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CCGPS Math 6 Unit 5 – Lesson 1 Unit Outline Title: Area and Volume Name of Lesson: Area Standards: Solve real-world and mathematical problems involving area, surface area, and volume. MCC6.G.1 Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Essential Question(s): Unit: What is the relationship among area, volume, and surface area? Lesson: How can we find the area of figures? How can we cut and rearrange irregular polygons in order to find their area? How can we use one figure to determine the area of another? Is there a common way to calculate area? How do you know? How can shapes be combined to create new shapes? How can a shape be broken down into smaller shapes? How do we figure the area of a shape without a formula for that shape? How are the areas of geometric figures related to each other? How can the formulae for the area of plane figures be used to solve problems? How can we find the area of regular and irregular polygons when you don’t have a specific formula? Assessment Description/Performance Task: Constructed response: Decomposing Polygons to Find Area Base and Height Same Base and Height Variation 1 Same Base and Height Variation 2 Informal assessment: Various Interactive Online Activities Formative assessment: Area of Composite Figures Performance Tasks: The following performance task are from the GA DOE Who Put the Tang in Tangram?, What's My Area?, King Arthur's New Table Rectangle Wraparound Finding Areas of Polygons Selected response: Area of Triangle Quiz - Form A, Area of Triangle Quiz - Form B CCSD Version Date: 2/9/2016 Instructional Methods It is expected that students will have prior knowledge/experience related to using parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols, generating two numerical patterns using two given rules, interpreting a fraction as division, and operations with whole numbers, fractions, and decimals. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these concepts. The Conceptual Framework may be used to build teacher understanding of representing inequalities in context and on a number line. By the conclusion of this lesson, students should be able to demonstrate the following competencies: Find areas of right, equilateral, isosceles, and scalene triangles, and special quadrilaterals Find areas of composite figures and polygons by composing into rectangles and decomposing into triangles and other shapes Solve real-world and mathematical problems involving area Know the properties of various regular and irregular polygons Compose and decompose regular and irregular polygons using various shapes Apply formulas to find areas of regular and irregular polygons Solve real-world and mathematical problems involving area Understand The area of irregular and regular polygons can be found by decomposing the polygon into rectangles, triangles, and other shapes. Opening Word Splash – Write the words area, parallelogram, triangle, rectangle, square, etc. in the middle of the board or chart paper. You may choose other vocabulary terms related to the lesson. Students make predictions and generate statements about the topic. After the lesson, students will spend time correcting their statements. Encourage students to make corrections to their statements during the lesson. To review finding area of a rectangle, you may use Holt Mathematics Course 1, 10-1 Hands-on Lab, page 1 “Estimating and Finding Area.” Study Jams – Area of a Parallelogram, Area of a Triangle Create a Fortune Teller Foldable for Formulas. See page two of the document for a visual on how to create the foldable Work Session Holt Mathematics Course 1, 10-1 Hands-on Lab, page 2 “Estimating and Finding Area” allows students to derive area formulas. Special quadrilaterals include rectangles, squares, parallelograms, trapezoids, rhombi, and kites. Students can use tools such as the Isometric Drawing Tool on NCTM’s Illuminations site to shift, rotate, color, decompose and view figures in 2D or 3D. Students will use the Area Tool and Geoboard Recording Paper during the task. GeoGebra – Interactive Online Activities o Finding Triangle Areas o Finding Area of a Parallelogram (one parallelogram) o Finding Area of a Parallelogram (two polygons – rectangle and parallelogram) In collaborative pairs, students may complete Decomposing Polygons to Find Area. Performance Task: Who Put the Tang in Tangram? This task will help students determine the area of tangram pieces without using formulae. Then students will use their knowledge to help them develop and use formulae to determine the area of squares, rectangles, triangles, and parallelograms. Performance Task: What's My Area? Performance Task: King Arthur's New Table Performance Task: Rectangle Wraparound Performance Task: Finding Areas of Polygons CCSD Version Date: 2/9/2016 Closing Mini-Quiz on Area of Triangles (Form A and Form B) In the Know Surface Area Formula Summarizer o Create the chart below on the board, Smart Board, Chart Paper, etc. for the entire class to view. o Give students post-it notes. o Students will draw the three dimensional figures and write the surface area formula for each on the post-it. o Students will place their three dimensional figures and formulas in one of the columns. (As students progress throughout the lesson and unit, they can move their post-it. The teacher will monitor student understanding using the results on the chart.) ? – Students will place the formula in this column if the formula is unknown to them , - Students understand the formula, but they cannot use it correctly. ! – Students understand the formula and can use it to correctly to solve a problem. ? , ! Resources Arizona Department of Education Granite School District, Salt Lake City, Utah Georgia Department of Education Differentiation: (to be created) Tiered Assignments Differentiation Strategies for Mathematics: Tiered Assignments Grades 6-8, Rectangular Prims, Cylinders, and Cones (modify to exclude cylinders and cones) (Focus on the Surface Area Portion) Leveled Questions Multiple Intelligences Using Realia/CRA Choices Board Open-Ended Tasks Problem-Based Learning Learning Contracts Tiered Graphic Organizers CCSD Version Date: 2/9/2016 Textbook/Online Resources: McGraw-Hill Georgia Math Grade 6: Chapter 8, Lessons 1-5 Mathematics Course 1 Textbook Connection: Chapter 10, Lessons 1-4 Mathematics Course 2 Textbook Connection: Hands-on Standards: Grades 5-6: (Measurement section) Area of Trapezoids; Constant Perimeter and Changing Area Hands-on Standards: Grades 7-8: (Measurement section) Perimeter and Area; Area of a Parallelogram; Area of a Triangle Graphing Calculator Strategies-Middle School Math: Lesson 18 (Computing Area and Perimeter) Math in Context: Reallotment: Geometry and Measurement: Section B-Area Patterns, Section C-Measuring Area, Section D-Perimeter and Area Connected Math (Grade 6): Covering and Surrounding: Two-Dimensional Measurement Isometric Drawing Tool Online Dot Paper Vocabulary: 2-Dimensional area compose decompose dimension equilateral triangle formula isosceles triangle kite parallelogram CCSD Version Date: 2/9/2016 polygon quadrilaterals rectangle rhombus right triangle scalene triangle square trapezoid triangles vertices