Math-in-CTE Lesson Plan

Lesson Title: Smokin’ / Lesson #: AM06
Occupational Area: Agriculture
CTE Concept(s): Use a tape measure, construct projects and equipment using an arc welder.
Math Concepts: Percent, computation in context, convert measurement units, calculating, perimeter/area/volume of a rectangle, circle, triangle
Lesson Objective: / Student will demonstrate a working knowledge of how to:
·  Apply a wide variety of problem-solving strategies to solve problems from within and outside mathematics. (ie: Volume, diameter, radius, circumference, and percentage)
·  Identify the problem from a described situation, determine the necessary data and apply appropriate problem-solving strategies. (using appropriate formulas to find volume and circumference)
·  Use applications in agriculture power and technology, while recognizing it in other contexts.
Supplies Needed: / Pop cans, Milk Jugs, 55 gallon barrels,PVC pipe various sizes, pipe cutters (hacksaw), tape. Useful texts:
Mitchell, N. H. (2004). Mathematical applications in agriculture. Clifton Park, NY: Thomson, Delmar Learning.
Nichols, E. D., Schwartz, S. L. (1998). Mathematics dictionary and handbook. (3rd ed.). Honesdale, PA: Nichols Schwartz Publishing. (ISBN 1-882269-07-1)
Link to Accompanying Materials: / Agriculture Mechanics AM06 Downloads
The "7 Elements" / Teacher Notes
(and answer key)
1. Introduce the CTE lesson.
DJC Barbecue wants us to build a new smoker on a 4’ X 8’ trailer. They are willing to donate the material and make a small donation to the Chapter upon completion. Due to a limited budget and restricted funds, we are limited to a pipe size of 12” x 36”.
Remember that the hot box will equal a total 40% of the cooking box.
2. Assess students’ math awareness as it relates to the CTE lesson.
What is volume?
Can you find the volume of a column?
Can you use the same formula for square and round tubing?
Have you ever used or seen this procedure before?
Why are square units used when measuring volume area?
In your own words give a definition of the volume of a column?
Dividing a large problem to smaller steps is a good problem solving strategy. / Have questions on projector. Section class into small groups and have each group answer the questions to the best of their knowledge.
Volume: space inside, capacity to hold
Volume of Cylinder: Pi∙R2∙L (Pi==3.14, R=Radius, L=Length)
Circumference: 2R = d (d=diameter)
Pythagorean theorem: a2 + b2 = c2 (for right triangles (900))
Give students a copy of definitions from math dictionary.
3. Work through the math example embedded in the CTE lesson.
Pipe Dimensions = 3.5” x 1’
What length would you have to cut off to have your hot box equal 40% of your cooking box?
Remember to convert feet to inches to keep like units of measurement.
Volume = Pi x Radius Squared x length
= ∙ R2 ∙ L
= 3.14 ∙ (1.75 in) 2 ∙ 12 in lg. pipe
= 115.4 cu in
Total volume of pipe = 115.4 cubic inches of volume
This box = x
Cooking
Box

Hot Box
This box = .4x
What formula do you need to solve this problem?
.4x + x = Total Length
1.4x = 12”
x = 8.57” Cooking box
What is the length of the hot box? 3.43”
Can you figure volume of new lengths of pipe?
3.14 (1.75 in) 2 (8.57 in) = 82.41 in cubed cooking box
3.14 (1.75 in) 2 (3.43 in) = 32.98 in cubed hot box
Does this rate meet the minimum required for smoker to function properly?
Hot box volume over Cooking box volume
32.98 in cubed / 82.41 in cubed = 40%.
Yes, it meets volume requirements. / Here is where the pieces of PVC pipe are used to represent the starting material and allows you to incorporate hands-on CTE and mathematics.
Volume of a rectangular pipe or box is found with this formula:
Length x Width x Height
(L ∙ W ∙ H)
Conversion formula:
Convert 6.25 miles to inches
6.25 mi x 5280 ft x 12 in
1 mi 1 ft
= 396,000 in
4. Work through related, contextual math-in-CTE examples.
Mathematical Applications in Agriculture book problems from ex. 2-3, prob. 5 & 6 pg 30. / Smokin’ worksheet.
5. Work through traditional math examples.
Find the volume of these figures.
A cylinder with a radius of 2 ft. and a length of 48 in.
A cylinder with a diameter of 18 in. and a length of 5 ft. / Practice volume & area problems.
6. Students demonstrate their understanding.
Under supervised instruction the students will properly layout and start to build the smoker.
7. Formal assessment.
Additional contextual and traditional problems on an exam. / See Smokin’ Test.

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