Math-in-CTE Lesson Plan Template
Lesson Title: Fence building and construction Occupational Area: Construction, Architecture, Landscaping Vocabulary: CTE Concepts(s): Fence planning and construction Perimeter Math Concept(s): Measurement, area, perimeter, cost analysis, Proportion Scale drawing problem solving, proportionality Scale model Similar Unit rate Ratio Pythagorean Theorem 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 1. How many of you have a fenced in back yard? Fence Purposes: 2. Brain storm: What is the purpose of a fence? - Restrict access 3. Brain storm: What type of materials can be used to - Confine build a fence? - Privacy 4. How does a fence’s purpose determine the material - Environmental Enhancement to be used? - Mark Boundaries
We are going to create a scale drawing of a cedar post and Fence Materials barbed wire cattle confinement fence. You will be using - Live fences your measuring skills to determine the size and shape of - Stone the fence. You will also calculate the cost of the - Brick materials. - Wood - Electric Define the different types of wire that is used in different - Metal fences and the materials. - Plastic Tensile strength – The resistance of a material to a - “Invisible” fence 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 Math-in-CTE Lesson Plan Template
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 Math-in-CTE Lesson Plan Template
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 Math-in-CTE Lesson Plan Template
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 to the CTE Unit of Measurement lesson. - unit will depend on purpose of the fence 1. What unit of measurement would you use to find - i.e. fencing of a rabbit vs. fencing the length, width and height of a fence? large game animals 2. 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 3. 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 Math-in-CTE Lesson Plan Template
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 on the perimeter of the pasture and the number of strands of wire, calculate the number of posts and the length of barbed wire needed to be purchased. 65 posts needed for fence 10 posts needed for brace So, let’s begin by creating a scale drawing of the pasture. Step 1 – Using graph paper, let each square Figure perimeter of pasture equal 4 ft. Remember to include the scale and (2)(96 ft) + (2)(160 ft) = 512 ft. Key. Step 2- Place posts at 8ft. intervals. Remember to take into account your gate. 512 ft – 8 ft = 504 ft Step 3- Draw in your gate Step 4 – Based on scale drawing, determine the 504 ft. X 5 = 2520 ft. number of posts needed to be purchased. Remember to take into account your horizontal To compare calculate either the unit price or set brace posts when answering this question. up a proportion.
Now, how can we figure out the amount of wire needed? TSC (Brainstorm- remind about 5 strands and gate) Posts Step 1- How much wire is needed for 1 strand? $140 / 25 = $5.60 How did you figure that out? 25 / 140 = 75 / X Step 2- Subtract the length of the gate from the 25X = (140) (75) perimeter. You have now found the wire needed to X = 10500 / 25 complete one strand. X = $420
Step 3- Find the total amount of wire needed for Wire all five strands. 400 yd X 3 ft / 1 yd =1200 ft 2520 ft / 1200 ft = 2.1 therefore you must purchase 3 rolls of barbed wire. (discuss Math-in-CTE Lesson Plan Template
Now let’s compare the cost of our materials from two wrapping of wire around corner posts) different retailers. 3 X $48.48 = $145.44 for wire Tractor Supply Company sells: 25 cedar posts for $140 McCoys 1 spool of barded wire that is 400 yd for $48.48 $85 /15 = $5.60
15 /$85 = 75 / X McCoy sells: 15X = ($85) (75) 15 cedar posts for $85 X = 6375 /15 1 spool of barded wire that is 400 yd for X = $425 $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) = 960 ft2 examples. Water trough area (4)(6)= 24 ft2 You decide to provide your calf a 2 foot deep 6’ X 4’ water trough . How much how many square feet of
Work through traditional math-in-CTE examples. You might see these same concepts in your math class. A. Find perimeter P = 2l + 2w 1. (12)(2) + (8)(2) = 40 ft. Jaime is building a rectangular dog run that is 12 ft by 8 ft. A. How many ft. of chain link fence is 2. Convert 36 in. into feet = 3 ft needed to build the dog run if you put in a 3. Subtract gate from perimeter 36 in. gate? 40 - 3 = 37 ft. B. If you are going to plant grass, how many square feet of grass is needed? B. A = lw C. If you are going to pour a 3 in. concrete 1. A = (12 X 8) slab instead of grass, how many cubic feet 2 of concrete do you need to order? 2. A = 96 ft C. V = lwh or V = Bh; B= lw See Perimeter and Area of Rectangles Worksheet 1. Convert 3 in. into feet. 1 ft = 12 in. 3 in. = ¼ ft or .25 ft. 2. V= (12)(8)(.25) 3. V = 24 ft3
Math-in-CTE Lesson Plan Template
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 group a different fence located on the school grounds. Extended activities: Each group will: Have the students build a scale model - measure the length and width to calculate of their fence. 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