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Unit 5 Geometry Math 7 Unit Goals – Stage 1 Number of Days: 29 days 3/13/17 – 4/28/17 Unit Description: Students will begin to explore the concepts of congruency and similarity by investigating the relationships between angles formed by intersecting lines, constructing geometrical figures with given conditions, and using scale drawings. They also solve problems involving area and circumference of circles. Additionally, students examine cross-sections of three-dimensional figures. Their work with expressions and equations is applied to finding unknown angles and problems involving area, surface area, and volume. Materials: protractor*, compass, GeoSolids, modeling dough, calculators (* Paper tool available at LBUSD Curriculum Intranet Instructional Tools Middle School Mathematical Tools) Standards for Mathematical Transfer Goals Practice Students will be able to independently use their learning to… SMP 1 Make sense of problems • Make sense of never-before-seen problems and persevere in solving them. and persevere in solving • Construct viable arguments and critique the reasoning of others. them. Making Meaning SMP 2 Reason abstractly and UNDERSTANDINGS ESSENTIAL QUESTIONS quantitatively. Students will understand that… Students will keep SMP 3 Construct viable considering… • Geometric awareness develops through visualizing, diagramming, and arguments and critique constructing. • How can geometry be the reasoning of others. used to understand and • The area of irregular and regular polygons can be found by decomposing SMP 4 Model with mathematics. explain the world around the polygon into triangles and quadrilaterals. SMP 5 Use appropriate tools you? • Using the formulas for finding area, surface area, and volume can help solve strategically. • How do geometric real-world problems. SMP 6 Attend to precision. relationships help solve • Scale drawings and scale models involve proportional reasoning and are SMP 7 Look for and make use of problems? used in real-world applications. structure. • How can you draw, • Cross-sections of three-dimensional objects can result in a variety of SMP 8 Look for and express construct, and describe two-dimension figures, depending on the angle of the cut with the base of regularity in repeated geometrical figures? the object. reasoning. Acquisition KNOWLEDGE SKILLS Standards for Mathematical Students will know… Students will be skilled at and/or be able to… Content Clusters Addressed • The measures of complementary angles • Use facts about supplementary, complementary, vertical, [a] 7.G.A Draw, construct, and and adjacent angles to write and solve equations for add up to 90° and the measures of describe geometrical unknown angles in a figure. supplementary angles add up to 180°. figures and describe the • Draw (freehand, with ruler and protractor, and/or with • Vertical angles are congruent. relationships between technology) geometric shapes with given conditions. • The ratio of the circumference to the them. • Construct triangles from three measures of angles or sides [a] 7.G.B Solve real-life and diameter is “pi” (π). and notice when the conditions determine a unique mathematical problems • The formula for circumference of a circle is triangle, more than one triangle, or no triangle. involving angle C = πd. • Solve problems involving scale drawings of geometric 2 measure, area, surface • The formula for area of a circle is A = πr . figures. area, and volume. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 2/1/17 2016-2017 Unit 5 Geometry Math 7 Unit Goals – Stage 1 • The formula for volume of right prism is V = Bh and for pyramids is V = 1 Bh where 3 B is the area of the base. LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 2 • Reproduce a scale drawing at a different scale. • Find the circumference and area of a circle. • Informally derive the relationship between circumference and area of a circle. • Use the formulas for area of triangles, quadrilaterals, and circles to solve real-world and mathematical problems involving composite figures. • Use the formulas for volumes of right prisms and pyramids to solve real-world and mathematical problems including composite solids. • Describe the two-dimensional figures that result from slicing three-dimensional figures. Posted 2/1/17 Unit 5 Geometry Math 7 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 3 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.A Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. [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.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 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. Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 3 Posted 2/1/17 Unit 5 Geometry Math 7 Evidence of Learning – Stage 2 Assessment Evidence Unit Assessment 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.A • The student creates scale drawings. • The student solves problems involving scale drawings using proportional reasoning. • The student draws, constructs, or describes geometric shapes given certain conditions. • The student describes a two-dimensional figure resulting from slicing a three-dimensional figure by a plane. 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 involving angle measure including problems requiring writing and solving equations. • 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. 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.A • 7.G.B Claim 3: 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 3: • 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.A • 7.G.B Other Evidence Formative Assessment Opportunities • • • • • • • • • 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 2016-2017 4 Posted 2/1/17 Unit 5 Geometry Math 7 Learning Plan – Stage 3 Days Learning Target I will explore geometry by participating in the Opening Task. 1 day I will apply facts about angle relationships by… 2-3 days Suggested Sequence of Key Learning Events and Instruction Big Ideas Math Course 2 Expectations (Activities and Lessons) 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, 3) • Identifying adjacent, vertical, complementary, and supplementary angles. • Writing and solving equations to find unknown angle measures using properties of adjacent and vertical angles. • Writing and solving equations to find unknown angle measures using properties of complementary and supplementary angles. • Writing and solving equations to find unknown angles in more complex figures that combine adjacent, vertical, complementary, and supplementary angles. • Answering questions such as… o Explain why two angles cannot be vertical and adjacent at the same time. o Ariana claims that two angles are complementary only if they are adjacent and make a right angle. Is Ariana correct? Justify your reasoning. o How can you use angle pairs to solve problems? o How do you use vertical angles to solve problems with figures? o Synergy Item Bank: Item ID 61644, 71305 LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 5 • Section 7.1 (Activities 2 and 3; Examples 1, 2, and 3) • Section 7.2 (Activities 1 and 2; Examples 1, 2, and 3) Curriculum Intranet Conceptual Understanding: • Candle Box Conceptual Understanding: • Vertical Angles Dynamic Tool • Complementary Angles Dynamic Tool • Supplementary Angles Dynamic Tool Procedural Skills and Fluency: • Finding Unknown Angles Video • Solving for Unknown Angles Using Equations (EngageNY) • Flipbook: Angle Relationships • Complementary Angles Interactive Application: • Truss Bridge Performance Task Posted 2/1/17 Unit 5 Geometry Math 7 Learning Plan – Stage 3 Days Learning Target I will draw geometric shapes with given conditions by… • • • 3-4 days • I will solve problems involving scale drawings by… • Using proportional reasoning to compute actual lengths and areas from a scale drawing involving geometric figures. (SMP 6) • Determining the scale of a drawing given the ratios of lengths in the drawing and the actual dimensions. • Reproducing a scale drawing at a different scale. (SMP 5) • Answering questions such as… o How are scale drawings used in real-life? o Explain how you can find an actual measure when you know a measure on a scale drawing and you know the scale. (SMP 3) o How do proportions relate to a scale drawing? o How do you draw in different scales? I will check my understanding of geometry by participating in the FAL. FORMATIVE ASSESSMENT LESSON (choose 1) • Drawing to Scale: A Garden (SMP 1, 2, 3, 4, 5, 6, 8) • Describing and Defining Triangles (SMP 1, 2, 3, 5, 6, 7, 8) 3-4 days 2-3 days Suggested Sequence of Key Learning Events and Instruction Big Ideas Math Course 2 Expectations (Activities and Lessons) Using freehand, ruler and protractor, or geometric • What You Learned software. (SMP 5, 6) Before (p. 269) Constructing triangles and quadrilaterals with given • Section 7.3 side lengths and angle measures. (SMP 6) (Activities 1 and 3; Examples 2 and 3) Justifying whether a triangle is unique, if you can draw more than one triangle, or if no such triangle • Section 7.4 exists given such conditions. (SMP 3) (Example 3) Answering questions such as… o Can a triangle be formed by three segments of any side lengths? Why or why not? o Given three segments with side lengths that form a triangle, do you get a unique triangle or more than one triangle? o How many different triangles can be drawn given two angle measures? Explain. (SMP 3) LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 6 • Section 7.5 (Activities 1, 2, 3, and 4; Examples 1, 2, 3, and 4) • STEM Video: Matte Shots in Film Curriculum Intranet Conceptual Understanding: • Constructing a Triangle Given Three Sides • Linkage-Strip Constructions Procedural Skills and Fluency: • Drawing Geometric Shapes (EngageNY) • Drawing Triangles (EngageNY) Application: • Ladybug Walk Task Application: • Photographs Task • Architecture Performance Task • Rescaling Washington Park Task • STEM Performance Task: Matte Artist • Modeling: How Much Bigger Should They Make Zoolander’s School? (SMP 4) Posted 2/1/17 Unit 5 Geometry Math 7 Learning Plan – Stage 3 Days Learning Target I will explore circles by … • • • • • 3-4 days I will find the area of composite figures and surface area of composite solids by… 4-5 days Suggested Sequence of Key Learning Events and Instruction Big Ideas Math Course 2 Expectations (Activities and Lessons) Investigating the ratio between circumference and • Section 8.1 (Activities 1 and 2; diameter known as π . (SMP 8) Examples 1, 2, and 3) Discovering the formulas for circumference and • Section 8.2 area. (Example 3) Applying the formulas for circumference and area to • STEM Video: Track and solve real-life and mathematical problems. (SMP 2) Field Finding the relationship between circumference and • Section 8.3 area. (Activities 1 and 2; Answering questions such as… Examples 1 and 3) 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 46763, 46764 • 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. • Answering questions such as… 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 3) o Describe a scenario where you would need to find the area of a composite figure. LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 7 • Section 8.4 (Activities 1 and 3; Examples 1, 2, and 3) • Section 9.2 (Activities 2 and 3; Exercises 14 -17) • Section 9.3 (Activities 2; Examples 1, 2, and 3) Curriculum Intranet Conceptual Understanding: • myPD Course #3274: Discovering Pi • Circumference of a Circle Task Procedural Skills and Fluency: • Formulas for a Circle Video Application: • 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) Procedural Skills and Fluency: • Designs Task • Surface Area of Composite Figures (EngageNY) Application: • Stained Glass Task • Parallelogram Task • Winter Hat Task Posted 2/1/17 Unit 5 Geometry Math 7 Learning Plan – Stage 3 Days Learning Target I will explore volume of composite solids by … • • 2-3 days I will describe crosssections of three dimensional figures by … 2 days • • • Suggested Sequence of Key Learning Events and Instruction Big Ideas Math Course 2 Expectations (Activities and Lessons) Reviewing how to find volume of right prisms. • Section 9.4 (Activities 4; Finding volume of pyramids. Examples 1 and 2) Decomposing into right prisms and pyramids, finding • STEM Video: Paper each individual solid’s volume, and adding them to Measurements find the total volume. (SMP 7) • Section 9.5 Solving real-life and mathematical problems. (Activities 1-use Answering questions such as… GeoSolids; and 4; o Can you think of some geometric solids for which Examples 1 and 2) 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? • Slicing models and observing the exposed face. (SMP 5) • Using technology to display the animation of a plane cutting through a solid. (SMP 5) • Visualizing the different cross-sections of the same solid using parallel, perpendicular, and neither parallel nor perpendicular plane intersections to the base of the solid. (SMP 7, 8) • Answering questions such as … o How are cross-sections of three-dimensional figures different from faces of three-dimensional figures? How are they similar? o Which cross-sections are easier to visualize than others? Why? o Describe a profession that might slice a threedimensional figure to use cross-sections. How would they use it? LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 8 • Extension 9.5 (Examples 1 and 2) Curriculum Intranet Conceptual Understanding: • 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) Application: • A Drink Carton Task • Boxes Task Conceptual Understanding: • Cross Sections of a Cube Interactive • Slicing with Modeling Dough • Slicing Three Dimensional Figures Video Application: • Slicing Puzzles Performance Task • Cube Ninjas! Posted 2/1/17 Unit 5 Geometry Math 7 Learning Plan – Stage 3 Days Learning Target I will prepare for the unit assessment on geometry by… 1 day Suggested Sequence of Key Learning Events and Instruction Big Ideas Math Course 2 Expectations (Activities and Lessons) • Incorporating the Standards for Mathematical • Ch. 7 Review Practice (SMPs) along with the content standards to (p. 307 – 309) review the unit. • Ch. 8 Review (p.345 – 347) • Ch. 9 Review (p.391 – 393) 1 day Curriculum Intranet Application: • Which is Bigger? Task • Trough Performance Task Unit Assessment Synergy: 2016-17 Math 7 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. LONG BEACH UNIFIED SCHOOL DISTRICT 2016-2017 9 Posted 2/1/17