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2022 Geometry Learning Progression

Page history last edited by Brigit Minden 10 months, 3 weeks ago

Welcome to the learning progression for Geometry. This progression incorporates the overall topics of this grade-level's mathematics and is formatted with Overarching Questions, Essential Questions, and Big Ideas for each unit. This progression model takes the work of bundling standards to the next level by grouping together grade-level concepts in the Big Ideas sections. The Big Ideas are designed to represent the critical mathematics of this grade level in a manner that is more coherent and productive as a guide for planning instruction, assessment, and intervention. Big Ideas are for progression and planning and are not a replacement for the OAS-M objectives.

Click on the unit numbers below to see essential understandings, student activities, and suggested sequencing.

The use of an asterisk (*) indicates an objective is repeated in another unit or an objective that is partially taught in a unit and will be taught in its entirety in a later unit. The parts of the objective that will be taught in a later unit is indicated by the “strikethroughs.” Occasionally, new words are added to the objective to ensure the objective still makes sense considering the strikethroughs.

Unit	Overarching Question	Essential Questions	Big Ideas	Full Objectives
Unit 0: Math with a Growth Mindset	How does improving students attitudes towards math affect their learning?		Math is about learning, not performing. Math is about making sense. Math is filled with conjectures, creativity, and uncertainty. Mistakes are beautiful things.	Students will understand the importance of a growth mindset (e.g., that math is not about talent or natural ability but is about thoughtful practice) and what it means to talk and listen. Students will also understand that class is where students practice thinking and doing math. Students will learn the value of taking time to think about math and listen to how others make sense of their work to arrive at a common understanding. Students will build the habits of using precise language, practicing, and sharing their thoughts.
Unit 1: Tools of Geometry Timing 2-3 weeks Objectives G.2D.1.6 G.RL.1.1	What tools are essential to understanding Geometry?	How can we use multiple representations to communicate geometry notation? How are coordinates used to prove relationships between lines/segments and within segments?	Undefined terms are the cornerstone of geometry. Line segment relationships are determined by length and direction on the coordinate plane.	G.2D.1.6 Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments. G.RL.1.1 Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs.
Unit 2: Logical Reasoning Timing 2-3 weeks Objectives G.RL.1.2 G.RL.1.3	How can we justify our reasoning with logic?	How is a conditional statement used to explain arguments in Geometry? What are the similarities and differences of Inductive and Deductive Reasoning? Why can a good definition be written as a biconditional?	Reasoning is the key to logical arguments. Conditional Statements have hypotheses and conclusions.	G.RL.1.2 Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive. G.RL.1.3 Assess the validity of a logical argument and give counterexamples to disprove a statement.
Unit 3: Intersecting Lines and Angles Measures Timing 2-3 weeks Objectives G.2D.1.1 G.2D.1.2 G.2D.1.3	How do intersecting lines determine angle relationships?	What are the differences and similarities between different angle pairs? How do we prove a statement is true about parallel lines?	Intersecting lines determine relationships among angle measures. Relationships between angles prove whether lines are parallel.	G.2D.1.1 Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems. G.2D.1.2 Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs. G.2D.1.3 Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.
Unit 4: Congruence Timing 5-6 weeks Objectives G.2D.1.4 G.2D.1.5 G.2D.1.7 G.2D.1.8* G.2D.1.9	What does it mean for geometric figures to be congruent?	How do we know when two geometric figures are congruent? How do we prove a statement is true about triangles, quadrilaterals, and other polygons? How can we classify a quadrilateral by its properties?	How do we know when two geometric figures are congruent? How do we prove a statement is true about triangles, quadrilaterals, and other polygons? How can we classify a quadrilateral by its properties?	G.2D.1.4 Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs. G.2D.1.5 Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs. G.2D.1.7 Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures). G.2D.1.8 Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning. G.2D. 1.9 Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL).
Unit 5: Similarity Timing 2-3 weeks Objectives G.2D.1.8* G.2D.1.10	How do we know when two geometric figures are similar?	How do we know when two geometric figures are similar? What relationships can be found between the angles and the sides of similar triangles/polygons? How do we use similarity to prove relationships among figures or parts of figures?	Similar polygons are defined by their congruent angles and proportional sides. Congruent corresponding angles and proportional corresponding sides are used to prove triangles are similar.	G.2D.1.8 Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning. G.2D.1.10 Construct logical arguments to prove triangle similarity (AA, SSS, SAS).
Unit 6: Right Triangle Trigonometry Timing 2-3 weeks Objectives G.RT.1.1 G.RT.1.2 G.RT.1.3 G.RT.1.4	What relationships exist between the sides of similar right triangles?	What relationships exist between the sides of similar right triangles? What is the relationship between angles and sides of a right triangle?	Corresponding sides of similar triangles prove the Pythagorean Theorem is true for all right triangles. Corresponding Sides of Special right triangles are proportional. Sine, Cosine, and Tangent are constant ratios that relate the angles and sides of a right triangle.	G.RT.1.1 Apply the distance formula, the Pythagorean theorem, and the Pythagorean theorem converse (approximate and exact values, including Pythagorean triples) to solve problems, using algebraic and logical reasoning and mathematical models. G.RT.1.2 Verify and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems using algebraic and logical reasoning. G.RT.1.3 Use the definition of the trigonometric functions to determine the sine, cosine, and tangent ratio of an acute angle in a right triangle. Apply the inverse trigonometric functions to find the measure of an acute angle in right triangles. G.RT.1.4 Apply the trigonometric functions as ratios (sine, cosine, tangent) to find side lengths in right triangles in mathematical models, including the coordinate plane.
Unit 7: Transformations Timing 2 weeks Objectives G.2D.1.9	How can we manipulate and move objects on the coordinate plane?	What are the different ways to map a polygon to a congruent polygon on a coordinate plane? How can we change the size of a polygon without changing it’s shape on a coordinate plane?	Corresponding parts of a polygon map to a congruent polygon under a rotation, reflection or translation. Corresponding parts of a polygon map to a similar polygon under a dilation.	G.2D.1.11 Use numeric, graphic, and algebraic representations of transformations in two dimensions (e.g., reflections, translations, dilations, rotations about the origin by multiples of 90 ̊) to solve problems involving figures on a coordinate plane and identify types of symmetry.
Unit 8: 3 Dimensional Shapes Timing 3-4 weeks Objectives G.3D.1.1 G.3D.1.2	How can we expand our knowledge of Geometry to 3D Objects?	What are surface area and volume? How do 3D similar figures compare/contrast to 2D similar figures?	3 Dimensional figures have surface area. 3 Dimensional figures have volume. Ratios are formed by similar 3 dimensional figures.	G.3D.1.1 Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures). G.3D.1.2 Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume.
Unit 9: Circles Timing 4-5 weeks Objectives G.C.1.1 G.C.1.2 G.C.1.3	What rules and properties can found in circles and how can they be applied to real world situations?	What is a circle and how can we find its equation? What are the parts of a circle? What relationships are formed by lines intersecting with, inside and outside the circles?	A circle is uniquely defined in the coordinate plane using its center and radius. There is a constant proportional relationship between an angle and its arc measures on a circle. Congruence and similarity criteria prove relationships between segments and figures of a circle.	G.C.1.1 Apply the properties of circles to solve problems involving circumference and area, using approximate values and in terms of pi, using algebraic and logical reasoning. G.C.1.2 Use the distance and midpoint formula, where appropriate, to recognize and write the radius r, center (h,k), and standard form of the equation of a circle (x − ℎ)²+ (y − k)² = r² with and without graphs. G.C.1.3 Apply the properties of circles and relationships among angles; arcs; and distances in a circle among radii, chords, secants, and tangents to solve problems using algebraic and logical reasoning.
Culminating Unit Timing 4-5 weeks	How can geometric properties be used and applied?
Distance Learning Resources/ Supplemental Activities	How can students develop and show evidence of understanding?			Multiple objectives are covered in this material. These math tasks are designed to enhance current curriculum and support distance learning.