Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will be able to:
- calculate percent change
- calculate the volume of a right circular cone and use it to solve real-world and mathematical problems
- calculate the volume of a truncated right circular cone (conical frustum) and use it to solve real-world and mathematical problems
- calculate the lateral surface area of a right circular cone and use it to solve real-world and mathematical problems
- calculate the lateral surface area of a truncated right circular cone (conical frustum) and use it to solve real-world and mathematical problems
- use geometric shapes (cones and conical frustum), their measures, and their properties to describe objects
- translate quantitative or technical information expressed in words in a text into visual form
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should know or review:
MAFS.7.RP.1.3 - Use proportional relationships to solve multi-step ratio and percent problems (percent increase and decrease).
MAFS.8.G.3.9 - Know the formula for the volume of cones and use it to solve real-world and mathematical problems.
- order of operations
- conversion between inches and feet, 12 inches = 1 foot, 144 square inches = 1 square foot, and 1728 cubic inches = 1 cubic foot
- vocabulary and relationships associated with right circular cones
- the definition, appearance, and characteristics of a right circular cone
- the formula to calculate lateral surface area of a right circular cone
- how to use graph paper and a ruler (straightedge) to create and label scale drawings
- how to convert among ratios, decimals, and percents
Guiding Questions: What are the guiding questions for this lesson?
- How do we determine/calculate the percent something has changed? (difference between original value and new value compared to original value)
- What is the formula for calculating the volume of a right circular cone?
- How is a truncated right circular cone (conical frustum) different from a right circular cone? (the pointy part or tip is removed; there are two circular bases)
- What is the formula for calculating the volume of a truncated right circular cone (conical frustum)?
- What are the similarities and differences in the formulas for volume of a right circular cone and a truncated right circular cone (conical frustum)? (both involve 1/3, pi, radius and height, but the truncated cone has two radii due to the presence of two circular bases)
- What is the formula for calculating the lateral surface area of a right circular cone?
- What is the formula for calculating the lateral surface area of a truncated right circular cone (conical frustum)?
- What are the similarities and differences in the formulas for lateral surface area of a right circular cone and a truncated right circular cone (conical frustum)? (both involve pi, radius, and slant height; but the truncated cone has two radii due to the presence of two circular bases; the formula for the truncated cone is more complex; and the Pythagorean Theorem is used to calculate l, the slant height)
- What are the known and unknown values and variables for this situation and how have you defined and represented them? (answers will vary; students should be encouraged to organize and categorize information)
- What is a good scale factor for this drawing? (answers will vary; students should be encouraged to consider range of dimensions)
- What unit of measure is best for this situation and why? (possible answers include: inches, square inches, cubic inches, feet, square feet, and cubic feet)
- How does adding mortar to a brick change its dimensions? (the height, width, and length are all affected; the thickness of the mortar must be added to the height, width, and length to account for a 3-dimensional change in volume)
Teaching Phase: How will the teacher present the concept or skill to students?
The teacher may wish to re-distribute marked (not graded) copies of the formative assessment (which was administered during a previous session) to review students' strengths (provide praise) and weaknesses, facilitate activation of prior knowledge, and/or serve as a basis for remediation, reinforcement, and discussion of theoretical concepts and calculations prior to engagement in the real-world problem solving tasks.
If the Cape Florida Lighthouse - Reference Sheet.pdf is used, lead students through each formula. Be sure to discuss variables, order of operations, value to be used to approximate pi, and accuracy, presentation and unit of measure for final numerical answer.
The teacher may discover that some students are not familiar with the concept of, or formulas for lateral surface area of, a right circular cone. This may need to be taught via review of the formative assessment or by doing a few sample problems on the board. Labeled diagrams of right circular cones should accompany problems.
The teacher can set the scene by asking students to close their eyes and visualize a lighthouse. The teacher may pose the questions, "What do you know about lighthouses? Has anyone ever visited a lighthouse? How and why were lighthouses built?" and solicit student knowledge and experiences especially with respect to lighthouses on the east coast of Florida.
The teacher will distribute the Activity 1 worksheet and ensure that students have graph paper, 12" rulers (straightedges), and calculators, then lead students through the tasks either as a whole class or in cooperative learning groups (teacher's choice). The teacher will pose and discuss answers to the Guiding Questions as needed. The teacher will circulate around the room and provide clarification, assistance, and praise. Discussion, debriefing, and consensus should occur. Misconceptions such as inconsistent scale within a drawing, improper substitution of values into formulas, non-adherence to order of operations, and inattentiveness to units of measure should be monitored and clarified.
Students may not be familiar with the terms brick and mortar. The teacher may have to clarify, illustrate, demonstrate, and facilitate a whole group discussion related to this concept and what it "looks" like when mortar is applied to a brick as referenced in question 4. Students may use manipulatives (centimeter cubes, folded paper nets, small boxes, etc.) to model a brick with and without mortar. Students should be guided to think about the appearance of a structure made of bricks and mortar. Emphasis upon how the mortar affects the dimensionality of the brick (increase to length, width, and height) in three directions is important for calculation of volume. Additionally, teacher may want to do an Internet search for an appropriate image of "bricks and mortar."
The attached PowerPoint.pptx may be used as a visual aid during or at the conclusion of Activity 1.
Guided Practice: What activities or exercises will the students complete with teacher guidance?
The teacher will distribute Activity 2 and either direct students to complete it individually, with a partner, in a triad, or as a whole class (teacher's choice).
The teacher will pose and discuss answers to Guiding Questions as needed.
The teacher will circulate around the room and provide clarification, assistance, and praise. Students should be encouraged to employ Mathematical Practices to persevere and use appropriate tools strategically. Discussion, debriefing, and consensus should occur.
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
The teacher will distribute the summative assessment and direct students to complete it individually/independently. Students will submit their work and solutions, and provide justifications. The evaluation scheme will be at the teacher's discretion.
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
1. The teacher may facilitate whole class discussion to compare and contrast the Cape Florida and Jupiter Inlet lighthouses in both general and mathematical terms. Format, structure, and method of execution are determined by teacher's preference.
- Graphic organizers such as a Venn diagram, two-column list, or web mapping may be used.
- Possible similarities: both made of brick and cement (mortar), both classified by the U.S. Coast Guard as conical towers, both on east coast of Florida peninsula, both worked on by George G. Meade, both are among the oldest structures in their respective counties (Miami-Dade and Palm Beach)
- Possible differences: age, color, height, volume, profile, number of bricks, and location
2. The teacher may re-administer the formative assessment as a "post-test" or "final survey."
- Have students compare their performance on the second iteration to that on the "pre-test"/"initial survey."
- Ask students to cite, either in writing or verbally, specific instances within the lesson where targeted skills were applied.
The teacher will use the Summative Assessment.pdf to determine if students demonstrate mastery of the learning goals and are able to transfer concepts and apply skills to a new situation (Jupiter Inlet Lighthouse) similar to that explored in the body of the lesson (Cape Florida Lighthouse).
The teacher will distribute the Formative Assessment and direct students to complete it individually. The teacher should inform students this is a "pre-test" or "initial survey" so they are not expected to know how to do everything on it, and responses of "I do not know" or "I am unsure" are acceptable.
The teacher will use the formative assessment instrument to gather information about students' initial skill sets. An item analysis done on the results of the formative assessment will determine the classes' strengths and weaknesses. The teacher will tailor the lesson and provide instruction, practice, feedback, clarification, assistance, and remediation for the class and individual students accordingly throughout the lesson.
It is recommended that the formative assessment be done a day or more before activities 1 and 2 as the teacher needs time to analyze student performance on prerequisite skills and develop a plan of action.
Feedback to Students
Students will receive feedback via internal, oral, and written methods throughout the lesson from themselves, the teacher, and classmates as follows:
- Formative Assessment - self (internal) and teacher (written)
- Activity 1 - self (internal), classmates (oral), and teacher (oral)
- Activity 2 - self (internal), classmates (oral), and teacher (oral)
- Summative Assessment - teacher (written)