paper/pencil, and technology or techniques such as mental math estimation, and number sense to solve problems.
2010 The University of Texas at Dallas
UTeach Dallas 5E Lesson Plan Template Concepts Statement: The volume is the measure of the space occupied by a solid. Standard measures of volume are cubic units such as cubic inches (in 3) or cubic feet (ft3). The standard equations for volume is Base multiplied by height (B*h)=V or V=l*w*h. The surface area is the measurement of the area of all the sides of a 3 dimensional object. Standard measures of surface are units squared such as inches squared (in2) or feet squared (ft2). There are different formulas for surface area based on the figure but the standard way is to find the area of each face and then add them up to find the total surface area. There are two types of surface area, lateral and total. Lateral surface area is the area of all the faces except for the bases. Total surface area is the area of all the faces and the bases.
Objectives: Students will be able to: Measure the lengths of the sides of 3-dimensional figures to the nearest millimeter Calculate the volume of a rectangular prism and cylinder Calculate the surface area of a rectangular prism and cylinder. Choose the correct equations for the surface area and volume of different 3-dimensional shapes. Discriminate between lateral and total surface area, and when to use the appropriate one
Appropriateness of Lesson to the Grade Level: Students will be asked to calculate the total surface area of a rectangular prism so that they know how much wrapping paper is needed to completely cover it. They will also be asked to find the volume of the box to make sure it is large enough to hold the present. To further students knowledge they will be working in groups and using hands on experiences. Afterward the students connect volume and surface area to real life examples, such as painting a house or packing for a trip. Materials List:
9 empty boxes (one for each group) 26 rulers (one for each student) 26 copies of the pre-assessment (one for each student) 26 copies of the post-assessment (one for each student) 26 copies of the worksheet (one for each student) 1 role of wrapping paper
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UTeach Dallas 5E Lesson Plan Template
Tape 1 empty glass jar 2 bags of jolly ranchers 26 calculators (one for each student)
Advanced Preparations:
The night before teaching the lesson, fill the empty glass jar with jolly ranchers, making sure there is enough for each student to have one, neatly wrap the jar in wrapping paper. Measure the radius and height of the jar and write it down. Pre cut the wrapping paper for each group making sure there is enough for the group to cover the box. Before class, starts pass out the pre-assessment, one on every desk. Place the name tents.
Safety:
Students should not ingest any materials other than the jolly ranchers at the end of class. Students should not throw or hit others with any materials. ENGAGEMENT What the Teacher Will Do Students will have a preassessment on their desks when they walk into class. At the beginning of class, the teacher will give the students 5 minutes to complete the What Do I Already Know? At the end of the 5 minutes, the teacher will pick up the preassessment. Then lead the class, by asking questions, in answering the problems in the What Do I Already Know? Ask students, Do you think it is possible for two shapes to have the same surface area, yet be different geometric figures? Why is that? Take a few answers from the class. Ask students, What about volume, is it possible for two shapes to have the same volume, but be different geometric figures? Why is Probing/Eliciting Questions Time: ___10___ Minutes Student Responses and Misconceptions
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UTeach Dallas 5E Lesson Plan Template
that? Take a few answers. Ask students, Could two shapes have the same surface area and the same volume, but be different geometric figures? Think about these questions throughout todays lesson, we will come back to them at the end. EXPLORATION What the Teacher Will Do Say, Please raise your hand if you have ever had to wrap a present for a birthday or holiday? What types of shapes do you often wrap when you are wrapping presents? Great, how many of you have run out of wrapping paper midway through wrapping presents? Yea me too, what do you think we could use to make sure we dont run out? Thats correct, we use surface area. What are the two types of surface area? What is the difference between them? Which one would you use to find out how much wrapping paper you need? Probing/Eliciting Questions Time: ___20___ Minutes Student Responses and Misconceptions
What 3-D figures do you wrap when you are wrapping presents? What measurement do we use when wrapping presents?
[an assortment of 3figures (ie. Cubes cylinders and other odd shapes)] [Surface Area]
What are the two types of surface area? What is the difference between lateral and total surface area? What type of surface area do you use to find the surface area of a present you need to wrap?
[lateral and total] [total surface area is all the sides, while lateral is area of all the sides except the base] [total]
Ask, What is another problem What measurement do we you could run into while looking use to find how much a for a box for a present? Right the box can hold? box could be too big or too small what measurement could we take to ensure that our box was just the right size?
[volume]
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UTeach Dallas 5E Lesson Plan Template
Teacher will pull out the demo box. Say, Ok so now that we know what math is used in wrapping our presents. Who can walk me through the steps in finding the volume of this box? What units should we use? Say, What does this measurement tell me about my box? Say, Ok now that we know our box is big enough we can put our present in it. What is next? Thats right, now we need to wrap it. What measurement should we use to figure out exactly how much wrapping paper we used? Say, Who would like to walk me through how to find the surface area of this box? How do you find volume? [measure the sides of the base of the box, find the area of the base, measure the height of the box. Multiply the area by the height] [units3] [how much it can hold]
What units is volume in? What does volume tell me about my box?
What measurement should we use to find out how much wrapping paper we need?
[surface area]
How do you find surface area?
[measure each side of a base, calculate the area of that base, do the same for each base. Add up all the areas of the bases.]
Pass out a box, ruler, some wrapping paper, and the assignment sheet to each group. Say, Ok now that you all have walked me through finding the volume and surface area of my present. Now I want you to do the same. So I will pass out to each group a box, a ruler, and some wrapping paper. Please calculate the volume and surface area of the box and write them down on your Assignment sheet. Be sure to show all of your work and remember drawing diagrams of your box would be useful. You guys will have 7 minutes to find both the surface area and the volume, be sure to
Dimensions of the box [16cm X 11.5cm X 5.8cm] Volume = 1067.2cm3 Surface Area = 687in2
Dimensions of present. [8.5in X 6.5in X 7.5in] Volume = 414.375 in3
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UTeach Dallas 5E Lesson Plan Template
share the work load, and show all of your work on the worksheet, you may use the back for this. Once the 7 minutes are over I will tell you the dimensions of Mrs. Congers Present and you guys will find the will do the same thing for her present. EXPLAINATION What the Teacher Will Do Now that each of you has had time to find the surface area and volume of your box. I will now call on each of your groups to help me explain how you guys did found it, and what troubles you had. Ask each group to explain to you how they found either the surface area or volume. Ask, So now that each of you has some hands on experience finding surface area and volume. Do you think it is possible to for two shapes to have the same surface area but different volumes? And what about different surfaces area and the same volume? Please take a minute to think about this and come up with an example to show the class. Say, Please raise your hand if you think the answer to my question is yes. Pick one student to come up to the projector to show their work. Now raise Is it possible for two shapes to have the same surface area but have different volumes? Can anyone give me an example of two shapes with the same surface area but different volumes? Is it possible for two shapes to have the same volume and different surface areas? How can this be true? [yes] [a cube 4X4X4 has SA 96in2 and V 64in3 but rectangular prism 4X2X(20/3) has SA 96in2 and V 160/3in3 approx(53.33)] Probing/Eliciting Questions Surface area = 335.5 in2
Time:
Minutes
Student Responses And Misconceptions
[yes] [Different geometric figures can have similar volumes but have different surface areas]
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UTeach Dallas 5E Lesson Plan Template
your hand if you think the answer is no. Pick another student to show his or her reasons. Say, So most of you are probably wondering why I am standing up talking about presents when the closest holiday is Easter, well to tell you the truth today is actually (with Mrs. Congers permission announce her birthday instead of mine) my birthday. And in my family, we have a very strange custom. On your birthday, you give a gift to your family as a way of saying thank you for all the things you have given me. So my gift to you guys is this Show them a rapped cylinder Now beings this is math class and nothing in this world is free I am going to give you the radius and height and now I want you guys to tell me the surface area and volume. Call on a student for their answer and ask them how they got it. Let that student unwrap the gift (a jar of jolly ranchers). Say, At the end of class I will let each of you randomly pick a jolly rancher as you walk out of the class.
ELABORATION What the Teacher Will Do
Probing/Eliciting
Time: ___5___ Minutes Student Responses
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UTeach Dallas 5E Lesson Plan Template
Say, Now besides presents who can give me some more examples of how we use surface area and volume in our everyday lives? Say, We use volume when packing for a trip. I need to make sure that my suite case is big enough to hold all of my clothes for my vacation. So in my head I quickly guess about how much volume my suite case has and how many clothes I need to pack. Say, So every summer I go and volunteer for my church and we go and paint houses for people. And every year we always run out of paint of the way. What measurement should we take to make sure that doesnt happen again? Say, So for my birthday last year my parents got me a fish, and a fish tank, and we needed to treat water for the new fish. But we didnt know how much water to treat. How would you guys figure out how much water we needed to treat? Walk me through your process. Questions How do we use surface area and volume? and Misconceptions [to many to count]
What measurement should we use to make sure we dont run out of paint?
[surface area]
What measurement do you use? How do you find it?
[volume] [find the lengths of the sides of the base, multiply them to get the volume of the base, multiply that by the height]
EVALUATION What the Teacher Will Do Say, Ok so now that you guys have had a refresher course in volume and surface area lets see how much you guys have learned. Pass out What I have Learned Say, You have 5 minutes to complete this assignment then we will pick it up.
Probing/Eliciting Questions
Time: ___5___ Minutes Student Responses and Misconceptions
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