Zooming In On Figures
Type of Unit: Concept; Project
Length of Unit: 18 days and 5 days for project
Students should be able to:
- Find the area of triangles and special quadrilaterals.
- Use nets composed of triangles and rectangles in order to find the surface area of solids.
- Find the volume of right rectangular prisms.
- Solve proportions.
- After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
- The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
- The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
- The unit ends with a unit examination and project presentations.
- Mathematics, Geometry
- Middle School
· Scissors (one pair for each student)
· Rulers (one for each student)
· Print copies of Area of Regular Polygons (one for each student). Print out, cut apart, and laminate if desired.
- Graphing chart paper that is 12-inch by 12-inch with 1-inch spacing (one for each student)
- A 12-inch by 12-inch piece of cardboard (one for each student)
- Glue (one for each pair of students)
- Ruler (one for each student)
· String (several spools for the class)
· Rulers (one for each student)
· Scissors (one for each student)
Ruler (one for each student)
· Centimeter grid paper (one for each student)
· Ruler (one for each student)
· Compass (one for each student)
· Base sheets for project (one for each student)
· Square foot cardboard pieces to mount base sheets on (one for each student)
· Rulers (one for each pair of students)
· Protractors (one for each pair of students)
Students’ centimeter grid layout to draw the nets
· Origami cubes
· Centimeter grid layout
· 1-inch grid paper
· Scissors, tape, protractors (available as needed)
Lesson 1House Plans
Lesson 3Building with Polygons
Lesson 4Measuring Circles
Lesson 5Area of a Circle
Lesson 7Changing Scale
Lesson 8Applying Scale to Project
Lesson 9Self Check Exercise
Lesson 10Gallery Problems Exercise
Lesson 11Calculating Volume
Lesson 12Applying The Volume Formula
Lesson 13Exploring Cross-Sections
Lesson 14Surface Area Of Prisms
Lesson 16Unit Review
Lesson 17Self Check Exercise
Lesson 18Gallery Problems Exercise
Lesson 19Unit Concepts Project Presentation
Lesson 20Project Presentations (Feedback)