LESSON PLAN 1 of 1
Name: Robert Duncan
Title of lesson: Using Similar Triangles to find Volume
Date of lesson:
Length of lesson:
One 55 minute period
Description of the class: Geometry
Course Title: Geometry
Grade level: 9-10
Source of the lesson: Original
TEKS addressed: ¤111.34. Geometry
(a) Basic understandings.
(1) Foundation concepts for high school mathematics
(2) Geometric thinking and spatial reasoning.
(3) Geometric figures and their properties.
4) The relationship between geometry, other mathematics, and other disciplines.
(5) Tools for geometric thinking.
(b) Geometric structure: knowledge and skills and performance descriptions.
(2) The student analyzes geometric relationships in order to make and verify conjectures.
(A) The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships.
(B) The student makes and verifies conjectures about angles, lines, polygons, circles, and three-dimensional figures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
(3) The student understands the importance of logical reasoning, justification, and proof in mathematics. Following are performance descriptions.
(B) The student constructs and justifies statements about geometric figures and their properties.
(4) The student uses a variety of representations to describe geometric relationships and solve problems.
(c) Geometric patterns: knowledge and skills and performance descriptions.
(1) The student uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles.
(d) Dimensionality and the geometry of location: knowledge and skills and performance descriptions.
(1) The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and uses these representations to solve problems. Following are performance descriptions.
(C) The student uses top, front, side, and corner views of three-dimensional objects to create accurate and complete representations and solve problems.
(e) Congruence and the geometry of size: knowledge and skills and performance descriptions.
(1) The student extends measurement concepts to find area, perimeter, and volume in problem situations. Following are performance descriptions.
(C) The student develops, extends, and uses the Pythagorean Theorem.
(D) The student finds surface areas and volumes of prisms, pyramids, spheres, cones, and cylinders in problem situations.
(2) The student analyzes properties and describes relationships in geometric figures. Following are performance descriptions.
(D) The student analyzes the characteristics of three-dimensional figures and their component parts.
(f) Similarity and the geometry of shape: knowledge and skills and performance descriptions.
(1) The student uses similarity properties and transformations to explore and justify conjectures about geometric figures.
(2) The student uses ratios to solve problems involving similar figures.
(3) In a variety of ways, the student develops, applies, and justifies triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples.
(4) The student describes the effect on perimeter, area, and volume when length, width, or height of a three-dimensional solid is changed and applies this idea in solving problems.
The Lesson:
Students will be able to recognize and work with situations where similar right triangles can be used to find unknown distances. Students will be able to find the volume of a truncated right square pyramid
Students will be able to:
III. Resources, materials and supplies needed
Attached origami diagram
Ruler
IV. Supplementary materials, handouts.
Five-E Organization
Teacher Does Student Does
| Engage: Learning Experience Students receive a new origami model to fold. |
Student Activity Students work individually or in groups to fold the design from the given diagram |
Evaluate
| Explore: Learning Experience(s) Ask questions about what this kind of shape is called; what properties it has; what we can measure about it; what we can find from these measurements. Students work in groups to apply what they have learned about similar triangles to determine how they can find the volume of the truncated pyramid. |
Student Activity Discuss the design they have made and strategies they might use to find the volume. Students find and measure the necessary parts of two similar triangles, one of which has a side that is also the height of the non-truncated pyramid this model is a part of. |
Evaluate
| Explain: Learning Experience(s) Review the procedure with the class or have groups present-discuss their processes with the class. Point out that many objects in the real world are not platonic solids, but that we can still discover information about them like we did with this truncated pyramid. |
Student Activity Compare the procedure discussed or presented with their own. |
Evaluate
| Extend / Elaborate: Learning Experience(s) Ask students to predict what would happen if a different sized piece of paper were used to make the pyramid. |
Student Activity Students are given various sized sheets of paper to make different sized truncated pyramids to explore the next class day. |
Evaluate