Full Course

#### Description:

This collection includes resources that are used throughout the six projects of Curriki Geometry. Curriki is grateful for the tremendous support of our sponsor, AT&T Foundation. Our Team Curriki Geometry would not be possible if not for the tremendous contributions of the content contributors, editors, and reviewing team. Janet Pinto, Lead Curriculum Developer & Curriki CAO Sandy Gade, Editor Thom Markham, PBL Lead Aaron King, Geometry Consultant Welcome to Curriki Geometry, a project-based geometry course. This course offers six complete projects. All the projects are designed in a project-based learning (PBL) format. All Curriki Geometry projects have been created with several goals in mind: accessibility, customization, and student engagement—all while encouraging students toward high levels of academic achievement. In addition to specific CCSS high school geometry standards, the projects and activities are designed to address the Standards for Mathematical Practice, which describe types of expertise that mathematics educators at all levels should seek to develop in their students. How to Use Curriki Geometry Curriki Geometry has been specially created for you to use in the manner that suits your needs best. You have the option to use all the projects or only some projects in any order as supplements to your own curriculum. You can customize Curriki Geometry however works best for you. Projects Selling Geometry Designing a Winner What’s Your Angle, Pythagoras TED Talk: House of the Future The Art of Triangles How Random is My Life?

#### Subjects:

• Mathematics > General
• Mathematics > Geometry

#### Keywords:

PBL, problem-based learning, geometric theorems

English

#### Access Privileges:

Public - Available to anyone

#### Collections:

Geometry
Probability
Update Standards?

#### CCSS.Math.Content.HSG-CO.A.1: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSG-CO.A.2: Common Core State Standards for Mathematics

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).

#### CCSS.Math.Content.HSG-CO.A.3: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-CO.A.4: Common Core State Standards for Mathematics

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

#### CCSS.Math.Content.HSG-CO.A.5: Common Core State Standards for Mathematics

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

#### CCSS.Math.Content.HSG-CO.B.6: Common Core State Standards for Mathematics

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

#### CCSS.Math.Content.HSG-CO.B.7: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSG-CO.C.9: Common Core State Standards for Mathematics

Prove theorems about lines and angles.

#### CCSS.Math.Content.HSG-CO.D.12: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSG-CO.D.13: Common Core State Standards for Mathematics

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

#### CCSS.Math.Content.HSG-SRT.A.2: Common Core State Standards for Mathematics

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.

#### CCSS.Math.Content.HSG-SRT.A.3: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-SRT.B.5: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-SRT.C.6: Common Core State Standards for Mathematics

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

#### CCSS.Math.Content.HSG-SRT.C.7: Common Core State Standards for Mathematics

Explain and use the relationship between the sine and cosine of complementary angles.

#### CCSS.Math.Content.HSG-SRT.C.8: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-GPE.B.4: Common Core State Standards for Mathematics

Use coordinates to prove simple geometric theorems algebraically.

#### CCSS.Math.Content.HSG-GPE.B.7: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-GMD.A.3: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-MG.A.1: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-MG.A.2: Common Core State Standards for Mathematics

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

#### CCSS.Math.Content.HSG-MG.A.3: Common Core State Standards for Mathematics

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).?

#### CCSS.Math.Content.HSS-CP.A.1: Common Core State Standards for Mathematics

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

#### CCSS.Math.Content.HSS-CP.A.2: Common Core State Standards for Mathematics

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

#### CCSS.Math.Content.HSS-CP.A.4: Common Core State Standards for Mathematics

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

#### CCSS.Math.Content.HSS-CP.B.7: Common Core State Standards for Mathematics

Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

#### CCSS.Math.Content.HSS-CP.B.8: Common Core State Standards for Mathematics

(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

#### CCSS.Math.Content.HSS-MD.B.6: Common Core State Standards for Mathematics

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

#### CCSS.Math.Content.HSS-MD.B.7: Common Core State Standards for Mathematics

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

#### MA.9-12.G.1.1: Mathematics

Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments.

#### MA.9-12.G.1.2: Mathematics

State, use, and examine the validity of the converse, inverse, and contrapositive of "if-then" statements.

#### MA.9-12.G.1.3: Mathematics

Compare the properties of Euclidean geometry to non-Euclidean geometries (for example, elliptical geometry, as shown on the surface of a globe, does not uphold the parallel postulate).

#### MA.9-12.G.2.1: Mathematics

Use geometric tools (for example, protractor, compass, straight edge) to construct a variety of figures.

#### MA.9-12.G.2.2.a: Mathematics

Use the angle relationships formed by parallel lines cut by a transversal to solve problems.

#### MA.9-12.G.2.2.b: Mathematics

Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs.

#### MA.9-12.G.2.2.c: Mathematics

Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.

#### MA.9-12.G.2.3.a: Mathematics

Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).

#### MA.9-12.G.2.3.b: Mathematics

Apply the interior and exterior angle sum of convex polygons to solve problems, and verify using algebraic and deductive proofs.

#### MA.9-12.G.2.3.c: Mathematics

Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).

#### MA.9-12.G.2.3.d: Mathematics

Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each.

#### MA.9-12.G.2.4.a: Mathematics

Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs.

#### MA.9-12.G.2.4.b: Mathematics

Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

#### MA.9-12.G.2.5.a: Mathematics

Determine and verify the relationships of congruency of triangles, using algebraic and deductive proofs.

#### MA.9-12.G.2.5.b: Mathematics

Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

#### MA.9-12.G.2.6.a: Mathematics

Find angle measures and arc measures related to circles.

#### MA.9-12.G.2.6.b: Mathematics

Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle.

#### MA.9-12.G.3.1: Mathematics

Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles, and verify using algebraic and deductive proofs.

#### MA.9-12.G.3.2: Mathematics

Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems, and verify using algebraic and deductive proofs.

#### MA.9-12.G.3.3: Mathematics

Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems.

#### MA.9-12.G.3.4: Mathematics

Use the trigonometric ratios to find the area of a triangle.

#### MA.9-12.G.4.1.a: Mathematics

Identify, describe, and analyze polyhedra (for example, regular, decahedral).

#### MA.9-12.G.4.1.b: Mathematics

Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each.

#### MA.9-12.G.4.2.2: Mathematics

Similarity: Use ratios of similar 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

#### MA.9-12.G.4.3: Mathematics

Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings).

#### MA.9-12.G.5.1: Mathematics

Find the distance between two points; the midpoint of a segment; and calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

#### MA.9-12.G.5.2.a: Mathematics

Given a set of points determine the type of figure formed based on its properties.

#### MA.9-12.G.5.2.b: Mathematics

Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

#### MA.9-12.CCSS.Math.Content.HSG-CO.A.1: Mathematics

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.

#### MA.9-12.CCSS.Math.Content.HSG-CO.A.2: Mathematics

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).

#### MA.9-12.CCSS.Math.Content.HSG-CO.A.3: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-CO.A.4: Mathematics

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

#### MA.9-12.CCSS.Math.Content.HSG-CO.A.5: Mathematics

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

#### MA.9-12.CCSS.Math.Content.HSG-CO.B.6: Mathematics

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

#### MA.9-12.CCSS.Math.Content.HSG-CO.B.7: Mathematics

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.

#### MA.9-12.CCSS.Math.Content.HSG-CO.C.9: Mathematics

Prove theorems about lines and angles.

#### MA.9-12.CCSS.Math.Content.HSG-CO.D.12: Mathematics

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

#### MA.9-12.CCSS.Math.Content.HSG-CO.D.13: Mathematics

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

#### MA.9-12.CCSS.Math.Content.HSG-SRT.A.2: Mathematics

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.

#### MA.9-12.CCSS.Math.Content.HSG-SRT.A.3: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-SRT.B.5: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-SRT.C.6: Mathematics

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

#### MA.9-12.CCSS.Math.Content.HSG-SRT.C.7: Mathematics

Explain and use the relationship between the sine and cosine of complementary angles.

#### MA.9-12.CCSS.Math.Content.HSG-SRT.C.8: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-GPE.B.4: Mathematics

Use coordinates to prove simple geometric theorems algebraically.

#### MA.9-12.CCSS.Math.Content.HSG-GPE.B.7: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-GMD.A.3: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-MG.A.1: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-MG.A.2: Mathematics

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

#### MA.9-12.CCSS.Math.Content.HSG-MG.A.3: Mathematics

Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

#### MA.9-12.CCSS.Math.Content.HSS-CP.A.1: Mathematics

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (?or,? ?and,? ?not?).

#### MA.9-12.CCSS.Math.Content.HSS-CP.A.2: Mathematics

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

#### MA.9-12.CCSS.Math.Content.HSS-CP.A.4: Mathematics

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

#### MA.9-12.CCSS.Math.Content.HSS-CP.B.7: Mathematics

Apply the Addition Rule, P(A or B) = P(A) + P(B) ? P(A and B), and interpret the answer in terms of the model.

#### MA.9-12.CCSS.Math.Content.HSS-CP.B.8: Mathematics

Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

#### MA.9-12.CCSS.Math.Content.HSS-MD.B.6: Mathematics

Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

#### MA.9-12.CCSS.Math.Content.HSS-MD.B.7: Mathematics

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Curriki Rating
On a scale of 0 to 3
3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2016-01-25.

#### Component Ratings:

Standards Alignment: 3
Subject Matter: 3
Support Steaching: 3
Assessments Quality: 3
Deeper Learning: 3