Objective

Assessment

End of Year Assessment

1 teachers like this lesson

Print Lesson

Objective

SWBAT demonstrate their understanding of the concepts learned in the course.

Big Idea

This is a comprehensive assessment of all content learned to date.

Lesson Author

Marisa Laks

New York, NY

Grade Level

Tenth grade

Subjects

Math

Geometry

Proofs

Triangles

Similarity and Congruence

Trigonometric functions

Standards

HSG-CO.A.1

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

HSG-CO.A.2

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

HSG-CO.A.3

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

HSG-CO.B.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

HSG-CO.C.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

HSG-CO.C.11

Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

HSG-CO.D.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

HSG-SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor:

HSG-SRT.A.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

HSG-SRT.A.3

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

HSG-SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

HSG-SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.*

HSG-C.A.2

Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

HSG-GPE.B.4

Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

HSG-GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*

HSG-GMD.A.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

HSG-GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*

HSG-MG.A.1

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

HSG-MG.A.2

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Assessment

90 minutes

Gallery of Student Work

Geometric Modeling Student Work.jpg

AA Similarity Student Work.jpg

Cavelieri's Principle Student Work.jpeg

Trigonometry Student Work.jpg

Coordinate Geometry Student Work.jpg

Several times throughout the year, my students take interim assessment. These assessments cover material from each unit to date.

This assessment contains 38 questions, 28 multiple choice, 6 short answer questions worth 2 points each, 3 questions worth 4 points each, and 1 question worth 6 points. I grade the exam on using a scale depending on how the students do. It should take the students approximately 90 minutes. Students need a compass and straight edge for the constructions.

Interim assessments help teachers gather information about what their students know and can be used to inform teaching. If I notice many students difficulty with specific topics even after the assessment, I build in extra practice into future lessons.

In my school, we have time set aside for Interim Assessments; however, this assessment can be split into two lessons. I usually average the students' grades on the assessment into their semester grade, but it can also be used strictly as a formative assessment to show student progress.

Previous Lesson

Next Lesson

6th Grade Science » Density