Math-in-CTE Lesson Plan Template - secure.lcisd.org

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Fence building and construction Occupational Area: Construction, Architecture, Landscaping Vocabulary: Perimeter. Proportion. Scale drawing. Scale model
Lesson Title: Fence building and construction | | | | | |Occupational Area: Construction, Architecture, Landscaping |Vocabulary: | | |Perimeter | | |Proportion | | |Scale drawing | | |Scale model | | |Similar | | |Unit rate | | |Ratio | | |Pythagorean Theorem | |CTE Concepts(s): Fence planning and construction | | |Math Concept(s): Measurement, area, perimeter, cost | | |analysis, problem solving, proportionality | | | | |Lesson Objective: plan and construct fence | |Supplies Needed: tape measure, handouts | |Resources: http://www.diyonline.com | |www.mytscstore.com | |www. mccoys.com | |www.lowes.com | | | |The “7 Elements” |Teacher Notes and Answer Key | |How many of you have a fenced in back yard? |Fence Purposes: | |Brain storm: What is the purpose of a fence? |Restrict access | |Brain storm: What type of materials can be |Confine | |used to build a fence? |Privacy | |How does a fence’s purpose determine the |Environmental Enhancement | |material to be used? |Mark Boundaries | | | | |We are going to create a scale drawing of a |Fence Materials | |cedar post and barbed wire cattle confinement|Live fences | |fence. You will be using your measuring |Stone | |skills to determine the size and shape of the|Brick | |fence. You will also calculate the cost of |Wood | |the materials. |Electric | | |Metal | |Define the different types of wire that is |Plastic | |used in different fences and the materials. |“Invisible” fence | |Tensile strength – The resistance of a | | |material to a force tending to tear it apart,| | |measured as the maximum tension the material | | |can withstand without tearing. | | |Galvanization - To coat (iron or steel) with | | |rust-resistant zinc. | | |Gauge - Thickness or diameter, as of sheet | | |metal or wire. | | |Know we will look at the differences and | | |similarities between the different types of | | |fence. | | |Barb wire fence | | |Horse fence | | |Hi and low tensile fence | | |Field fence | | | | | |Gauges of wire | | |Fencing is made from various gauges of wire | | |-- from very heavy to very light. The larger | | |the number, the smaller the wire. | | | | | | | | |We will start today by determining the | | |different types of posts. | | |Posts – there are three different types of | | |posts used in fencing. Wood posts are the | | |most commonly used due to the initial cost | | |and ease of erecting and maintenance. | | |Concrete and steel posts are used in some | | |locations as dictated by environment and/or | | |economics. | | |Wood posts are by far the most popular posts | | |throughout ranching and farming areas. The | | |durability of untreated and treated wood | | |posts of different species are compared as | | |follows: | | |Black locust and mesquite – 15 years or more | | |Cedar – 7 to 15 years | | |Ash, elm, red oak, pine, and sweetgum, - 1 to| | |7 years | | |Treated posts – 20 to 30 years | | |Pressure treated posts last longer than home | | |treated posts. In fact, home treating posts | | |has become less popular during the last | | |several years because of the cost of treating| | |is expensive, the life of home treated posts | | |is shorter than pressure treated posts, and | | |insect damage is greater in home treated | | |posts than pressure treated posts. | | |The recommended sizes of posts in diameter | | |and heights are: | | |Line posts (treated) – 3 to 5 in. x 6½ to 7 | | |feet | | |Line posts (untreated) – 4 to 6 in. x 6½ to 7| | |feet | | |Gate posts – 6 in. or more 7½ to 8 feet | | |Corner and brace posts – 6 in. or more 7½ to | | |8 feet | | |When fencing in sandy or wet soils, | | |hillsides, and on the contour, use 4 – 5 in. | | |line posts that are 6½ to 7 feet I length. | | |Posts 4 – 5 in. in diameter and 8 feet in | | |length should be used around tanks, lakes and| | |barn yards. 6 – 8 in. diameter posts should | | |be used for corners and gates. | | |Types of fence posts | | | | | |Metal posts are used mainly as line posts in | | |fencing pastures and fields. However, metal | | |corner, brace, and gate posts may be used in | | |building strong fences if these posts are | | |anchored properly. Three common types of | | |metal posts are: “U” bar, studded “Y”, and | | |studded “T”. | | | | | |The advantages of using metal steel posts | | |are: | | |They protect the livestock against lightning,| | |if the animal touches the fence and the soil | | |is moist. | | |They are easily handled. | | |They are fireproof. | | |They are easily driven in moist soil, which | | |reduces time and labor in fence building. | | |They can be set in places where it is | | |difficult to set wood posts. | | | | | |The major disadvantages of metal posts is | | |that the livestock may bend or force them out| | |of line by crowding against the post or | | |fence. | | | | | |If pipe posts are used, the line posts should| | |be at least 1¾ in. in diameter and the corner| | |posts and gate posts should be 6-8 in. in | | |diameter. Pipe posts are usually more | | |expensive than wood posts. | | | | | |Concrete posts are used in areas where it is | | |difficult to get wood posts and where the | | |soil is extremely sandy. The breaking | | |strength of a 3 in. top concrete post is | | |higher than steel, but less than a 3 in. top | | |wood post. Well made concrete posts will | | |last as long as steel posts (20-30 years). | | | | | |Now we will talk about fasteners. | | |The most common types of fasteners are | | |staples, nails and wire. There are two types| | |of staples used to fasten wire or wood post. | | |These are “U” shaped and “L” shaped. The | | |U-shaped is the most popular staple used in | | |fencing. The L-shaped staple is used for | | |soft wood posts. | | | | | |Both of these fasteners are made of 9 gauge | | |wire. The U-shaped staple is available in | | |lengths of 7/8 to 2 inches and the L-shaped | | |is made in lengths 1¼ to 2 inches. One inch | | |staples are used on cedar posts and One and a| | |half to two inch staples are used on treated | | |soft wood posts. | | | | | |Most staples will last as long as the wire, | | |if they remain on the post. Ungalvanized | | |staples may start rusting the wire at the | | |point of contact. | | | | | |Galvanized wire fasteners are used to connect| | |wire to steel posts. The wire fastener is a | | |piece of wire approximately the same gauge as| | |the fence wire that fastens the fence to the | | |post. | | | | | |Now we will talk about types of gates. | | |Types of gates used in a fencing program | | |depend upon the type of passageway needed. | | |The passage of farm machinery requires a | | |large opening. A livestock and pedestrian | | |fence opening will usually require less width| | |than a machinery opening. | | | | | |Gate information is as follows: | | | | | |Widths – 8-16 feet | | |Heights – 4 feet and up | | |Kinds – Steel, aluminum and wood | | |Cost – the aluminum gate is the most | | |expensive and the wood gate is the least | | |expensive. | | |Durability – wood and steel gates are more | | |durable under livestock pressure than | | |aluminum. | | | | | |Assess student’s math awareness as it relates|Unit of Measurement | |to the CTE lesson. |unit will depend on purpose of the | | |fence | |What unit of measurement would you use to |i.e. fencing of a rabbit vs. fencing | |find the length, width and height of a fence?|large game animals | |How would you find the perimeter of a fence? |inches, fractions of an inch, feet, | |What would the unit of measurement be for |yards, miles | |perimeter? |Slice of bread activity | |What math term would you use to describe the |the crust is the perimeter and the | |space enclosed within the fence? (Area) |white is the area | | |cut crust off and measure then relate| | |to fence perimeter | | |unit of measurement: inches, feet, | | |etc….(not squared) | | | | | |Perimeter of a rectangle | | |P= 2l + 2w | | |Perimeter of a square | | |P = 4s | | |Circumference of a circle | | |C= 2r or C= d | | |Any other polygon | | |P= sum of all sides | | | | | |Area = units squared | | | | | |Area of rectangle = lw or bh | | |Area of square = s2 | | |Area of a triangle = ½ bh or bh/2 | |Work through the math example embedded in the| | |CTE lesson. | | | | | |Your back pasture measures 160 ft by 96 ft. | | |You have planned to use 6 ½ ft cedar posts | | |that will be buried 2 ft. in the ground. You| | |have purchased one 8 ft. gate and will run 5 | | |strands of barbed wire. Your posts will be | | |placed 8 ft. apart. Your gate needs to be | | |centered on one of the 160 ft. sides. Based |65 posts needed for fence | |on the perimeter of the pasture and the |10 posts needed for brace | |number of strands of wire, calculate the | | |number of posts and the length of barbed wire|Figure perimeter of pasture | |needed to be purchased. |(2)(96 ft) + (2)(160 ft) = 512 ft. | | | | |So, let’s begin by creating a scale drawing |512 ft – 8 ft = 504 ft | |of the pasture. | | |Step 1 – Using graph paper, let each square |504 ft. X 5 = 2520 ft. | |equal 4 ft. Remember to include the scale | | |and Key. |To compare calculate either the unit | |Step 2- Place posts at 8ft. intervals. |price or set up a proportion. | |Remember to take into account your gate. | | |Step 3- Draw in your gate |TSC | |Step 4 – Based on scale drawing, determine |Posts | |the number of posts needed to be purchased. |$140 / 25 = $5.60 | |Remember to take into account your horizontal| | |brace posts when answering this question. |25 / 140 = 75 / X | | |25X = (140) (75) | |Now, how can we figure out the amount of wire|X = 10500 / 25 | |needed? (Brainstorm- remind about 5 strands |X = $420 | |and gate) | | |Step 1- How much wire is needed for 1 strand?|Wire | |How did you figure that out? |400 yd X 3 ft / 1 yd =1200 ft | | |2520 ft / 1200 ft = 2.1 therefore | |Step 2- Subtract the length of the gate from |you must purchase 3 rolls of barbed | |the perimeter. You have now found the wire |wire. (discuss wrapping of wire | |needed to complete one strand. |around corner posts) | | | | |Step 3- Find the total amount of wire needed |3 X $48.48 = $145.44 for wire | |for all five strands. | | | |McCoys | | |$85 /15 = $5.60 | |Now let’s compare the cost of our materials | | |from two different retailers. |15 /$85 = 75 / X | | |15X = ($85) (75) | |Tractor Supply Company sells: |X = 6375 /15 | |25 cedar posts for $140 |X = $425 | |1 spool of barded wire that is 400 yd for | | |$48.48 | | | | | | | | |McCoy sells: | | |15 cedar posts for $85 | | |1 spool of barded wire that is 400 yd for | | | | | |$48.48 | | | | | | | | |So, it would cost a total of $565.44 at TSC | | |and $570.44 at McCoy’s. | | |Work through related, contextual math-in-CTE |total pasture area : (96) (160) = | |examples. |960 ft2 | | | | |You decide to provide your calf a 2 foot |Water trough area (4)(6)= 24 ft2 | |deep 6’ X 4’ water trough . How much how | | |many square feet of grazing area will remain?| | | |960 – 24 = 936 ft2 | |Work through traditional math-in-CTE | | |examples. |A. Find perimeter P = 2l + 2w | |You might see these same concepts in your |1. (12)(2) + (8)(2) = 40 ft. | |math class. |2. Convert 36 in. into feet = 3 ft | | |3. Subtract gate from perimeter | |Jaime is building a rectangular dog run that |40 - 3 = 37 ft. | |is 12 ft by 8 ft. | | |How many ft. of chain link fence is needed |B. A = lw | |to build the dog run if you put in a 36 in. |1. A = (12 X 8) | |gate? |2. A = 96 ft2 | |If you are going to plant grass, how many | | |square feet of grass is needed? |C. V = lwh or V = Bh; B= lw | |If you are going to pour a 3 in. concrete |1. Convert 3 in. into feet. | |slab instead of grass, how many cubic feet of|1 ft = 12 in. | |concrete do you need to order? |3 in. = ¼ ft or .25 ft. | | |2. V= (12)(8)(.25) | | |3. V = 24 ft3 | |See Perimeter and Area of Rectangles | | |Worksheet | | |Students demonstrate their understanding. | | | | | |Students will tour school grounds identifying| | |fencing, purpose, materials, etc…. Remind | | |students to make note of gates and post | | |spacing. | | | | | |Divide class into groups and assign each |Extended activities: | |group a different fence located on the school|Have the students build a scale model| |grounds. | | | |of their fence. | |Each group will: | | |measure the length and width to calculate the| | |perimeter and area | | |draw a scale diagram of the fence | | |create materials list | | |research online to determine cost of | | |materials needed to build fence | | | | | |Formal assessment. | | | | | |Unit Test | |

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