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Stage 1 – Desired Results ESTABLISHED GOALS Learners will identify different 3-D solids and surfaces that make up the surfaces of a home and apply appropriate formulas to calculate surface areas.  calculate overall surface area by finding the areas of the individual surfaces and adding them together.  identify the different components of the surface area formulas: base, height, slant height, lateral area.  calculate the surface area of a composite figure, both when two+ figures are combined and when a figure is removed from another, accounting for any hidden surfaces. TEKS Section 11: Two-dimensional and three-dimensional figures. The student uses the process skills in the application of formulas to determine measures of 2- and 3-dimensional figures. The student is expected to: G.11B: Determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure G. 11C: Apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure UNDERSTANDINGS Students will understand that…  The surface area of a 3-dimensional figure is the sum of the areas of its individual 2-dimensional surfaces.  The base and the height of a prism, cylinder, pyramid, or cone are always perpendicular. Tools of right triangles (Pythagorean Theorem, Trigonometry, Special Right Triangles) can be utilized to find the height or and dimensions.  The lateral surface area is the sum of the areas of the faces of a figure without including the bases. The total surface area is sum of the lateral surface area and the area of the bases.  When two figures are combined together to create a composite solid, the area of the hidden surface must be removed from the total surface area.  When one figure is removed from another to create a composite solid, the volume is decreased but the surface area increases. The removal and addition of surface are must be accounted for.

ESSENTIAL QUESTIONS  Which faces of a prism are determined to be the bases?  When are areas subtracted and when are they added when calculating the surface area of composite figures?  When would the lateral surface area be used instead of the total surface area?  How can decreasing the volume increase the surface area?  How is the perimeter/circumference related to lateral surface area?

Students will know…  Key terms: base, height, slant height, radius, perimeter, lateral surface area, total surface area  Formulas: area of two-dimensional figures (parallelograms, triangles, regular polygons, trapezoids, circles, kites), lateral and total surface area of three-dimensional solids (prisms, cylinders, pyramids, cones, spheres, and hemispheres)  How to identify the base, height, slant height, radius, and other dimensions on a threedimensional object

Students will be able to…  Calculate the surface areas of prisms, cylinders, pyramids, cones, spheres, and hemispheres  Derive the surface area of a hemisphere (with and without a base) formulas from the sphere surface area formula  Apply Pythagorean Theorem, Trigonometry, or Special Right Triangles in order to calculate the height, slant height, or other dimensions  Calculate the surface area of composite figures, both when solids are stacked on top of each other/next to each other and when one solid is removed from another

Stage 2 – Assessment Evidence Performance Tasks: Other Evidence:  Home Design Project  Formative Assessments: Exit Tickets/Quick o Part 1 – Model Home Construction: Learners Checks- short mini problem sets to assess if will work in groups to construct a threestudents can correctly apply the surface area dimensional “model home/room” out of a formulas to a variety of 3-D figures variety of materials and objects, creating  Summative Assessments: Quizzes and Unit Tests, composite figures. They will measure all of the particularly the written response question(s) – dimensions and then calculate the surface area. students will be assessed according to the accuracy o Part 2 – Home Tour Video: Learners will create and thoroughness of their explanations and produce a “Home tour” video highlighting  Unit Survey and Self Reflection: are students able the different surfaces around their house, how to answer the essential questions? the surface areas were calculated, which  Home Design Self Reflections: to determine if materials were chosen to cover the surfaces, students have internalized the process of how much material will be necessary, and how calculating surface area of composite figures. Do the cost of the materials is calculated. they know when to add/subtract surfaces and can o Part 3 – Home Optimization: Leaners will work they articulate and describe the process of finding with their group to make adjustments to their surface areas of composite figures? Can students initial home design in order to make their home articulate how calculating surface area is essential as space- and cost-efficient as possible. for building a house? o Part 4 – Purchase Order/Requisition Form: Students will work with their groups to create a final proposal Purchase Order/Requisition for all of the supplies necessary to build their home. They will need to research prices from a variety of vendors (Lowe’s, Home Depot), determine the total cost of their design, and provide thorough calculations to justify their costs. Students will also have to account for any excess/wasted materials (for example, if marble can only come in a rectangular slab and a hole for a sink needs to be cut out). o Students’ performances of understanding will be judged according to a rubric. They will be evaluated according to  the accuracy of their measurements and calculations  the thoroughness and clarity of their explanations, both written and oral  the analysis of their home design and the evidence provided to justify their optimization choices  the analysis of their home design and the evidence provided to create their PO/Requisition form for their home Stage 3 – Learning Plan Learning Activities: Day 1 (Whole-class, Face-to-face)  Magazine Scavenger Hunt: Learners will “build a home” using pages from home magazines, identifying and listing 

out the different surfaces found in a home and identifying which 3-D solids (prisms, cylinders, spheres/hemispheres, cones, and pyramids) create these surfaces. W, H “Home Tour”/Gallery Walk: Learners will walk around the room to view each other’s “homes” and fill in a graphic organizer recording the different 3-D solids and which home surfaces and objects are created by these solids. E, R

Day 2 (Whole-class, Face-to-face)

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Prism Wrapping Paper hands-on inquiry/discovery-based group activity: Working in groups, students will be given a rectangular prism (Kleenex, cereal box) and a ruler. They will be asked to calculate how much wrapping paper will be necessary to cover the prism in its entirety. Students will discover the surface area formula through this process. Then, in order to discover the process for finding the surface area of a composite figure, two boxes will be stacked on top of each other. Students will compare the amount of wrapping paper that would be necessary to cover the 2 “packages” individually versus the amount of paint that would be necessary to cover the composite solid. W, H, E

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Class Discussion following Prism Wrapping Paper activity to debrief process of finding surface area of composite figures. E, R, E Day 3 – 7 (Independent/Small group work with teacher monitoring and targeted check-ins)  Flipped/Blended, digital lessons involving video lessons and questions (with students receiving instant feedback) on Formative for practice with applying surface area formulas E, R, O  Writing prompt: Discuss the uses of πr² (circle), 2πr² (half-sphere/hemisphere without a base), 3πr² (hemisphere with a flat circular base), and 4πr² (sphere). E, R  Discussion Board on itsLearning: students will collaborate on Formative problems R, E, T Day 8  Composite Solids Gallery Walk E, R, E  Quick Check R, E, O Day 9 – 16 (Independent/Small group work with teacher monitoring and targeted check-ins)  Model Home Construction E, T, O  Home Tour Video E, R, T, O  Home Optimization R, E, T, O  PO/Requisition Form R, E, O Day 17 (Whole-class, Face-to-face)  Peer evaluation of Home Tour Videos E, R, E, T  Home Design Project Self Reflection R, E, T Day 18 (Whole-class, Face-to-face)  Summative Assessment (Unit Test)  Unit Survey and Self Reflection R, E, T W.H.E.R.E.T.O.? What learning experiences and instruction will enable students to achieve the desired results? How will the design… W: Help the students know WHERE the unit is going and WHAT is expected? WHERE are the students coming from? H: HOOK all students and HOLD their interest? E: EQUIP students, help them EXPERIENCE the key ideas and EXPLORE the issues? R: Provide opportunities to RETHINK and REVISE their understandings and work? E: Allow students to EVALUATE their work and its implications? T: Be TAILORED (personalized) to the different needs, interests, and abilities of learners? O: Be ORGANIZED to maximize initial and sustained engagement as well as effective learning?