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Math-in-CTE Lesson Plan Lesson Title: The Foundations of Building Lesson #: AM02 Occupational Area: Agriculture CTE Concept(s): Calculate cost of materials, determine cost of materials, use a tape measure, calculate volume of concrete. Math Concepts: Computation in context, convert measurement units, calculating perimeter/area/volume of a rectangle, circle, triangle. Lesson Objective: Student will demonstrate a working knowledge of: *Translating word phrases and sentences into expressions and equations and vice versa. (Pass: Algebra I, Standard 1, Objective 1) *Using the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context. (Pass: Algebra I, Standard 2, Objective 8a) *Drawing and analyzing 2- and 3-dimensional figures. (Pass: Geometry, Standard 2, Objective 2) and its application in agriculture power and technology, while recognizing it in other contexts. Supplies Needed: Link to Additional Materials: Agriculture Mechanics AM02 Downloads TEACHER NOTES (and answer key) THE "7 ELEMENTS" 1. Introduce the CTE lesson. What types of materials are used in This lesson is anticipated to take building/construction? about a week to complete. Of these, we will work specifically on concrete which is used for floors, walls, Have the students make a list. We drainage systems, walkways, patios, are looking for steel, lumber, footings, foundations, and anchoring concrete, etc. systems. 1 Students need to be told that is measured in cubic yards Why do we need to know how to concrete 3 calculate volume in cubic yards for (yd ). If the material is concrete, they need to make sure their final result is concrete? in these units. 1) It allows us to estimate the cost of the materials prior to a project which in turn allows us to make decisions relating to scaling up or down or even scrapping the project do to budgeting reasons, 2) We can cross check the supplier’s figures to make sure the proper amount will be delivered and billed. 2. Assess students’ math awareness You may either divide the class into as it relates to the CTE lesson. groups using the think-pare-share When we talk about pouring or running method, or just record answers from concrete, we start by building a form in the class in a general discussion. which to pour it. The form is usually The shape of a cube is basically that cubic, rectangular, or cylindrical in of a box with equal sides. shape. The size of a cubic yard is 1 yd x 1 What is the shape of a cube? yd x 1 yd. What is the size of a cubic yard? V = length x width x height (depth). What is the formula for determining 1 yard = 3 feet volume? 1 foot = 12 inches How many feet are in a yard? Most forms are measured in feet or How many inches are in a foot? inches (which need to be converted When getting our volume in cubic yards, to feet), but concrete is measured in cubic yards. So, if a cubic yard is 1 why do we divide by 27? yd x 1 yd x 1yd and 1 yard = 3 feet, then a cubic yard is also 3 ft x 3 ft x 3 ft and when we multiply 3 x 3 x 3 we get 27. Use a model made of pvc pipe or boards and colored string to reinforce how 27 is obtained in the formula. This may help if the students forget the number 27, and help trigger their memory of how to figure this divisor. 2 3. Work through the math example embedded in the CTE lesson. When we start calculating the volume of your given form, we find the area by multiplying your length and width (usually in feet). Most likely, the height or depth will be in inches. This must be converted to feet and then multiplied by the answer from the other two (length and width). Then, to convert from cubic feet to cubic yards (if the material is concrete), this answer must be divided by 27. L W H LxWxH 27 Use the formula to find the amount of concrete needed to fill a form that is 60 ft long by 40 ft wide by 6 inches deep. 60feet 40ft 6 in Change 6 inches to feet 6 in. ÷ 12 in. = 0.5 in. Use formula, multiply the three dimensions, then divide by 27. (60 ft) x (40 ft) x (.5 ft) 27 Answer: 44.44 yd3 (For more problems see “Concrete” worksheet). 3 4. Work through related, contextual math-in-CTE examples. Find the amount of concrete needed for Change 4 inches to feet. a sidewalk from a house to a driveway that is 12 feet long, 3 feet wide, and 4 4 in. ÷ 12 in. = 1/3 ft. inches thick. Multiply the dimensions, then divide by 27. (12 ft) x (3 ft) x (1/3 ft) 27 Answer: .44 yd3 Emphasize that this time answer is to be in cubic feet and there will be Find the volume in cubic feet of a wheat no need to divide by 27. Just truck bed that is 20 feet long, 7 feet multiply the three dimensions. wide, and 4.5 feet deep. (20ft) x (7 ft) x (4.5ft) Answer: 630 ft3 Note: It may seem more logical to give this answer in bushels but we are dealing with “non-grain" Once again, answer is to be in cubic Find the volume in cubic feet of the city feet. swimming pool, if the dimensions of the Volume = (101 ft) x (42 ft) x (7 ft) pool are 101 feet long, 42 feet wide, and Volume= 29,694 ft3 7 feet deep. 5. Work through traditional math examples. Multiply dimensions. Do not divide Find the volume in cubic feet of a by 27. rectangular prism that is 6 feet long, 4 (6 ft) x (4 ft) x (2 ft) feet wide and 2 feet high. Answer: 48 ft3 For additional problems see “Math” problems worksheet. 4 6. Students demonstrate understanding. their For class field trip, the teacher may create groups for students to work in Students are assigned the task of or do individually. finding the measurements of an existing structure at their home (ex. sidewalk, patio, etc) and determining the amount of concrete used in building that structure. Class will take a short field trip to find the measurements of an existing structure around the campus or school farm (ex. sidewalk, tennis court, etc) and determine the amount of concrete used in building that structure. 7. Formal assessment. 1. Find the amount of concrete Convert 6 inches to feet. needed to pour a driveway that is 6 in. ÷ 12 in. = 0.5 in. 40 feet long, 25 feet wide, and 6 Multiply the dimensions and divide inches deep. by 27. (Material is concrete.) (40 ft) x (25 ft) x (0.5 ft) 27 Answer #1: 18.52 yd3 2. 3. Find the amount of concrete (3 ft) x (3 ft) x (3 ft) needed to pour a base for an 27 antenna tower that measures 3 Answer #2: 1 yd3 feet by 3 feet by 3 feet. (Concrete) Find the volume in cubic feet of a (5 ft) x (3 ft) x (1 ft) (Do not rectangular prism that is 5 feet divide – answer requested in ft3) long by 3 feet wide by 1 foot high. Answer #3: 15 ft3 For additional test questions see Material Costs Test. 5