Mathematics Curriculum Document for 8 th grade

Transcription

1 Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Time Frame: 18 days Grading Period: 3 Unit Number: 3B Curriculum Enduring Understandings (Big Ideas): Formulas are used to take known information to discover unknown information. Complex problem solving involves creativity, flexibility, reflection, and persistence to arrive at a solution. Geometry and measurement represent real world objects, properties, and situations. (TEACHER NOTES ON THE FOLLOWING PAGE) The student will know: B represents the area of the base P represents the perimeter of the base The hypotenuse is always the longest side of a right triangle The vertex of the legs of a right triangle is a right angle a 2 + b 2 = c 2, when a and b are legs and c is the hypotenuse of a right triangle Lateral surface area is the sum of the areas of all faces excluding the bases Total surface area is the sum of the areas of all faces (including the bases) The student will be able to: Make connections to geometric formulas Describe the volume formula, V=Bh, of a cylinder in terms of its base area and height Model the relationship between the volume of a cylinder and a cone having the same base area and height Solve problems involving the volume of cylinders, cones, and spheres Solve surface area problems (lateral and total) involving rectangular prisms, triangular prisms, and cylinders Use previous knowledge of surface area to make connections to Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 1 of 6

2 Teacher Notes: 7cd New: 8.6C 8.7A 8.7C 8.7D Extend: 7.8c from circumference and are formula to 8.6A volume of a cylinder 7.8C relationship to formulas of circumference and area to 8.6B include the volume formula 7.8A modeling the relationship between the volume of prisms and pyramids to 8.6B include the relationship between the volume of a cylinder and cone 7.9D finding surface area using nets of rectangular and triangular prisms to 8.7B using the surface area formula and 3D object not just nets and include cylinders the formulas for lateral and total surface areas of rectangular prisms, triangular prisms, and cylinders Use models and diagrams to explain the Pythagorean Theorem Use the Pythagorean Theorem to solve problems Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle Determine the distance between two points on a coordinate plane using the Pythagorean Theorem Essential Questions: How does math make complex problems simpler? How do we use algebra to solve geometry problems? What new information does the solution provide? How do we use geometry to represent real life? Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 2 of 6

3 Student Understanding (student friendly TEKS): Content: I can describe the parts of the volume formula, V = Bh, for a cylinder. (taken from 8.6A) I know the relationship between the volume of a cylinder and a cone with the same base and height. (taken from 8.6B) I can model and solve problems using the Pythagorean Theorem. (taken from 8.6C and 8.7C) I can solve problems involving the volume of cylinders, cones, and spheres. (taken from 8.7A) I can solve problems involving lateral and total surface area of prisms and cylinders. (taken from 8.7B) I can determine if a triangle is a right triangle using the Pythagorean Theorem. (taken from 8.7C) I can use the Pythagorean Theorem to find the distance between two points. (taken from 8.7D) Process: I can apply math to everyday life. (taken from 8.1A) I can create and use a problem solving plan. (taken from 8.1B) I can check my answer to see if it makes sense. (taken from 8.1B) I can solve problems with different stuff. (taken from 8.1C) I can solve problems with different resources (manipulatives, technology, etc.). (taken from 8.1C) I can use multiple ways to communicate math ideas. (taken from 8.1D) I can explain ways to solve math problems. (taken from 8.1D) I can use different representations to keep information organized when solving problems. (taken from 8.1E) I can think and talk about the relationships between math ideas. (taken from 8.1F) I can use math language to explain and defend mathematical ideas in writing or out loud. (taken from 8.1G) TEKS: Content: (6) Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: (A) describe the volume formula V = Bh of a cylinder in terms of its base area and its height; (B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 3 of 6

4 that relationship to the formulas; and (C) use models and diagrams to explain the Pythagorean theorem. (7) Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: (A) solve problems involving the volume of cylinders, cones, and spheres; (B) use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders; (C) use the Pythagorean Theorem and its converse to solve problems; and (D) determine the distance between two points on a coordinate plane using the Pythagorean Theorem. Process: (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. Targeted College Readiness Standards: IB1, IIA1, IIIA1, IIIA2, IIIA3, IIIB2, IIIB3, IIIC1, IIIC3, IIID1, IVA1, IVC1, IVC3, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1, IXA2, IXA3, IXB1, IXB2, IXC1,IXC2,IXC3, XA1, XA2,XB1,XB2, XB3 Targeted ELPs: 1C, 1E, 1F, 2C, 2D, 2E, 2F, 2G, 2H, 2I, 3B, 3D, 3E, 3F, 3H, 3J, 4C, 4D, 4F, 4K, 5B,5F,5G Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 4 of 6

5 Academic Vocabulary: P = perimeter of the base Pythagorean Theorem Language of Instruction: Lateral surface area Total surface area Legs Hypotenuse Base Perimeter Height Cylinder Cone Prism Sphere B = area of the base Slant height Composite Figures Converse Instruction Instructional Resources: Springboard Course 3 Activity 22 Activity 23 Activity 24 Embedded Assessment 4 Activity 25 Activity 26 Lesson 26-1 (optional- review of 7 th grade TEKS) Lesson 26-2 SUPPLEMENT: volume of cylinder, V=Bh from TEKS 8.6A Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 5 of 6

6 Lesson 26-3 Embedded Assessment 5 Unit 3B COMMON ASSESSMENT Technology: Suggested ways to incorporate technology and/or websites into the unit. Exemplar Lessons: Assessment Student self-assessment & reflection: Unit 3B CA Feedback Form Career Connections/Real Life Application: Suggested ways to make content relevant. Research Based Instructional Strategies: Acceptable evidence or artifacts: Embedded Assessments Unit 3B COMMON ASSESSMENT (see O drive for official version) Unit Title: Geometry- Pythagorean Theorem/Surface Area/Volume Unit Number 3B Page 6 of 6