Unit 5 Two- and Three-Dimensional Geometry
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1 Number of Days: 15 /6/17 /24/17 Unit Goals Stage 1 Unit Description: Students will solve problems involving area and circumference of circles. Additionally, their work with expressions and equations is applied to solving problems involving area, surface area, and volume. Materials: compass, GeoSolids, calculators Standards for Mathematical Practice SMP 1 SMP 2 SMP SMP 4 SMP 5 SMP 6 SMP 7 SMP 8 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Standards for Mathematical Content Clusters Addressed [a] 7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. [a] 8.G.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Transfer Goals Students will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Making Meaning UNDERSTANDINGS Students will understand that Geometric awareness develops through visualizing, diagramming, and constructing. The area of irregular and regular polygons can be found by decomposing the polygon into triangles and quadrilaterals. Using the formulas for finding area, surface area, and volume can help solve real-world problems. ESSENTIAL QUESTIONS Students will keep considering How can geometry be used to understand and explain the world around you? How do geometric relationships help solve problems? Acquisition KNOWLEDGE SKILLS Students will know Students will be skilled at and/or be able to The ratio of the circumference to the diameter is pi (π). Find the circumference and area of a circle. The formula for circumference of a circle is C = π d. Informally derive the relationship between The formula for area of a circle is A = π r 2. circumference and area of a circle. The formula for volume of right prism is V = Bh and for Use the formulas for area of triangles, 1 quadrilaterals, and circles to solve real-world pyramids is V = Bh where B is the area of the base. and mathematical problems involving composite figures. 2 The formula for the volume of a cylinder is V = π r h. Use the formulas for volumes of right prisms 1 and pyramids to solve real-world and 2 The formula for the volume of a cone is V = π r h. mathematical problems including composite The formula for the volume of a sphere is 4 solids. V = π r Use the formulas for the volumes of cones,. cylinders, and spheres to solve real-world and mathematical problems. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 2/7/17
2 Assessed Grade Level Standards Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content [a] 7.G.B Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [a] 8.G.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 2/7/17
3 Assessment Evidence Unit Assessment Evidence of Learning Stage 2 Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Concepts and skills that may be assessed in Claim1: 7.G.B The student solves real-life and mathematical problems for the circumference and area of circles. The student solves real-life and mathematical problems for the area of two-dimensional objects composed of polygons. The student solves real-life and mathematical problems for the volume and surface area of three-dimensional objects composed of right prisms and cubes. 8.G.C The student solves real-world and mathematical problems by applying the formulas for the volumes of cylinders, cones, and spheres. Claim 2: Students can solve a range of wellposed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Standard clusters that may be assessed in Claim 2: 7.G.B 8.G.C Other Evidence Formative Assessment Opportunities Claim : The student can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Standard clusters that may be assessed in Claim : NONE Claim 4: The student can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Standard clusters that may be assessed in Claim 4: 7.G.B 8.G.C Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Modeling Lessons (SMP 4) Tasks Formative Assessment Lessons (FAL) Quizzes / Chapter Tests Big Ideas Math Performance Tasks SBAC Interim Assessment Blocks Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website M Mathematics Curriculum Documents LONG BEACH UNIFIED SCHOOL DISTRICT Posted 2/7/17
4 Days Learning Target Expectations 1 day I will explore geometry by participating in the Opening Task. Learning Plan Stage Suggested Sequence of Key Learning Events and Instruction OPENING TASK Candle Box Pass out the activity, Candle Box, for students to work independently. Then have students work as a group to compare and improve their drawings. After working as a team, facilitate a large group discussion about their drawings. If time permits, show student-work examples that are included so that your students can analyze them. Display only the drawings to have students critique the reasoning of others. This task is a gateway into the entire unit of geometry. (SMP 1, ) Big Ideas Math Advanced 2 (Activities and Lessons) Curriculum Intranet Candle Box -4 I will explore circles by Investigating the ratio between circumference and diameter known as π. (SMP 8) Discovering the formulas for circumference and area. Applying the formulas for circumference and area to solve real-life and mathematical problems. (SMP 2) Finding the relationship between circumference and area. o Describe the relationship between the distance around a circle and the distance across the center of the circle. o How does the circumference of a circle relate to its area? o Why would it be useful to find the circumference of a circle? Connect it to a real-life scenario. o Synergy Item Bank: Item ID 4676, Section 8.1 (Activities 1 and 2; Section 8.2 (Example ) STEM Video: Track and Field Section 8. (Activities 1 and 2; Examples 1 and ) mypd Course #274: Discovering Pi Circumference of a Circle Task Procedural Skills and Fluency: Formulas for a Circle Video Eight Circles Task Historic Bicycle Task Hiking Performance Task Modeling: How Much Purple Ribbon Will You Need? (SMP 4) Modeling: Volcano (SMP 4) Modeling: Rolling Tires (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 2/7/17
5 2- Learning Plan Stage Suggested Sequence of Key Learning Events and Instruction Days Learning Target Expectations Big Ideas Math Advanced 2 (Activities and Lessons) I will find the area of composite figures and surface area of composite solids by Decomposing into triangles, quadrilaterals, and circles, using known area formulas and adding them to find the total area. (SMP 7) Reviewing how to find surface area of prisms and pyramids by applying these procedures to find the surface area of composite solids. Finding surface area of cylinders. Solving real-life and mathematical problems. o Why are you not able to use one simple formula to find the area of a composite figure? o Can you decompose a composite figure only one way? o Explain how to find the surface area of a composite solid. (SMP ) o Describe a scenario where you would need to find the area of a composite figure. Section 8.4 (Activities 1 and ; Section 9.2 (Activities 2 and ; Exercises 14-17) Section 9. (Activities 2; Curriculum Intranet Procedural Skills and Fluency: Designs Task Surface Area of Composite Figures (EngageNY) Stained Glass Task Parallelogram Task Winter Hat Task 2- I will explore volume of composite solids by Reviewing how to find volume of right prisms. Finding volume of pyramids. Decomposing into right prisms and pyramids, finding each individual solid s volume, and adding them to find the total volume. (SMP 7) Solving real-life and mathematical problems. o Can you think of some geometric solids for which the formula V = Bh would not apply? Why? o Compare and contrast the formulas for volume of prisms and pyramids. o How do you find the volume of a figure made up of prisms and pyramids? Section 9.4 (Activities 4; Examples 1 and 2) STEM Video: Paper Measurements Section 9.5 (Activities 1-use GeoSolids; and 4; Examples 1 and 2) How Many Pyramids Does It Take To Fill a Prism? (Task #1 and Task #2) Procedural Skills and Fluency: Volume of Composite Three-Dimensional Objects (EngageNY) A Drink Carton Task Boxes Task LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 2/7/17
6 Learning Plan Stage Suggested Sequence of Key Learning Events and Instruction Days Learning Target Expectations Big Ideas Math Advanced 2 (Activities and Lessons) I will apply the formulas for the volumes of cylinders, cones, and spheres by -4 1 day I will prepare for the unit assessment on two- and threedimensional geometry by Explaining how they are related. (SMP ) Solving real-world and mathematical problems. o How are the formulas for the volumes for a cylinder, cone, and sphere related? o What is the relationship between the volume of a cylinder and a cone with the same height? o How can you solve problems using the formula for the volume of a cylinder, cone, and/or sphere? o Where are cylinders, cones, and spheres found in the real-world? o Synergy Item Bank: Item ID 5118, 51505, 619 Incorporating the Standards for Mathematical Practice (SMPs) along with the content standards to review the unit. Section 8.1 (Activities 1 and 4; Section 8.2 (Activities 1 and 2; Section 8. (Activity 1; STEM Video: Canning Salsa Ch. 1 Review (p ) Ch. 14 Review (p ) Ch. 8 Review (p.6 65) Curriculum Intranet Cone and Cylinder Volumes Task Coffee Task STEM Performance Task: Packaging Salsa Modeling: How Big Is the Guatemalan Sinkhole? (SMP 4) Modeling: How Many Gumballs Fit in the Gumball Machine? (SMP 4) Modeling: Popcorn Picker (SMP 4) Modeling: I Pour, You Choose (SMP 4) Which is Bigger? Task Trough Performance Task Unit Assessment Synergy: Unit 5 or LBUSD Math Intranet/Assessment At this point, all standards addressed in the Math 7 SBAC Interim Assessment Block Geometry and Mathematics Performance Task have been covered. These blocks may now be administered. 1 day LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 2/7/17
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