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Unit Plan DescriptionOur mission for this 7th grade geometry unit is to give students not only knowledge and understanding of area concepts, but how formulas for area are developed as students learn how to apply concepts of area and volume to complex 3-dimensional figures and real-life situations. Students will then translate their understanding of area in 2-dimensional figures to decompose 3-dimensional figures and use nets to understand how to apply concepts of surface area and volume to 3-dimensional figures. Students will use the decomposition of 3-dimensional figures to understand and develop formulas for surface area and volume of 3-dimensional figures. Students will then use their understanding of area and volume concepts to find solutions to multi-step real-life problems involving area, surface area, and volume. Although the students studied area in relation to complex and irregular 2–dimensional shapes in a previous unit, there is vertical articulation between units as the students study the standard in more depth related to surface area in real life applications. This unit plan covers several of the Indiana State 7th grade geometry standards which will be used to address these concepts over the course of this unit.Indiana State Standards covered in unit: MA.7.4.4 2000 Construct two-dimensional patterns (nets) for three-dimensional patterns objects, such as right prisms, pyramids, cylinders, and cones. New 2014 Standard: 7.GM.7:MA.7.5.4 2000: Use formulas for finding the perimeter and area of basic two-dimensional shapes and the surface area and volume of basic three-dimensional shapes, including rectangles, parallelograms, trapezoids, triangles, circles, right prisms, and cylinders. New 2014 Standard: 7.GM.5, 7.GM.6MA.7.5.5 2000: Estimate and compute the area of more complex or irregular two-dimensional shapes by breaking them down into more basic shapes. New 2014 Standard: no correlating standardMA.7.5.6 2000: Use objects and geometry modeling tools to compute the surface area of the faces and the volume of a three-dimensional object built from rectangular solids. New 2014 Standard: 7.GM.6Students in 7th grade have already studied simple algebraic equations and how to develop equations from simple word problems. Students have also developed an understanding of the concept of perimeter and area in relation to simple 2-dimensional figures (i.e. rectangles, triangles, circles). Students have learned how the transformation and slides of 2-dimensional shapes can be used to evaluate 2-dimensional figures and create formulas for the areas of more complex 2-dimensional shapes. Students have also studied scale drawings and know how to solve problems in relation to these drawings. Prerequisite skills needed for unit:Write a formula using variables and appropriate operations from a story problem.Solve and check two-step equations in one variable.Solve an equation or formula with two variables for a particular variable.Use formulas to find perimeter of basic two-dimensional figures.Calculate areas related to the shapesDivide complex or irregular two-dimensional figures into basic figures.Estimate the area of complex or irregular two-dimensional pute the area of complex or irregular two-dimensional figures.Understand and compute problems based on a scale drawingPrerequisite Indiana state standards:MA.7.3.1 2000: Use variables and appropriate operations to write an expression, a formula, an equation, or an inequality that represents a verbal description. New 2014 standard: 7.AF.3.MA 7.3.2 Write and solve two-step linear equations and inequalities in one variable and check the answers. New 2014 Standard: 7.AF.3.MA.7.5.4.1 2000: Use formulas for finding the perimeter and area of basic two-dimensional shapes. New 2014 Standard: 7.GM.5, 7.GM.6.MA.7.5.5 2000: Estimate and compute the area of more complex or irregular two-dimensional shapes by breaking them down into more basic shapes. New 2014 Standard: no correlating standard.This Unit plan will be taught in the month of November toward the end of the semester and before the Christmas Holidays. This unit will last approximately four weeks. There will be several assessments that take place over the course of the unit including pre-assessments, homework assignments, in-class projects, formative assessments, and a summative assessment at the end of the unit. Although this unit is aimed at the average student, it can easily be modified for a low or high ability student. Goals:It is particularly beneficial for students to be able to apply volume and surface area concepts in real life situations. A practical understanding of geometry concepts such as area, surface area, and volume can help students to be independent in their adult life. Upon completing this unit students will understand that many people apply the concepts of area and volume in their lives and jobs. Although students will understand and will be able to apply the concepts of area and volume at the end of this unit, the main goal of this unit is to give students an understanding of how measurement, area, and volume can apply in real-life situations from figuring out how much flooring will be needed and how much the flooring will cost to install new flooring in a room, to how much paint will be needed and how much the paint will cost to paint that same room. These examples are just a few examples of why an understanding of the concepts of measurement, area, and volume are important concepts that everyone should know and understand how to analyze various situations and apply these concepts in their everyday lives.The main goal of this unit: Students will be able to use their understanding of measurement, area, surface area, and volume to apply higher-order-thinking skills to analyze various situations and apply these concepts in real-life situations. Instructional Outcomes and Examples of Instructional outcomes: Construct two-dimensional patterns (nets) for three-dimensional objects. (right prisms, pyramids, cylinders, cones)Identify the three-dimensional object given its two-dimensional pattern (net). Example: Draw a rectangle and two circles that will fit together to make a cylinder.Use formulas to find surface area of basic three-dimensional figures.Use formulas to find volume of basic three-dimensional figures.Example: Find the surface area and volume of a cylindrical can 15 cm high and with a diameter of 8 cm.Use objects and geometry modeling tools to compute surface area of the faces of a three-dimensional object built from rectangular solids.Use objects and geometry modeling tools to compute volume of the faces of a three-dimensional object built from rectangular solids.Example: Build a model of an apartment building with blocks. Find its volume and total surface area.Calculate areas, surface areas, and volume related to specific shapesThree-Part Assessment PlanAssessment is a part of life. We are all assessed in some way or another every day. It is important to teach young students to do their best in whatever they do because doing one’s best is actually a way they can assess themselves. Teaching students to not only work hard but to have high expectations of the work they accomplish will help them be successful because they will have a positive attitude toward being assessed by others and the skill required to self-assess. Assessment is a necessary part of teaching. As a future math teacher, I will make assessments of some kind almost every day. Although creating assessments can be a tedious task, it is still an important part of teaching as assessments monitors students’ progress and ensures students’ success. Teachers need to assess students to make sure that students understand what they are being taught. These assessments will also help me modify my instruction and speed up, slow down, or differentiate instruction based on the students’ needs. Assessments will help me monitor my students’ progress and to ensure that they all have a chance to learn and be successful.Pre-assessment:It is important for an instructor to pre-assess students’ knowledge prior to instruction. Pre-assessments are assessments that are used to determine whether or not a student is ready to learn a specific topic CITATION She11 \l 1033 (Shermis & Di Vesta, 2011). A valid pre-assessment gives the teacher an understanding on how much a student knows about a specific topic and how much review the teacher will need to do before the introducing new material CITATION She11 \l 1033 (Shermis & Di Vesta, 2011). Pre-assessment: The students will be given a chart with the drawing of various 2-dimensional and 3-dimensional shapes. This is a chart I designed that would allow students to fill in what they know and add more information as they go along.? It would be placed in their math reference guide that they will create over the course of the year and fill with important mathematical formulas as well as mathematical vocabulary and definitions. Students will be asked to come up with as many formulas as they can remember for area, surface area, and volume of the various shapes. The purpose of this pre-assessment is to determine what the students already know about the prerequisite material, what the student is ready to learn , as well as what they may already know about the concept being taught (i.e. volume and surface area of 3-dimensional shapes). Desired Outcome:The goal of the pre-assessment is to determine if students know the prerequisite skills and are ready to learn about volume. The desired outcome of this pre-assessment is that the students at least know the formulas for the perimeter and area of the 2-dimensional shapes. Although they have seen 3-dimensional shapes, it is not necessary for them to remember the formulas for volume and surface area of shapes as that is part of the 7th Grade Indiana Standards this unit aims to cover.7th Grade Geometry Pre-Assessment Formula Guide Name:___________________Geometric ShapeFormulas if Applicable ShapeDrawingPerimeter /CircumferenceAreaSurface AreaVolumeCircleTriangleSquareRectangleParallelogramTrapezoidSphereCubeRectangular PrismCylinderConeTriangular Prism 7th Grade Geometry Pre-Assessment Formula Guide Answer SheetGeometric ShapeFormulas if Applicable ShapeDrawingPerimeter /CircumferenceAreaSurface AreaVolumeCircleP=2πrA=πr2TriangleP= a+b+c A= 12 b hSquareP=4aA=a2RectangleP= 2(a+b)A= abParallelogramP= 2(a+b)A= bhTrapezoidP=a1+a2+a3+a4A=a1+a22SphereSA=4πr2V=43πr3CubeSA=6s2 V=s3Rectangular PrismSA=2LW+2HW+2LHV=LWHCylinderSA=2πr2+(2πrH)V=πr2HConeSA=(πrs)+(πr2)V=13πr2HTriangular PrismSA = Sum of the areas of the facesV= Area of the base times the heightFormative Assessment:Formative assessments occur before and during instructionCITATION Woo10 \l 1033 (Woolfolk, 2010). The main purpose of formative assessment is to inform the instructor on whether or not the students understand what is currently being taught CITATION She11 \l 1033 (Shermis & Di Vesta, 2011). Formative assessments also help teachers improve and plan their instruction and to improve a students’ ability to learnCITATION Woo10 \l 1033 (Woolfolk, 2010). One type of formative assessment is called performance assessment. Watching students as they work and inspecting the finished product is a way for an instructor to assess students as they complete their work CITATION Wau08 \l 1033 (Waugh & Gronlund, 2008). This type of assessment is instantaneous and feedback can be given just as quickly. As an instructor, I believe the most important type of assessment occurs during instruction. Constantly monitoring students’ progress while teaching allows the teacher to modify and differentiate instruction so that all students can grasp what is being taught.Formative Assessment #1, Whiteboards:During each lesson of the unit, a teacher can instantly assess students for understanding through the use of whiteboards. As the teacher finishes the lesson and starts on a set of guided practice examples, the students can answer example problems on their whiteboard and hold the board up when they are finished so that the teacher can check their understanding. This instant assessment and feedback will allow for immediate modification or clarification of the days lesson before students start independent practice.For this assessment, the teacher will post a series of 2-dimensional patterns (nets) for three-dimensional patterns objects, such as right prisms, pyramids, cylinders, and cones on the overhead projector. The students will use their whiteboards to write the name of the shape (i.e.: right prisms, pyramids, cylinders, and cones) that they believe the 2-dimensional pattern represents and hold it up for the teacher to see. This assessment will give the teacher immediate information about whether or not students can use higher-order-thinking skills to evaluate 2-D composite shapes and understand how they can be used to create a 3-dimensional object. This assessment gives the teacher specific feedback concerning students’ understanding of how 3-D object can be broken down into a 2-dimensional patterns or nets. Here are some examples the teacher may place on the overhead: Desired Outcome of Assessment#1, Whiteboards:It is important that students can represent a 3-dimensional shape in 2-dimensions and vis-a-versa. This skill may seem juvenile, but it requires students to evaluate 2-dimensional composite shapes and determine which 3-D object the net creates. It is essential when calculating surface area of prisms, cylinders, and cones that students understand the 2-dimensional shapes that make up a 3-D object. The main goal of this assessment is to determine if students recognize that the above 2-D composite shapes are really a net of 3-D shapes. These are the desired answers wanted on the students’ whiteboards. Square Pyramid Cylinder Triangular Prism Rectangular Prism ConeFormative Assessment #2, Transfer and Apply:The following formative assessment will be given to students in the form of a take-home-quiz. Students will be asked to create a table containing four rows and three columns. The first row will contain headings: the heading over the first column will say the 3-D shape and name, the second and third column headings will each contain a concept of student’s choice relating to 3-D shapes. The first column will contain the 3-D shape and its name, the second column and third column will require the students to give an example of the application of the concept of they have picked for that specific shape. It is important that students not only know and understand a concept, but that they can also apply a mathematical concept.Desired Outcome of Assessment#2 Transfer and Apply:This is a possible table that could be turned in by the student. A completed table like this shows that a student can apply the concepts of Surface area and Volume to 3-D shapes.Transfer and Apply Formative AssessmentName:________________________3-D Shape and name of your choiceExample of Application of Surface AreaExample of Application of Volume-215903365500Rectangular PrismSA=2LW+2HW+2LHH=2 inW=3 inL=5 inSA=2*5*3+2*2*3+2*5*2= 62 in2V=LWH H=2 inW=3 inL=5 inV=LWH =2*3*5= 30 in306794500CylinderSA=2πr2+(2πrH)r = 4 cmH = 6 cmSA=2π*42+2π*4*6= 80π cm2V=πr2Hr = 4 cmH = 6 cmV=π*42*6=96π cm3889012192000SphereSA=4πr2r = 2 ftSA=4π*22= 16π ft2V=43πr3r = 2V=43π*23=323π ft3Formative Assessment # 3, Basic Six-Task Grid:Students will be divided into groups of 3 or 4 based on their ability and asked to pick a task from the following Basic Six-Task Grid, and share with the class their completed project. Dividing the students based on ability gives the teacher an opportunity for everyone to have an active role in the project and allows all students to be challenged equally while maximizing their Bloom’s taxonomy potential. VerbFact/Concept/IdeaProduct(Knowledge)DescribeMeasurementsWrite an email describing how measurements are used to find the volume of a container.Can two containers with different measurements have the same volume? When looking at a numerical value that includes a unit of measure, how do you know if that unit of measure implies volume? (What is a necessary component of the unit of measure for volume?)(Understand)ExplainSizeMake a pamphlet that explains how the size of an object affects the volume.Is there a direct or indirect relationship between size and volume? How does the size of the object affect other units of measure?(Apply)ImplementFormulaGive a demonstration in Geometer’s Sketchpad Software implementing the various formulas for volume.How do you find the volume of a composite shape (i.e. one that contains two shapes combined into one)?What concepts do you need to understand when writing a formula for an irregular shape?(Analyzing)CompareShapeStudent will give a sales pitch comparing the different shapes of reusable containers (i.e. Tupperware, Rubbermaid, Glad ware, etc.) to their relative volume and recommend the brand of containers that when filled and stacked in the refrigerator maximize the total internal volume of the containers while minimizing the total volume taken from the refrigerator. If you were actually recommending types storage containers as a job, what mathematical language would you use to explain to your customer the benefits of this particular storage container?Can you think of any shape of container or its contents that either contradicts your sales pitch?(Evaluating)Collaboration/hypothesisSurface AreaIn collaborative groups, form a hypothesis about the relationship between the volume and the surface area of an object. Use calculations to verify or refute your hypothesisHow does the surface area of an object affect its volume? Is it possible for two objects to have the same surface area but different volumes? Plan/ devise Definition of Volume?Plan a skit / comedy between two people one English speaking and one who is learning the English language, in which the ELL only understands the meaning of volume as a book in a series, or degree of loudness, but has no understanding that the word volume has a mathematical definition of space an object occupies in cubic units. The native English speaker must convey the mathematical definition and concept of volume.What simple key words did you use to help explain volume in its simplest form?What mathematical concepts does one need to know before they can understand the concept of volume?Desired Outcome Assessment # 3: Students will be graded on their projects using the following rubric:Math Project Rubric for Basic Six-Task-Grid: Students will complete one of projects from the basic six-task-grid covering the concept of volume.Student: _____________________ Grade: _______________________________ Volume: Six Task Grid ?Excellent20 pts Good15 pts Fair10 pts Poor5 pts Display Creative display with a variety of materials and high creativity. Display with materials and some creativity. Display with minimal materials and creativity. Bare display created. Math Idea Explained Idea labeled and fully explained, very easy to follow and understand.Students show higher-order-thinking in their explanations. Idea labeled and explained, but details are left out Only Idea labeled or explained, but not both. No Idea labeled or explained Math Operations Numbers and operations are clear, correct and logical. Numbers and operations are clear and most are correct with some order shown. Numbers and operations are attempted but out of order Numbers and operations are not clear or correct Presentation Project is easily read, math is correct as is spelling and organization. Student easily explains project without reading a script and answers questions easily. Most of project can be read, spelling is correct, numbers are correct, organization is mostly logical. Student can explain project, reads some of it but can answer questions easily. Some of the project could be read, spelling and organization are confusing, but all numbers are correct. Student stumbles over words and has problems explaining project. Could not read project, words not spelled correctly, numbers mixed up and project not organized. Student can't read or explain own project. In Class Work Effort Used all time effectively in class and completed work diligently. Used time effectively, but still social. Used time somewhat effectively, but was loud and off task. Did not use time effectively in class CITATION Rea14 \l 1033 (Reazon Systems, Inc., 2014)Formative Assessment # 4, group project applied real-life skills:In this assessment, students will be split into their groups and will be given a floor plan of a house, a Do-It-Yourself Store advertisement, a copy of a Paint label from a gallon of paint, and a table to fill out that will help them in their discovery process. Students will analyze the drawing as if they were a contractor paid to do a home improvement project for a client. Students will determine how much flooring, (carpet, tile, or hardwood), and how many gallons of paint it would require to completely floor and paint the inside of the house. The students will also be required to compare and contrast the cost of various types and cost of flooring according to the advertisement from the local do-it-yourself superstore. Finally, students will have to choose paint and flooring for each room of the house and create an estimate to give to the homeowner for the cost of materials to refurbish their home. To help students in their discovery, they will be given a list of instructions and questions to will guide them through their discovery and estimate process.Desired Outcome of Assessment #4, group project applied real-life skills:The point of this assessment is to help students think for themselves and figure out on their own that they should use the mathematical concept of area and surface area to solve real world problems such as estimation of construction projects. By asking the question, “How big is the house?” the teacher encourages students to make the connection between the “bigness” of the house to the sizes of the rooms that need carpet. Students will then think about buying carpet and how the carpet comes from the store. By asking carefully worded questions the teacher encourages the students to come up with the mathematical concepts needed to solve the problem on their own. Most students will know that carpet comes from the store in the form of a roll which when unrolled is a rectangle which means that it is measured in area not in linear feet. This will encourage students to use the mathematical concept of area when figuring out how much carpet the homeowner needs to buy. Should the students still seem a little confused, the teacher can ask about the “units” that apply to the bigness of the room which will encourage the students to realize the implication of square feet. By periodically stopping and asking the students for what they have discovered, the teacher steers them toward the goal of applying area to find out how much carpet is needed. The teacher can then use the same method to encourage students to figure out how much paint is needed by introducing one more dimension to the scale drawing: height. She then asks the students “How much paint do I need?” Students should be able to figure out on their own that walls are 3- dimensional and will then interpret the necessity of using surface area to find out how much surface area the walls have. By asking the students to read the paint label, the teacher encourages them to use a conversion process to change surface area into the volume of paint one needs to paint the house (i.e.: amount of gallons). This discovery learning process encourages students to the final goal of interpreting scale drawings into area and surface area and then converting to volume. The students then learn how to solve real-world problems by thinking of mathematical concepts and discovering how to apply them for themselves. Discovery learning is a method that allows students to come to the final goal by exploring ideas on their own and thinking through previous knowledge and interpreting what they know into what they need to learn. Finally, the students will have to create an estimate to give the imaginary homeowner that describes the total cost of the materials the homeowner wishes to purchase. This project requires a high degree of bloom’s taxonomy with its requirement of creative thinking, attention to detail, and evaluative processes students must use to complete the project. Students will be graded on their projects using the rubric attached at the end of the materials for the project. CITATION Exe14 \l 1033 (Exemplars, Inc., 2014)Instructions and Questions for students:Read all materials given to groupCome up with a written plan of what you need to do to solve the problem.Create a list of questions that need to be answered that will help solve the problem.What mathematical concept could apply to the question, “How ‘big’ is the house?”Give students Menards ad and ask them to compare and contrast the types of flooring that could be installed in each of the rooms, (i.e.: Tile, Hardwood, Carpet)Ask students, “How much will the flooring cost?” (The students will hopefully be able to translate the size of the room into the cost per square foot into the cost per room and total cost for the whole house.)If the standard height of all the ceilings in the house is 8 ft., how much paint do you need to paint the ceilings and the walls of all the rooms in the house? How can you convert what you know about the size of the walls to be painted be converted into the volume of paint needed to paint the walls?Ask students, “If I paint the entire inside of the house, how much will the paint cost?” Have students write in table the amount of money spent on each room for flooring and paint and the total for the whole house.Discovery Table: How Big Is the House?How Big?How much flooring?Walls + Ceiling?How much paint?Flooring Cost?Paint Cost?pantrykitchenutilitydining roomliving roombedroom 1bedroom 2bath 1master suitemaster bathtotal-10033035496500Paint Label:Floor Plan:723900000 Do-It-Yourself Store Advertisement: CITATION Men14 \l 1033 (Menards, 2014)Desired Outcome Assessment # 4: Students will be graded on their projects using the following rubric:Rubric for Math project: CITATION Exe14 \l 1033 (Exemplars, Inc., 2014)Formative assessment #5, Homework:Students will be given the following worksheets as homework so that they can practice the concepts they learned in class at home. Although the homework is not graded for correctness, the teacher will check for understanding and accurate use of mathematical formulas in order to know if the students need to be re-taught or if it is necessary to modify instruction. Desired Outcome assessment #5, Homework:The answer keys to the given homework are the desired outcome for the homework. Should students not show understanding; the teacher can re-teach concepts in a different manner.Name:__________________________________31178587566500998220480377500967740769937500436181577101700010591806130925004323715468630000975360317309500Topic: Surface Area and Volume of Solids and Cylinders - Worksheet 11050290683260004331335424180001a = 14 m b = 49kmb2aa = 6m b = 8m 3ba = 8 cmb = 15 cm a4b = 8kma = 28 km5a = 4 km b =21kmb6aa = 1.6m b = 1.2m 7a = 9cmbb = 12cm a8a = 7 kmb = 4.2 km9a = 4.2km b = 10 km10baa = 12 m b = 13 m 30924588201500Topic: Surface Area and Volume of Solids and Cylinders - Worksheet 1-321437037782500ANSWERS1Surface area =2 r2 + 2rh= 2 x22/7 x7x7 + 2x22/7x7x49=308 + 2156= 2464Volume= r2h= 22/7 x 7 x 7 x 49= 75462s2 = a2 + b2 s2 = 62 + 82s2 =36 + 64s = √100s = 10Surface area= rs+r2=22/7x6x10+22/7x6x6= 188.57 + 113.14= 301.71Volume = 1/3r2h= 1/3x22/7x6x6x8= 301.713s2 = a2 + b2 s2 = 82 + 152s2 = 64 + 225s = √289s = 17Surface area= rs+r2=22/7x8x17+22/7x 8x8= 427.43 + 201.143= 628.57Volume= 1/3r2h= 1/3x22/7x8x8x15= 1005.7129337001443355003703320140843000298259537064950037522153671570004Surface area=r2 + 2 rh= 2x22/7 x4x4 + 2x22/7x4x28=100.57 + 704= 804.57Volume= r2h= 22/7 x 4 x 4 x 28=14085Surface area=r2 + 2 rh=2x 22/7x2x2 + 2x22/7x4x21=25.14 + 528= 553.14Volume= r2h= 22/7 x 2 x 2 x 21= 2646s2 = a2 + b2s2 = 1.22 + 1.62s2 =1.44 + 2.56s = √4s = 2 Surface area= rs+ r2=22/7x1.2x2+22/7x1.2x1.2= 7.54 + 4.53= 12.06Volume= 1/3r2h= 1/3x22/7x1.2x1.2x1.6= 2.41350075535039300035007555119370007s2 = a2 + b2 s2 = 92 + 122s2 = 81 + 144s = √225s = 15Surface area=rs+r2=22/7x9x15+22/7x9x9= 424.29 + 254.57= 678.86Volume= 1/3r2h= 1/3x22/7x9x9x15= 1272.868Surface area=r2 + 2rh=2x 22/7x2.1x2.1 + 2x22/7x2.1x7=27.72 + 92.4= 120.12Volume= r2h= 22/7 x 2.1 x 2.1 x 7= 97.029Surface area=r2 + 2rh=2x 22/7x2.1x2.1 + 2x22/7x2.1x10=27.72 + 132= 159.72Volume= r2h= 22/7 x 2.1 x 2.1 x 10= 138.610s2 = a2 + b2s2 = 122 + 132s2 = 144 + 169s = √313s = 17.69Surface area=rs+r2=22/7x6x17.69+22/7x12x12= 333.58 + 452.57= 786.15Volume= 1/3r2h= 1/3x22/7x12x12x13= 1961.1410s2 = a2 + b2s2 = 122 + 132s2 = 144 + 169s = √313s = 17.69Surface area=rs+r2=22/7x6x17.69+22/7x12x12= 333.58 + 452.57= 786.15Volume= 1/3r2h= 1/3x22/7x12x12x13= 1961.14CITATION Jul1 \l 1033 (Leonard, 7th Grade Math Worksheets: Geometry, 2014)Name:____________________________________________________Find the volume and surface area.1350645728280014 in.Find the volume and surface area.12742481399190012 in.The volume of a sphere is 1200 ft3, what is the radius? What is the surface area?The circumference of a basketball is approximately 75 cm, how much leather does it take to make the basketball?An ice cream cone 6 inches tall, with a 2 inch radius is completely filled, including a perfect hemisphere sitting on top. How much ice cream is there?Answer Key:1. Find the volume and surface area.1332756952500014 in. V=43πr3=43π(14)3=11,494 in3 SA=4πr2=4π(14)2=2,463 in22. Find the volume and surface area.13691911936750012 in.V=43πr3=43π(6)3=904.8 in3 SA=4πr2=4π(6)2=452.4 in23. The volume of a sphere is 1200 ft3, what is the radius? What is the surface area?V=43πr3 ? r=33V4π = 6.5922 ftSA=4πr2= 4π(6.5922)2=546.1 ft24. The circumference of a basketball is approximately 75 cm, how much leather does it take to make the basketball?C=2πr? r=C2π=752π=11.94 cmSA=4πr2=4π(11.94)2=1790.49 cm25. An ice cream cone 6 inches tall, with a 2 inch radius is completely filled, including a perfect hemisphere sitting on top. How much ice cream is there? Answer: remember cone is filled and there is a perfect ? sphere on top. Volume of cone +Volume of ? a sphere. Vtotal=1243πr3=13πr2H=1243π23=13π226=41.89 in3 Name:______________________________________Volume and Surface Area of Rectangular Prisms (A)Instructions: Find the volume and surface area for each rectangular prism.1)2)1828800-63507.9 cm4.5007.9 cm4.5cm4.0 cm5029200327025002.2 mi8.0 mi5.0 mi3)4)1786255250155006.6 km2.0 km3.3 km4966970230505007.1yd 6.6 yd7.8 yd5)6)1828800151130001.8 mm1.9 m486727527368500in 6.8 in5.9 inVolume and Surface Area of Rectangular Prisms Answer KeyInstructions: Find the volume and surface area for each rectangular prism.Formula: Volume (V) = lwh, Surface Area (A) = 2(lw+wh+lh)18805581182427.9 cm4.5 cm007.9 cm4.5 cm1)2)4.0 cm5120640-888365002.2 mi8.0 mi5.0 miV = 7.9x4.5x4.0 = 142.2 cm3A = 2((7.9x4.5)+(4.5x4.0)+(7.9x4.0)) = 170.3 cm2V = 8.0x2.2x5.0 = 88.0 mi3A = 2((8.0x2.2)+(2.2x5.0)+(8.0x5.0)) = 137.2 mi21796415133985003) 6.6 km4) 2.0 km3.3 km5127625-98996500 7.1 yd6.6 yd7.8 ydV = 6.6x2.0x3.3 = 43.6 km3A = 2((6.6x2.0)+(2.0x3.3)+(6.6x3.3)) = 83.2 km2V = 7.1x6.6x7.8 = 365.5 yd3A = 2((7.1x6.6)+(6.6x7.8)+(7.1x7.8)) = 307.4 yd25)6)1943100129722001.8 mm1.9 m50292008191500in6.8 in5.9 inV = 6.3x1.8x1.9 = 21.5 m3A = 2x((6.3x1.8)+(1.8x1.9)+(6.3x1.9)) = 53.5 m2 CITATION Mat142 \l 1033 (Math-, 2014) V = 6.8x6.4x5.9 = 256.8 in3A = 2x((6.8x6.4)+(6.4x5.9)+(6.8x5.9)) = 242.8 in2Name:__________________________________________Answer key:Volume and Surface Area Story Problem Worksheet1. Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 2 cm. 2. The diameter of an iron sphere is 8 cm. What is the surface area of the sphere?3. A hundred metal spheres with a radius of 4 cm each are melted. The melted solution is filled into a cube with a base area of 16 cm × 10 cm. Find the height of the cube filled with the solution.4. A rectangular box has the dimensions 6in × 3in × 7in. How many rectangular boxes with the dimensions of 3 in x 4 in x 2 in can be fitted into the cubical box?5. Milk is sold in aluminum cans that measure 13 inches in height and 6 inches in diameter. How many cubic inches of milk are contained in a full can?6. 6. A rectangular box has the dimensions 6in × 7in × 2in. How many cubes with the dimensions of 4 in x 4 in x 4 in can be fitted into the rectangular box? 7. The diameter of an iron sphere is 6 cm. What is the volume of the sphere?8. A glass is 20 cm deep and 16 cm wide. How much liquid can the glass hold? CITATION Jul3 \l 1033 (Leonard, Grade 8 Math Worksheets: Geometry, 2014)Volume and Surface Area Story Problem Worksheet Answer Key1. Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 2 cm.SA=6s2=6*22=24 cm22. The diameter of an iron sphere is 8 cm. What is the surface area of the sphere?SA=4πr23. A hundred metal spheres with a radius of 4 cm each are melted. The melted solution is formed into a rectangular prism with a base area of 16 cm × 10 cm. Find the height of the rectangular prism formed by the solution.Total Volume of spheres: 100*V=100*43πr3=100* 43π43=20106.19298 cm3Total volume of spheres = Volume of rectangular prism Volume of rectangular prism =lwh=16*10*h=20106.19298 cm3h=20106.19298 cm316cm*10cm=125.66 cm4. A rectangular box has the dimensions 6in × 3in × 7in. How many rectangular boxes with the dimensions of 3 in x 4 in x 2 in can be fitted into the cubical box? 0127000Since both boxes have a dimension of 3, then it would be possible for 4of the smaller boxes to fit into the big box. See diagram.5. Milk is sold in aluminum cans that measure 13 inches in height and 6 inches in diameter. How many cubic inches of milk are contained in a full can?V=πr2H=π622*13=9*13*π=368 in36. A rectangular box has the dimensions 6in × 7in × 2in. How many cubes with the dimensions of 4 in x 4 in x 4 in can be fitted into the rectangular box? None, first you make the assumption that you are going to close the rectangular box after you place the cube inside it. Then, because the rectangular box is only 2 inches high whereas the cubes are 4 inches high it would be impossible to close the box, so none of the cubes would fit inside the rectangular box. 7. The diameter of an iron sphere is 6 cm. What is the volume of the sphere?V=43πr3= 43π623=113 cm38. A glass is 20 cm deep and 16 cm wide. How much liquid can the glass hold?V=πr2H= π1622*20=64*20*π= 4021 cm3 CITATION Jul3 \l 1033 (Leonard, Grade 8 Math Worksheets: Geometry, 2014)Summative Assessment:Summative assessment occurs after instruction is completeCITATION Woo10 \l 1033 (Woolfolk, 2010). A Summative assessment gives teachers a summary of what students learned and accomplished throughout instructionCITATION Woo10 \l 1033 (Woolfolk, 2010). Summative Assessment: Name:__________________________________________Name the shape and Find the Surface Area and Volume of the Following Figures. Show Work!3505200179070001)2)-4762510668000SA=__________SA=__________V=___________V=___________ 247650048196500180975209550004914900211455003) 4)5) SA=__________SA=__________SA=__________V=___________V=___________ V=___________Answer the following word problems:6) Find the surface area of a wooden box whose shape is of a cube, and if the edge of the box is 2 cm.7) The circumference of a basketball is approximately 75 cm, how much leather does it take to make the basketball?8) A glass is 20 cm deep and 16 cm wide. How much liquid can the glass hold?9) An ice cream cone 6 inches tall, with a 2 inch radius is completely filled, including a perfect hemisphere sitting on top. How much ice cream is there?10) A hundred metal spheres with a radius of 4 cm each are melted. The melted solution is filled into a cube with a base area of 16 cm × 10 cm. Find the height of the cube filled with the solution.Summative Assessment Answer Key 1) Rectangular Prism: SA=2LW+2HW+2LH=2*7*1+2*3*1+2*7*3=62 cm2V=LWH=7*3*1=21cm32) Cube: SA=6s2=6*33=162 in2V=s3=33=27in33) Sphere: SA=4πr2=4π(5)2=314.2 cm2V=43πr3=43π(5)3=523.6 cm34) Cylinder: SA=2πr2+2πrH=2π*22+2π*2*6=100.5 in2V=πr2H=π32*7=198.0 in3 5) Cone: slant height of cone = s =r2+H2=7.62 cmSA=πrs+πr2=π*3*7.62+π32=100.1 cm2 V=13πr2H=13π32*7=65.97 cm36) Surface area of box: SA=6s2=6*22=24 cm2 7) Circumference of basketball: C=2πr ? r=C2π=752π=11.94 cm SA=4πr2=4π(11.94)2=1790.49 cm28) How much liquid can the glass hold?V=πr2H= π1622*20=64*20*π= 4021 cm39) Answer: remember cone is filled and there is a perfect ? sphere on top. Volume of cone +Volume of ? a sphere. Vtotal=1243πr3=13πr2H=1243π23=13π226=41.89 in3 10) Total Volume of spheres: 100*V=100*43πr3=100* 43π43=20106.19298 cm3Total volume of spheres = Volume of rectangular prism Volume of rectangular prism =lwh=16*10*h=20106.19298 cm3Height of rectangular prism: h=20106.19298 cm316cm*10cm=125.66 cmReliability and Validity:Another important part of assessment is to ensure that the assessments are reliable, valid, and useable. I can make assessments reliable by including clearly written directions, having a high number of items to evaluate, making sure the problems are of moderate difficulty, decreasing distractions during the assessment, and scoring the assessment objectively CITATION Moo12 \l 1033 (Moore, 2012). Assessments are considered valid when the assessment measures what was actually taught as well as measuring what the students have learned CITATION Moo12 \l 1033 (Moore, 2012). It is necessary when assessing students, that the questions on the test match the types of questions that were asked in the homework. The validity of an assessment should also match my stated learning objective for my students CITATION Moo12 \l 1033 (Moore, 2012). Validity is the most important aspect of assessment. The usability of an assessment is whether or not the assessment is suitable for gathering the needed information; assessments need to be easy to grade, to have an appropriate length, and to have a suitable degree of difficulty CITATION Moo12 \l 1033 (Moore, 2012). For an assessment to be used it needs to have all components: validity, reliability, and usability CITATION Moo12 \l 1033 (Moore, 2012).Reporting:It is essential when grading papers that the teacher maintains the confidentiality of students’ grades and records at all times. FERPA, the Family Education Rights and Privacy Act, is a Federal law that protects the privacy of student education records CITATION FPC14 \l 1033 (FPCO, 2014). The law applies to all schools that receive education funds from the U.S. Department of Education CITATION FPC14 \l 1033 (FPCO, 2014). Basically the law states that a school cannot share students’ records without written permission from parents of student except in the very specific cases such as a student transferring to a new school, financial aid organizations requesting information, and state and local authorities, within a juvenile justice system, pursuant to specific State law CITATION FPC14 \l 1033 (FPCO, 2014).” This law applies not only to schools, but also to teachers. Test scores, course grades, and all other required reporting needs to be confidential. With that in mind, I will ask students when completing homework and tests to write on only one side of the paper. When returning homework, I will fold the paper in half lengthwise with the score enclosed and place it on their desks so that students cannot see each other’s grades. I will keep copies of tests and project rubrics for student records in a locked filing cabinet should parents inquire about student scores, project rubrics, and/or grading policies. When reporting scores to administration, I will use a secured computer scoring system so that only the person for whom the scores were meant has access to the scores. Table of Specifications:Subject (concept)% CoveredPre-Assessment% CoveredFormative Assessment% CoveredSummative Assessment% CoveredPerimeter of 2-D Shapes30%5%5%Area of 2-D shapes30%5%0%2-D Nets of 3-D shapes0%5 %0%Surface Area of 3-D Shapes20%25%35%Volume of 3-D Shapes20%25%40%Real Life Applications of Volume and Surface Area0%25%10%Manipulating Algebraic Formulas0%10%10%Bibliography BIBLIOGRAPHY \l 1033 Exemplars, Inc. (2014). Assessment Rubrics: 3-level Math Rubric. Retrieved from Exemplars: We set the standard: . (2014, June 2). Laws & Guidance/ General: Family Education and Privacy Act. Retrieved from U.S.Department of Education: , J. (2014, September 21). 7th Grade Math Worksheets: Geometry. Retrieved from Math Work Sheets Land: , J. (2014, September 21). Grade 8 Math Worksheets: Geometry. Retrieved from Math Worksheets Land: , J. (n.d.). 7th Grade Math Worksheets: Word Problems Leading to Equations. Math Worksheets Land: Math Worksheets For All Ages, Retieved March 15, 2014 from . (n.d.). Geometry. Math-: Dynamically Created Math Worksheets, Retrieved March 15, 2014 from . (2014, September 21). Volume and Surface Area of Rectangular Prisms with Whole Numbers Measurement Worksheet. Retrieved from Math Volume and Surface Area of Rectangular Prisms with Whole Numbers (A) Measurement Workshee. Retrieved from Math-:: . (2014, September 14). Menards Fall Flyer. Retrieved from Weekly Ad at Menards: , K. D. (2012). Effective Instructional Strategies: FromTheory to Practice. Los Angeles, California: Sage Publications, Inc.Reazon Systems, Inc. (2014, September 21). Rubric Gallery. Retrieved from RCampus: , M. D., & Di Vesta, F. J. (2011). Classroom Assessment in Action. Lanham, Maryland: Rowman & Littlefieild Publishing Group, Inc.Waugh, K. C., & Gronlund, N. E. (2008). Assessment of Student Achievement. Upper Saddle River, New Jersey: Paerson Education, Inc.Woolfolk, A. (2010). Educational Psychology. Upper Saddle River, New Jersey: Pearson Education, Inc. ................
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