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Subject Area: 7th grade algebra Lesson Design Mathematics Grade Level: 7 Benchmark Period: CST Duration of Lesson: 1-2 hours Standard(s): 7th Grade: MG 2.2 Estimate and compute the area of more complex or irregular two-and three- dimensional figures by breaking the figures down into more basic geometric objects. Learning Objective: Students will determine the area of complex geometric shapes. Big Ideas involved in the lesson: Break down irregular or complex two-or three-dimensional figures to estimate and compute their areas. As a result of this lesson students will: Know: Vocabulary: Surface area – An area obtained by adding the area of all the faces of a solid (the amount of gift paper you need to wrap a gift). Area – The measure of the amount of plane occupied by a two-dimensional object. Complex or irregular figures – A figure composed of more than one geometric shape. Understand: How to break down a complex figure into more basic figures. They can use the area formulas to find the area of each basic object and add these areas to find the area of the complex object. Be Able To Do: How to compute the areas of two or three-dimensional geometric figures that are irregular. Assessments: Formative: ABWA, CFU Questions: What will be evidence Quiz and homework. Break up the figure into component geometric shapes. Show on of student knowledge, white boards. understanding & Summative: CST Determine the area of each component shape. ability? Determine the area of the whole shape. Lesson Plan Anticipatory Set: Given the diagram below, (also on a transparency) have students identify the a. T. focuses students shapes. b. T. states objectives CFU: c. T. establishes purpose of the How would you find the area of each shape? lesson We have formulas that help us to calculate the d. T. activates prior knowledge area of basic plane or solid objects. We will use them to find the area of a more complex figure that is composed of these basic figures. How would you find the area of the total shape? What would you need to know. Instruction: a. Provide information Explain concepts State definitions Provide exs. Model b. Check for Understanding 1 Why – This is a great application of geometry in everyday life, such as calculating flooring needs. Most building do not have pure rectangular floors. Teacher will give the students pictures of complex objects and show them how they can break them down to find their areas. Teacher will CFU (check for understanding) randomly. This is a rectangle + a semi-circle d 1 2 Area = base ( height) + ( r ) 2 b where r = half the diameter Lesson Design Mathematics Pose key questions Ask students to explain concepts, definitions, attributes in their own words Have students discriminate between examples and non-examples Encourage students generate their own examples Use participation h1 This is a rectangle + a triangle 1 h2 Area = base ( height2) + base ( height1) 2 The surface area = 4 faces of the pyramid + 4 walls of the prism + base of the prism Surface area = 2(0.5)(bh1) + 2(0.5)(ah3) + 2(bh2) + 2(ah2) + ab h1 h3 h2 a b Check for understanding on the white boards. Put the picture of each object on the over-head projector and ask the students to write down the formulas for the volume and the S.A. on their white boards. Check for understanding by asking students to demonstrate how they would break apart each problem with the correct formulas, etc. using their white boards. Find Area: 1. Label as follows: Rectangle Length= 6 m Triangle Height = 3 m, Rectangle Width = 4m 1 A bh lw 2 A = 0.5 (6m)(3m) + (6m)(4m) A 33m 2 2. Find Area: Draw a picture of a rectangle with two semi-circles on each end. Label the radius (or half of the width) of one of the circles as 50 yards and the length as 200 yards. 1 A 2( r 2 ) lw or 2 2 A r lw A 3.14(50yd)2 (100yd)(200yd) A 3.14(2500yd 2 ) 2000yd 2 A 9850yd 2 Remaining problems are in Problems for M&G 2.2 file. For 3-D rectangular prism related problems, students can build the figures using multilink cubes CFU – Have students use their whiteboards to break apart complex shapes into component parts. Discuss how to find the area of each part. CFU – Students randomly selected to answer questions about the process of dividing the figure into its components and finding the area of each component. 2 Guided Practice: a. Initiate practice activities under direct teacher supervision – T. works problem step-by-step along w/students at the same time b. Elicit overt responses from students that demonstrate behavior in objectives c. T. slowly releases student to do more work on their own (semi-independent) d. Check for understanding that students were correct at each step e. Provide specific knowledge of results f. Provide close monitoring What opportunities will students have to read, write, listen & speak about mathematics? Closure: a. Students prove that they know how to do the work b. T. verifies that students can describe the what and why of the work c. Have each student perform behavior Lesson Design Mathematics CFU – Students work with a partner to discuss each problem as they work through it with the teacher. The first 6 problems are done with partners and teacher, the next 2 problems students should work alone with guidance from the teacher. Teacher checks each student’s work on whiteboards and through questioning. Problems are on guided practice worksheet in Problems for M&G 2.2 file They read the learning objective in their pair share. They listen to instruction and write on their white boards. They work as partners on the guided practice problems and on problem in Closure. Allow students to work together to create their own 2- and 3- D shape that can be broken apart to find the area or the volume. Students demonstrate which formulas they will use. These are done on whiteboards that teacher checks. Independent Practice: a. Have students continue to practice on their own b. Students do work by themselves with 80% accuracy c. Provide effective, timely feedback See Independent Practice problems in Problems for M&G 2.2 file Resources Problems for M&G 2.2 file Man for M&G 2.2 file Multi-link cubes 3 Lesson Design Mathematics 4