Geometry H Unit Outline and Lesson Plans

All lesson plans are in the form of daily agendas located on our Google Classroom. The slides with agendas are provided below. 

In addition, a unit breakdown is provided with extra details. 

Unit 0: Data, Probability, Statistical Reasoning, and Equations Review

Relevance:

In this Mini-Unit Students will:

Gather and represent quantitative data from classmates to create scatter plots and analyze trends.

Use class categorical data to create and analyze Venn diagrams and frequency tables.

Review solving equations to help with future content in this course.

By completing these tasks, students are studying probability structures which will enhance students’ ability to organize information and improve decision making. 

Standards Covered During Unit:

GS.DPSR.1.1  Represent data for two quantitative variables on a scatterplot and describe how the variables are related. 

GS.DPSR.1.2  Use two representative points from the data to find an approximate line of fit and compare it to the line of best fit. 

GS.DPSR.1.3  Conduct an investigation for a statistical question, interpret statistical significance in the context of a situation, and answer investigative questions appropriately. 

GS.DPSR.2.1  Distinguish between correlation and causation. 

GS.DPSR.3.1  Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events. 

Unit 1: Foundations of Geometry

Project: 

⚔️ Geometry Guild: The Battle of Paper Keep

Your class has been recruited into the Geometry Guild, sworn to defend Paper Keep.

Each squad must design and test paper arsenal tools that demonstrate geometric concepts such as line symmetry and rotational symmetry, then train with them in math-based challenges. 

Relevance:

Students will learn the basic skills and vocabulary terms necessary for success with the Geometry Curriculum in this unit. Students will work with angle and segment formulas. Students will learn how to correctly label figures and use correct notation when writing geometric statements. There will be a brief review of polygons and symmetry in figures also in this unit. 

The elements of the project will allow the students to work with some of these standards in an engaging and hands-on way that is  geometry-driven but still keeps with the “training for battle” storyline of the project as a whole. 

Standards Covered During Unit:

GS.MGSR.3.1  Identify types of symmetry of polygons, including line, point, rotational, and self-congruence, and use symmetry to analyze mathematical situations. 

GS.MGSR.5.1  Justify and apply the attributes of angle relationships/lines in mathematical and real-world situations. 

GS.PAFR.3.2  Determine distance and midpoint of segments in a coordinate plane to find areas of triangles and quadrilaterals, when given coordinates

Unit 2: Transformations

Project: None

Relevance:

Students will learn how to see relationships between figures on a coordinate grid. These lessons will help: reinforce the student's ability to graph figures, label points appropriately, and determine what transformations make figures congruent or similar. This knowledge will help the students when we move into our units on Congruent and Similar Figures. 

Standards Covered During Unit:

GS.MGSR.2.1  Describe the results of transformations on a given figure using geometric terminology from the definitions of the transformations. 

GS.MGSR.2.2  Describe and apply a sequence of transformations that maps a preimage onto its image. 

GS.MGSR.4.1  Demonstrate experimentally the properties of dilations given by a center and a scale factor.

GS.MGSR.4.2  Justify experimentally that a dilation of a line segment is longer or shorter, given the ratio. 

Unit 2: Lines

Project: City Map

Relevance:

Students will learn about parallel line angle relationships during this unit and be tested on mastery. Parallel line angle relationships show up in other units in Geometry and then again in PreCalculus. Students need to be comfortable with how these lines and angle relationships can help them solve various problems. 

Standards Covered During Unit:

GS.PAFR.2.2  Analyze slopes of lines to determine whether lines are parallel, perpendicular, or neither. 

GS.PAFR.2.3  Determine the equation of a line passing through a given point that is parallel or perpendicular to a given line. 

Unit 3A: Triangles Introduction and Congruence

Project: Mission 3: Watch Towers

Relevance:

Students will review various triangle content throughout the unit that will take what they learned in middle school classes and move the questions to the next level. There will be a focus on how to use triangle information to solve problems and comparing two triangles to determine if the triangles are congruent. Students will learn how to prove triangles are congruent and use this knowledge to complete Mission 3. 

Students have previously developed base camps on the island Terra Novus and now they need to beef up their security for their section of the island. They don't know who to trust. They will be tasked with creating watch towers to add a protective layer to their camp layout using triangle trusses in the build design. 

Standards Covered During Unit:

GS.PAFR.3.1  Use coordinates to prove simple geometric theorems algebraically. 

GS.MGSR.5.1  Justify and apply the attributes of angle relationships/lines in mathematical and real-world situations. 

GS.MGSR.5.2  Apply the attributes of triangles in mathematical and real-world situations. 

GS.MGSR.3.2  Demonstrate that triangles and quadrilaterals are congruent by a combination of translations, rotations, and reflections. 

GS.MGSR.3.3  Recognize the criteria for showing triangles are congruent using a sequence of rigid motions that map one triangle to another and justify that the two triangles are congruent by applying the Side-SideSide, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, and Hypotenuse-Leg congruence conditions. 

Unit 3B: Triangle Similarity (skipped for now)

Project: 

Relevance:

Students will 

Standards Covered During Unit:

GS.MGSR.4.3  Recognize that the criteria for showing triangles are similar using a similarity transformation that maps one figure to the other and justify the two triangles are similar by applying the Angle-Angle, SideSide-Side, and Side-Angle-Side similarity conditions. 

Unit 4: Quadrilaterals 

Project: Drone in Disguise

Relevance:

Students will learn about the various quadrilaterials and their properties while in class. If there is time in the nine weeks, the students will create more security features for their part of Terra Novus including a drone that will be disguised as a kite. 

Standards Covered During Unit:

GS.MGSR.3.2  Demonstrate that triangles and quadrilaterals are congruent by a combination of translations, rotations, and reflections. 

GS.MGSR.5.3  Apply the attributes of quadrilaterals, including diagonals, sides, and angles, to prove that a given quadrilateral is a parallelogram in mathematical and realworld situations. 

GS.PAFR.3.1  Use coordinates to prove simple geometric theorems algebraically. 

Unit 5: Surface Area & Volume

Project: 

Relevance:

Students will 

Standards Covered During Unit:

GS.PAFR.1.1  Discover and apply the formulas for the length of an arc and the area of a sector in a circle to develop mathematical models and solve mathematical and realworld situations. 

GS.PAFR.1.2  Analyze and apply the derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone to model real phenomena and solve mathematical and real-world situations.

GS.PAFR.2.1  Apply surface area and volume formulas for prisms, cylinders, pyramids, cones, spheres, and/or compositions of figures to solve problems and justify results. 

GS.MGSR.1.1  Apply area and volume formulas of two- and three-dimensional figures to solve real-world situations. 

GS.MGSR.1.2  Identify the shape of a two-dimensional cross-section of a three-dimensional figure. 

GS.MGSR.1.3  Use cross-sections of three-dimensional figures to model and solve mathematical and real-world situations. 

Unit 7: Right Triangles with an Introduction to Trigonometry

Project: 

Relevance:

Students will 

Standards Covered During Unit:

GS.NR.1.1  Rewrite numerical expressions of irrational and rational numbers involving radicals, including addition, subtraction, multiplication, and division, to recognize geometric patterns. 

GS.MGSR.1.1  Apply area and volume formulas of two- and three-dimensional figures to solve real-world situations. 

GS.MGSR.6.1  Discover and apply the converse of the Pythagorean Theorem. 

GS.MGSR.6.2  Discover and apply the constant ratios of the sides in 30-60-90 and 45-45-90 right triangles. 

GS.MGSR.6.3  Define the trigonometric ratios using the properties of similar right triangles. 

GS.MGSR.6.4  Determine the sine, cosine, and tangent of an acute angle in a right triangle in the context of mathematical and real-world situations. 

GS.MGSR.6.5  Apply trigonometric ratios (sine, cosine, tangent) and the Pythagorean Theorem to solve right triangle problems in real-life situations. 

Unit 8: Circles

Project: 

Relevance:

Students will 

Standards Covered During Unit:

GS.MGSR.7.1  Use angle and segment relationships in circles to solve mathematical and realworld situations. 

GS.MGSR.7.2  Investigate and apply relationships in circles, inscribed angles, radii, secants, and chords; among inscribed angles, central angles, and circumscribed angles; and between radii and tangents to circles.