Essential Unit 9 (E09)

GEOMETRY

(SECONDARY)

ESSENTIAL UNIT 9 (E09)

(Area, Perimeter, Circumference Polyhedra)

(July 2013)

Unit Statement: Geometric Formulas in relation to area, perimeter and circumference are developed. The properties of solids are established and applied to their surface areas and volumes, plus the ratios of similarity in areas and volumes are used to solve problems.

Essential Outcomes: (these must be assessed for mastery)

Problem solving and higher order thinking components are essential for ‘A’ level mastery. Each outcome can contain problem solving and higher order thinking components (as found in suggested text).

1. The Student Will apply the formulas for the perimeter and areas of triangles and special quadrilaterals (10.1 pp 677 - 685).

2. TSW apply the formulas for area of polygons and circles and the circumference of circles (10.2 pp.688 - 693).

3. TSW find the area of composite figures using the Area Addition Postulate (10.3 pp. 694 - 700).

4. TSW find the perimeters and areas of figures in a coordinate plane (10.4 pp. 704 - 709).

5. TSW solve the effects of perimeter and area when one or more dimensions of a figure are changed (10.5 pp. 710 - 715).

6. TSW calculate geometric probabilities and predict results in real-world situations (10.6 pp. 718 - 724).

7. TSW use nets and cross sections and classify three-dimensional figures according to their properties (11.1 pp. 742 - 748).

8. TSW apply the formulas for the volumes of prisms and cylinders (11.2 pp. 749 - 756).

9. TSW apply the formulas for the volumes of pyramids and cones (11.3 pp. 757 - 764).

10. TSW apply the formulas for the volume and surface area of a sphere (11.4 pp. 766 - 773).

Introduced and Practiced Outcomes: (taught not assessed)

1. The Student Will find the theoretical probability of the likeliness an event will occur (10.5 pp. 716 - 717).

Key Terms and Concepts:

center of regular polygon geometric probability central angle of regular polygon

apothem circle center of circle

composite figure center of sphere face

radius of sphere cone great circle

sphere cross section hemisphere

vertex cube net

volume cylinder prism

edge pyramid

Suggested Assessment Tools and Strategies:

Attached Rubric or teacher generated rubric that assesses ALL essential outcomes (TSWs).

Suggested Resources:

Holt McDougal Geometry, Chapter 10, Sections 1 - 6.

Holt McDougal Geometry, Chapter 11, Sections 1 - 4.

Holt McDougal Geometry, Problem Solving Workbook

Holt McDougal Geometry, Practice Worksheets

Holt McDougal Geometry, Reading Strategies

Holt McDougal Geometry, Reteach Worksheets

Holt McDougal Geometry, Challenge Worksheets

Holt McDougal Geometry, Assessment Resources

Technology Links

Holt McDougal Geometry, Online Edition, 6-year subscription

Holt McDougal Geometry, Interactive Answers and Solutions CD-ROM

Holt McDougal Geometry, Lesson Tutorial Videos DVD-ROM

Holt McDougal Geometry, Teacher One-Stop DVD

On Core Mathematics Deluxe Eamview Grades 6-12 CD-ROM

On Core Mathematics High School Activity Generator CD-ROM

Follett Destiny WebPath Express (found on school’s automated library system)

Tenmarks www.tenmarks.com/

Khan Academy https://www.khanacademy.org/

PhET Simulations http://phet.colorado.edu/en/simulations/category/math

EVALUATION RUBRIC FOUND ON FOLLOWING PAGE…………………….UNIT EVALUATION RUBRIC

Geometry

Essential Unit 9 (E09)

· To receive a ‘B’, the student must show ‘B’ level mastery on all ten TSW’s.

· To receive an ‘A’, the student must show ‘A’ level mastery in at least 6 of the 10 available TSW’s and ‘B’ level mastery on all of the remaining TSW’s.

TSW / ‘A’ LEVEL / ‘B’ LEVEL / Notes
1- apply the formulas for the perimeter and areas of triangles and special quadrilaterals. / The student is able to develop and prove the formulas for the perimeter and areas of triangles and special quadrilaterals. / The student is able to apply the formulas for the perimeter and areas of triangles and special quadrilaterals.
2- apply the formulas for area of polygons and circles and the circumference of circles. / The student is able to expand the formula for the area of a regular n-gon to show that it approaches the formula for the area of a circle as n gets larger. / The student is able to apply the formulas for area of polygons and circles and the circumference of circles.
3- find the area of composite figures using the Area Addition Postulate. / The student is able to use the Area Addition Postulate to estimate the areas of irregular shapes. / The student can find the area of composite figures using the Area Addition Postulate.
4- find the perimeters and areas of figures in a coordinate plane. / The student is able to predict and approximate the area between curved functions and the x-axis. / The student can find the perimeters and areas of figures in a coordinate plane.
5- solve the effects of perimeter and area when one or more dimensions of a two-dimensional figure are changed. / The student can analyze and solve complex story problems involving changing areas of two-dimensional figures. / The student can solve the effects of perimeter and area when one or more dimensions of a two-dimensional figure are changed.
6. calculate geometric probabilities and predict results. / The student is able to calculate and justify geometric probabilities and predict results in multifaceted, real-world situations. / The student is able to calculate geometric probabilities and predict results.
7. use nets and cross sections and classify three-dimensional figures according to their properties. / The student is able to draw three-dimensional figures given a list of properties the figure must have. / The student is able to use nets and cross sections and classify three-dimensional figures according to their properties.
8. apply the formulas for the volumes of prisms and cylinders. / The student can solve for the lengths of the radius and height of a cylinder given its volume and surface area. / The student is able to apply the formulas for the volumes of prisms and cylinders.
9. apply the formulas for the volumes of pyramids and cones. / The student can find the volume of a pyramid given the coordinates of the vertices three-dimensionally. / The student is able to apply the formulas for the volumes of pyramids and cones.
10. apply the formulas for the volume and surface area of a sphere. / The student is able to find the ratio between the volumes of a cylinder and a sphere inscribed in it. / The student is able to apply the formulas for the volume and surface area of a sphere.

QSI GEOMETRY SEC E09