Geometry Curriculum Map Unit 1 st Quarter Content/Vocabulary Assessment AZ Standards Addressed Essentials of Geometry 1. What are points, lines, and planes? 1. Identify Points, Lines, and Planes 1. Observation 1. undefined terms 2. collinear points 3. coplanar points 4. defined terms 5. line segment 6. endpoints 7. ray 8. opposite rays 9. intersection 2. What are congruent segments? 2. Use Segments and Congruence 1. postulate, axiom 2. coordinate 3. distance 4. between 5. congruent segments 2. Observation
3. How do you find the distance and midpoint between two points? 3. Use Midpoint and Distance Formulas 1. midpoint 2. segment bisector 3. Observation 3. S4.C3.PO1 S4.C3.PO2 S4.C3.PO3 4. How do you classify angles? 4. Measure and Classify Angles 1. angle a. acute b. right c. obtuse d. straight 2. sides of an angle 3. vertex of an angle 4. measure of an angle 5. congruent angles 6. angle bisector 4. Observation Mid-Unit Assessment (Instructor Generated) 5. How do you identify complementary and supplementary angles? 5. Describe Angle Pair Relationships 1. complementary angles 2. supplementary angles 3. adjacent angles 5. Observation
4. linear pair 5. vertical angles 6. How do you classify polygons? 6. Classify Polygons 1. polygon a. side b. vertex 2. convex 3. concave 4. n-gon 5. equilateral 6. equiangular 7. regular 6. Observation D. Homework 7. How do you find the area and perimeter of a figure? 7. Find Perimeter, Circumference, and Area 1. perimeter 2. circumference 3. area 4. diameter 5. radius 7. Observation 7. S4.C1.PO1 S4.C1.PO6
Reasoning and Proof 1. How do you use inductive reasoning in mathematics? 1. Use Inductive Reasoning 1. conjecture 2. inductive reasoning 3. counterexample Unit Assessment (Instructor Generated) 1. Observation 1. S5.C2.PO8 2. How do you write statements? 2. Analyze Conditional Statements 1. conditional statement a. converse b. inverse c. contrapositive 2. if-then form a. hypothesis b. conclusion 3. negation 4. equivalent statements 5. perpendicular lines 6. biconditional statement 2. Observation 2. S5.C2.PO9 3. How do you construct a logical argument? 3. Apply Deductive Reasoning 1. deductive reasoning 3. Observation 3. S5.C2.PO8 S5.C2.PO10 S5.C2.PO11
4. How can you identify postulates from a diagram? 4. Use Postulates and Diagrams 1. line perpendicular to a plane 2. postulate (axiom) 3. theorem 4. Observation 4. S4.C1.PO5 Mid-Unit Assessment 5. How do you solve an equation? 5. Reason Using Properties from Algebra 1. equation 2. solve an equation 5. Observation 5. S5.C2.PO5 S5.C2.PO12 6. How do you write a geometric proof? 6. Prove Statements about Segments and Angles 1. proof 2. two-column proof 3. theorem 6. Observation 6. S5.C2.PO12 S5.C2.PO13
7. What are the relationships between angles? 7. Prove Angle Pair Relationships 1. complementary angles 2. supplementary angles 3. linear pair 4. vertical angles 7. Observation 7. S5.C2.PO12 Parallel and Perpendicular Lines 1. What angle pairs are formed by transversals? 1. Identify Pairs of Lines and Angles 1. parallel lines 2. skew lines 3. parallel planes 4. transversal 5. corresponding angles 6. alternate interior angles 7. alternate exterior angles 8. consecutive interior angles Unit Assessment 1. Observation 1. S4.C1.PO4
2. How are angles related for two parallel lines and a transversal? 2. Use Parallel Lines and Transversals 1. corresponding angles 2. alternate interior angles 3. alternate exterior angles 4. consecutive interior angles 2. Observation 2. S4.C1.PO4 3. How do you prove lines are parallel? 3. Prove Lines are Parallel 1. paragraph proof 2. converse 3. two-column proof 3. Observation 3. S5.C2.PO12 Mid-Unit Assessment 4. How do you find the slope of a line? 4. Find and Use Slopes of Lines 1. slope 2. rise 3. run 4. Observation 4. S3.C3.PO4 S3.C4.PO1
5. How do you write an equation of a line? 5. Write and Graph Equations of Lines 1. slope-intercept form 2. standard form 3. x-intercept 4. y-intercept 5. Observation 5. S3.C3.PO3 6. How do you find the distance between a point and a line? 6. Prove Theorems about Perpendicular Lines 1. distance from a point to a line 6. Observation 6. S4.C3.PO3 Probability 1. How do you define probability? How do you find the probability of an event? 1. Introduction to Probability 1. probability 2. favorable outcome 3. possible outcome Unit Assessment 1. Observation 2. Deal or No Deal 1. S2.C2.PO1
2. What is the difference between theoretical and experimental probability? 2. Experimental Probability 1. experimental probability 2. theoretical probability 3. simulation 2. Observation 2. Group Work 2. S2.C2.PO1 S2.C2.PO2 3. How do you make a prediction? 3. Predictions 1. prediction 2. probability of an event 3. Observation
Unit 2 nd Quarter Content/Vocabulary Assessment AZ Standards Addressed Congruent Triangles 1. How can you find the measure of the third angle of a triangle if you know the measure of the other two angles? 1. Apply Triangle Sum Properties 1. triangle a. scalene b. isosceles 1. Observation c. equilateral d. acute e. right f. obtuse g. equiangular 2. interior angles 3. exterior angles 4. corollary to a theorem 2. What are congruent figures? 2. Apply Congruence and Triangles 1. congruent figures 2. corresponding parts 2. Observation 2. S4.C1.PO8 3. How can you use side lengths to prove triangles congruent? 3. Prove Triangles Congruent by SSS 1. congruent figures 2. corresponding parts 3. Observation 3. S4.C1.PO8
4. How can you use two sides and an angle to prove triangles congruent? 4. Prove Triangles Congruent by SAS and HL 1. leg of a right triangle 2. hypotenuse 4. Observation 4. S4.C1.PO8 5. If a side of one triangle is congruent to a side of another triangle, what information about the angles would allow you to prove the triangles are congruent? 5. Prove Triangles Congruent by ASA and AAS 1. flow proof 5. Observation 5. S4.C1.PO8 Mid-Unit Assessment 6. How can you use congruent triangles to prove angles or sides congruent? 6. Use Congruent Triangles 1. corresponding parts 6. Observation 6. S5.C2.PO12
7. How are the sides and angles of a triangle related if there are two or more congruent sides or angles? 7. Use Isosceles and Equilateral Triangles 1. legs 2. vertex angle 3. base 4. base angles 7. Observation 7. S4.C1.PO6 Unit Assessment 8. What transformations create an image congruent to the original figure? 8. Perform Congruence Transformations 1. transformation 2. image 3. translation 4. reflection 5. rotation 6. congruence transformation 8. Observation 8. S4.C2.PO1 S4.C2.PO2 Relationships within Triangles 1. What is the midsegment relationship in a triangle? How do you write a coordinate proof? 1. Midsegment Theorem and Coordinate Proof 1. midsegment of a triangle 2. coordinate proof 1. Observation 1. S5.C2.PO12
2. How do you find the point of concurrency of the perpendicular bisectors of the sides of a triangle? What is the relationship? 2. Use Perpendicular Bisectors 1. perpendicular bisector 2. equidistant 3. concurrent 4. point of concurrency 5. circumcenter 2. Observation 2. S4.C1.PO3 3. When can you conclude that a point is on the bisector of an angle? What is the relationship between the three angle bisectors of a triangle? 3. Use Angle Bisectors of Triangles 1. incenter 2. angle bisector 3. distance from a point to a line 3. Observation 3. S4.C1.PO3 4. How do you find the centroid and orthocenter of a triangle? What are the relationships? 4. Use Medians and Altitudes 1. median of a triangle 2. centroid 3. altitude of a triangle 4. orthocenter 4. Observation 4. S4.C1.PO3
Mid-Unit Assessment 5. How do you find the possible lengths of the third side of a triangle if you know the lengths of two sides? 5. Use Inequalities in a Triangle 1. side opposite 2. inequality 5. Observation 5. S4.C1.PO9 6. How do you use inequalities to make comparisons in two triangles? How do you write an indirect proof? 6. Inequalities in Two Triangles and Indirect Proof 1. indirect proof 2. included angle 6. Observation 6. S5.C2.PO12 Similarity 1. How do you use ratios and proportions to solve a problem? 1. Ratios, Proportions, and the Geometric Mean 1. ratio 2. proportion Unit Assessment 1. Observation 1. S3.C4.PO2 S4.C4.PO1
3. means 4. extremes 5. geometric mean 2. How do you calculate actual distance from a scale drawing? 2. Use Proportions to Solve Geometry Problems 1. scale drawing 2. scale 2. Observation 2. S3.C4.PO2 3. If two figures are similar, how do you find the length of a missing side? 3. Use Similar Polygons 1. similar polygons 2. scale factor 3. Observation 3. S4.C4.PO4 Mid-Unit Assessment 4. How can you show that two triangles are similar? 4. Prove Triangles Similar by AA 1. similar polygons 4. Observation 4. S4.C1.PO8
5. How do you prove that two triangles are similar by using the similarity theorems? 5. Prove Triangles Similar by SSS and SAS? 1. ratio 2. proportion 3. similar polygons 5. Observation 5. S4.C1.PO8 6. What proportion can you write if a line is parallel to one side of a triangle? 6. Use Proportionality Theorems? 1. corresponding angles 2. ratio 3. proportion 6. Observation 6. S4.C4.PO4 7. How do you dilate a figure in the coordinate plane? 7. Perform Similarity Transformations 1. dilation 2. center of dilation 3. scale factor of a dilation 4. reduction 5. enlargement 6. transformation 7. Observation 7. S4.C2.PO1 S4.C2.PO2 S4.C2.PO4
Probability 1. How do you determine the number of possible outcomes, and what they are, using a chart, tree diagram, or the counting principle? 1. Sample Spaces 1. sample space 2. tree diagram 3. fundamental counting principle 4. probability 5. outcome Unit Assessment 1. Observation 2. Hop to the Pond 1. S2.C3.PO3 2. How do you find the probability of a compound event? What are mutually exclusive events? 2. Compound Events 1. compound event 2. mutually exclusive 3. complement of an event 2. Observation 2. S2.C2.PO1 S2.C2.PO2 3. How do you distinguish independent and dependent events? 3. Independent and Dependent Events 1. independent events 2. dependent events 3. compound events 3. Observation 3. S2.C2.PO3
Unit 3 rd Quarter Content/Vocabulary Assessment AZ Standards Addressed Right Triangles and Trigonometry 1. If you know the lengths of two sides of a right triangle, how do you find the length of the third side? 1. Apply the Pythagorean Theorem 1. Pythagorean Triple 2. right triangle 3. leg of a right triangle 4. hypotenuse 1. Observation 1. S3.C3.PO11 S4.C1.PO3 2. How can you use the sides of a triangle to determine if it right, acute, or obtuse? 2. Use the Converse of the Pythagorean Theorem 1. right triangle 2. acute triangle 3. obtuse triangle 2. Observation 2. S3.C3.PO11 S4.C1.PO3 3. How can you find the length of the altitude to the hypotenuse of a right triangle? 3. Use Similar Right Triangles 1. altitude of a triangle 2. geometric mean 3. similar polygons 3. Observation 3. S4.C4.PO4
Mid-Unit Assessment 4. How do you find the lengths of the sides of special right triangles? 4. Special Right Triangles 1. isosceles right triangle 4. Observation 4. S4.C1.PO10 5. How can you find the leg of a right triangle when you know the other leg and one acute angle? 5. Apply the Tangent Ratio 1. trigonometric ratio 2. tangent 5. Observation 5. S4.C1.PO11 6. How can you find the lengths of the sides of a right triangle when you are given the length of the hypotenuse and one acute angle? 6. Apply the Sine and Cosine Ratios 1. sine 2. cosine 3. angle of elevation 4. angle of depression 5. hypotenuse 6. Observation 6. S4.C1.PO11 7. How can you find all the sides and angles of a right 7. Solve Right Triangles 7. Observation 7. S4.C1.PO11
triangle? 1. solve a right triangle 2. inverse tangent 3. inverse sine 4. inverse cosine Quadrilaterals 1. How do you find a missing angle measure in a convex polygon? 1. Find Angle Measures in Polygons 1. diagonal 2. interior angle 3. exterior angle Unit Assessment 1. Observation 1. S4.C1.PO6 2. How do you find angle and side measures in a parallelogram? 2. Use Properties of Parallelograms 1. parallelograms 2. opposite sides 3. opposite angles 2. Observation 2. S4.C1.PO6 3. How can you prove that a quadrilateral is a 3. Show that a Quadrilateral is a Parallelogram 3. Observation 3. S4.C1.PO4
parallelogram? 1. parallelogram 2. opposite sides 3. opposite angles Mid-Unit Assessment 4. What are the properties of parallelograms that have all sides or all angles congruent? What are some important relationships among these parallelograms? 4. Properties of Rhombuses, Rectangles, and Squares 1. rhombus 2. rectangle 3. square 4. parallelogram 5. quadrilateral 4. Observation 4. S4.C1.PO7 5. What are the main properties of trapezoids and kites? 5. Use Properties of Trapezoids and Kites 1. trapezoid a. bases b. base angles c. legs 2. isosceles trapezoid 3. midsegment of a trapezoid 4. kite 5. Observation 5. S4.C1.PO7
6. How can you identify special quadrilaterals? 6. Identify Special Quadrilaterals? 1. parallelogram 2. rhombus 3. rectangle 4. square 5. trapezoid 6. kite 6. Observation 6. S4.C1.PO7 Properties of Transformations 1. How do you translate a figure using a vector? 1. Translate Figures and Use Vectors 1. image 2. preimage 3. isometry 4. vector a. initial point b. terminal point c. horizontal component d. vertical component 5. component form 6. translation Unit Assessment 1. Observation 1. S4.C2.PO2
2. How do you use matrix operations to translate a figure? 2. Use Properties of Matrices 1. matrix 2. element 3. dimensions 4. columns 5. rows 2. Observation 2. S4.C2.PO2 S3.C3.PO15 3. How do you reflect a figure in the coordinate plane? 3. Perform Reflections 1. line of reflection 2. reflection 3. isometry 4. image 5. preimage 3. Observation 3. S4.C2.PO2 S3.C3.PO15 4. How do you rotate a figure about the origin? 4. Perform Rotations 1. center of rotation 2. angle of rotation 3. rotation 4. Observation 4. S4.C2.PO2 S3.C3.PO15
4. image 5. preimage Mid-Unit Assessment 5. What is a glide reflection? 5. Apply Compositions of Transformations 1. glide reflection 2. composition of transformations 5. Observation 5. S4.C2.PO2 S4.C2.PO3 6. When does a figure have line symmetry? 6. Identify Symmetry 1. line symmetry 2. line of symmetry 3. rotational symmetry 4. center of symmetry 6. Observation 7. How do you use matrices to draw a dilation? 7. Identify and Perform Dilations 1. scalar multiplication 2. dilation 7. Observation 7. S4.C2.PO2 S4.C2.PO4
3. reduction 4. enlargement Probability 1. What is a permutation? 1. Permutations 1. permutation 2. factorial 3. set Unit Assessment 1. Observation 1. S2.C3.PO1 S2.C3.PO2 2. What is a combination? 2. Combinations 1. combination 2. factorial 3. set 2. Observation 2. S2.C3.PO1 S2.C3.PO2 3. How do you determine when to use combinations versus permutations? 3. Permutations and Combinations 1. permutation 2. combination 3. Observation 3. S2.C3.PO1 S2.C3.PO2
3. order 4. set
Unit 4 th Quarter Content/Vocabulary Assessment AZ Standards Addressed Properties of Circles 1. How can you verify that a segment is tangent to a circle? 1. Use Properties of Tangents 1. Observation 1. S4.C1.PO1 1. circle a. center b. radius c. diameter 2. chord 3. secant 4. tangent 2. How do you find the measure of an arc of a circle? 2. Find Arc Measures 1. central angle 2. minor arc 3. major arc 4. semicircle 5. measure a. minor arc b. major arc c. semicircle 6. congruent circles 7. congruent arcs 2. Observation 2. S4.C1.PO1 3. How can you tell if two 3. Apply Properties of Chords 3. Observation 3. S4.C1.PO1
chords in a circle are congruent? 1. chord 2. arc 3. semicircle Mid-Unit Assessment 4. How do you find the measure of an inscribed angle? 4. Use Inscribed Angles and Polygons 1. inscribed angle 2. intercepted arc 3. inscribed polygon 4. circumscribed circle 4. Observation 4. S4.C1.PO1 5. How do you find the measure of an angle formed by two chords that intersect inside a circle? 5. Apply Other Angle Relationships in Circles 1. chord 2. secant 3. tangent 5. Observation 5. S4.C1.PO1
6. What are some properties of chords, secants, and tangents to a circle? 6. Find Segment Lengths in Circles 1. segments of a chord 2. secant segment 3. external segment 6. Observation 6. S4.C1.PO1 7. What do you need to know to write the standard equation of a circle? 7. Write and Graph Equations of Circles 1. standard equation of a circle 7. Observation 7. S4.C1.PO1 S4.C1.PO5 Measuring Length and Area 1. How do you find the area of a triangle and a parallelogram? 1. Areas of Triangles and Parallelograms 1. bases of a parallelogram 2. height of a parallelogram 3. area 4. perimeter Unit Assessment 1. Observation 2. How do you find the area of a trapezoid, a kite, and a 2. Areas of Trapezoids, Rhombuses, and Kites 2. Observation
rhombus? 1. height of a trapezoid 2. diagonal 3. bases of a trapezoid 3. How is the ratio of the areas to two similar polygons related to the ratio of corresponding sides? 3. Perimeter and Area of Similar Figures 1. regular polygon 2. corresponding sides 3. similar polygons 3. Observation 3. S4.C4.PO4 Mid-Unit Assessment 4. How do you find the length of an arc of a circle? 4. Circumference and Arc Length 1. circumference 2. arc length 3. radius 4. diameter 5. measure of an arc 4. Observation 4. S4.C4.PO2
5. How do you find the area of a sector of a circle? 5. Areas of Circles and Sectors 1. sector of a circle 5. Observation 5. S4.C4.PO2 6. How do you find the area of a regular polygon? 6. Areas of Regular Polygons 1. center of a polygon 2. radius of a polygon 3. apothem of a polygon 4. central angle of a regular polygon 6. Observation 7. How do you find the probability that a point randomly selected in a region is in a particular part of that region? 7. Use Geometric Probability 1. probability 2. geometric probability 7. Observation 7. S2.C2.PO5 Surface Area and Volume of Solids 1. When is a solid a polyhedron? 1. Explore Solids Unit Assessment 1. Observation 1. S4.C1.PO2
1. polyhedron a. face b. edge c. vertex 2. base 3. regular polyhedron 4. convex polyhedron 5. Platonic solids 6. cross section 2. How do you find the surface area of a prism and a cylinder? 2. Surface Area of Prisms and Cylinders 1. prism a. lateral faces b. lateral edges 2. surface area 3. lateral area 4. net 5. right prism 6. oblique prism 7. cylinder 8. right cylinder 2. Observation 2. S4.C4.PO5 3. How do you find the surface area of a pyramid and a cone? 3. Surface Area of Pyramids and Cones 1. pyramid 3. Observation 3. S4.C4.PO5
2. vertex of a pyramid 3. regular pyramid 4. slant height 5. cone 6. vertex of a cone 7. right cone 8. lateral surface Unit Mini-Assessment 4. How do you find the volume of a right prism or a right cylinder? 4. Volume of Prisms and Cylinders 1. volume 4. Observation 4. S4.C4.PO5 5. How do you find the volume of a pyramid and a cone? 5. Volume of Pyramids and Cones 1. pyramid 2. cone 3. volume 5. Observation 5. S4.C4.PO5 6. How do you find the 6. Surface Area and Volume of Spheres 6. Observation 6. S4.C4.PO5
surface area and volume of a sphere? 1. sphere a. center b. radius c. chord d. diameter 2. great circle 3. hemisphere 7. What is the ratio of the surface areas and volumes of two similar solids? 7. Explore Similar Solids 1. similar solids 7. Observation 7. S4.C4.PO4 Unit Mini-Assessment
The following standards are woven throughout the entire curriculum for geometry. S1.C3.PO2 Use estimation to determine the reasonableness of a solution. S3.C3.PO5 Solve linear equations and equations involving absolute value, with one variable. S4.C1.PO3 Create and analyze inductive and deductive arguments concerning geometric ideas and relationships. S4.C1.PO4 Apply properties, theorems, and constructions about parallel lines, perpendicular lines, and angles to prove theorems. S4.C1.PO5 Explore Euclid s five postulates in the plane and their limitations. S5.C2.PO1 Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify implicit assumptions that have been made. S5.C2.PO2 Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s).
S5.C2.PO3 Evaluate a solution for reasonableness and interpret the meaning of the solution in the context of the original problem. S5.C2.PO4 Generalize a solution strategy for a single problem to a class of related problems; explain the role of generalizations in inductive and deductive reasoning. S5.C2.PO5 Summarize and communicate mathematical ideas using formal and informal reasoning. S5.C2.PO6 Synthesize mathematical information from multiple sources to draw a conclusion, make inferences based on mathematical information, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning. S5.C2.PO12 Construct a simple formal deductive proof. S5.C2.PO13 Identify and explain the roles played by definitions, postulates, propositions, and theorems in the logical structure of mathematics, including Euclidean geometry.