Course Description will provide a careful development of both inductive and deductive reasoning. While emphasizing the formal geometric topics of points, lines, planes, congruency, similarity, and characteristics of polygons and circles, this course will also stress the connections in geometry to everyday life experiences. Scope And Sequence Timeframe Unit Instructional Topics 3 Week(s) 2 Week(s) 4 Week(s) 5 Week(s) 2 Week(s) 3 Week(s) 8 Week(s) Power Standards Recall precise definitions in geometry. Apply trigonometry in right triangles for use in the real world. Recall laws of logic and use inductive and deductive reasoning to solve problems. Model real life situations and problems using geometric figures and constructions. Use a coordinate plane to find lengths and measurements for use with geometric problems. Prerequisites Passing grade in Algebra 1 Essential Questions How do shapes and their properties construct the world around you? How can you use geometry to model situations in the real world and gain information from that? What geometry concepts are used in everyday life? How can you apply coordinate plane geometry in 2 dimensions to spacial geometry in 3D? Materials and Resources scientific calculator ruler protractor compass Essentials of Reasoning and Proof Parallel and Perpendicular Lines Congruent & Similar Triangles Points of Concurrency Right Triangles & Trigonometry Properties of Shapes, Area, & Volume 1. Algebra One Skills 2. Points, Lines, and Planes 3. Measure and Precision 4. Distance and Midpoints 1. Inductive Reasoning and Conjectures 2. Conditional Statements 3. Deductive Reasoning 4. Algebraic Proof 5. Geometric Proof 1. Special Angle Relationships Formed from Intersecting Lines 2. Slopes of Parallel and Perpendicular Lines 3. Graphing and Writing Equations of Lines 4. Proofs of Parallel Lines 1. Apply Triangle Sum Properties 2. Apply Congruence and Triangles 3. Prove Triangles Congruent using shortcuts 4. Use Congruent Triangles 5. Use Isosceles and Equilateral Triangles 6. Apply Similarity and Triangles 1. Midsegments of Shapes 2. Perpendicular & Angle Bisectors 3. Use Medians and Altitudes 4. Triangle Inequalities 1. Pythagorean Theorem 2. Converse of Pythagorean Theorem 3. Special Right Triangles 4. Right Triangle Trigonometry 1. Polygon Angle Measures 2. Properties of Shapes 3. Properties of Circles 4. Area and Perimeter 5. Volume of Polyhedra Course Details Page 1
Unit: Essentials of Unit Description I can measure line segments in inches and centimeters. I can find angle measures using a protractor. I can identify rays, planes, lines, segments, angles, and their properties. I can use correct notation for rays, planes, lines, segments, and angles correctly. I can find and label angle bisectors, midpoints, and congruent segments. Essential Questions What are the geometric figures that construct the world around us? How do we use the language of geometry to describe the world around us? How do we use rulers and protractors to measure segments and angles? Academic Vocabulary acute angle adjacent angles angle angle bisector between collinear complementary angles congruent coplanar degree line linear pair line segment midpoint obtuse angles opposite rays perpendicular plane point ray right angle segment bisector supplementary angles vertex vertical angles Materials and Resources card stock glue string paper clips Technology Integration SMART Board and protractor tools, Ruler Summative Assessment Unit test - part multiple choice, part performance event Topic: Algebra One Skills Duration: 3 Week(s) Solve algebraic equations involving mutli-steps, including the distributive property. Students will simplify expressions using order of operations and graph lines. expression solve equation equality division multiplication subtraction addition algebra review test Page 2
Students will solve algebraic equations involving multiple steps. linked to Power Standard = Topic: Points, Lines, and Planes Duration: 4 Day(s) Develop an awareness of definitions, symbols, and visual models of basic geometric terms. point line plane ray line segment Points, lines, planes questions I can identify rays, planes, lines, segments, angles, and their properties. I can use correct notation for rays, planes, lines, segments, and angles correctly. linked to Power Standard = Topic: Measure and Precision Exposure to line segments, linear measurement, and congruence will take place. Students must use the language appropriately whether they are talking about the name of segments or segment measure. between segment addition postulate congruent segments Each student will be required to complete a problem using the segment addition postulate. I can measure line segments in inches and centimeters. I can find angle measures using a protractor. linked to Power Standard = Topic: Distance and Midpoints Duration: 5 Day(s) Students can find distances and midpoints in both 1 and 2 dimensions. midpoint segment bisector Students will each come up with their own ordered pair. They must then partner up with 3 other students (one at a time) and find the distance and midpoint between their points. Page 3
I can find and label angle bisectors, midpoints, and congruent segments. linked to Power Standard = Unit: Reasoning and Proof Unit Description I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. Essential Questions How do I reach logical conclusions about geometric figures? How can I prove a conjecture true or false? Academic Vocabulary conclusion conditional statement conjecture contrapositive converse counterexample deductive reasoning hypothesis if-then statement inductive reasoning inverse negation proof Materials and Resources police report pattern blocks Summative Assessment Unit test - part multiple choice, part work-it-out problems, and part proofs. Topic: Inductive Reasoning and Conjectures Duration: 2 Week(s) Duration: 2 Day(s) Use inductive reasoning to formulate conjectures and find couterexamples for false conjectures. inductive reasoning conjecture counterexample 2.1 Challenge Practice I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. linked to Power Standard = Topic: Conditional Statements Duration: 2 Day(s) Students will learn to interpret if-then statements, write sound definitions, and be able to translate conditionals into their converse, inverse, and contrapositive. conditional statement if-then form converse inverse contrapositive bi-conditional hypothesis conclusion Page 4
I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. Students will each write a conditional statement. They will trade with another student who will then have to write the converse. They will then trade with another student who will have to write the inverse. Lastly they will trade with a student and write the appropriate contrapositive. Students will have to check all three of the statements on their paper and edit them before turning them in. linked to Power Standard = Topic: Deductive Reasoning Duration: 1 Day(s) Students will understand deductive reasoning including the law of syllogism and the law of detachment. deductive reasoning Law of Syllogism Law of Detachment homework check 2.3 Practice B worksheet I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. linked to Power Standard = Topic: Algebraic Proof Duration: 1 Day(s) Deductive arguments are created through two-column proofs in order to justify the algebraic steps utilized to solve a problem. addition property subtraction property multiplication property division property distributive property substitution property Students will create their own equations and trade with another student. Each student must be able to solve the equation, write the correct properties, and check another student's work. I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. linked to Power Standard = Topic: Geometric Proof Through logical reasoning, connecting definitions, postulates, and theorems, an awareness of the structure of two-column and/or flow chart geometric proofs will be developed. postulate theorem proof statement reason conditional statement Page 5
Q.E.D. Students will complete a whole proof on their own at the end of each class. I can use postulates and theorems to prove geometric statements using a two column or paragraph proof. DOK Level 4 linked to Power Standard = Unit: Parallel and Perpendicular Lines Unit Description I can determine if a line is parallel or perpendicular to another line. I can use parallel lines and transversals to define special angle relationships. I can write the equation of a line in slope intercept form. Essential Questions What are the names of some special angle pairs? What are the relationships between the measures of special angle pairs? How do I prove lines parallel or perpendicular? What are the relationships between slopes of parallel and perpendicular lines? How do I graph and write equations of lines? Academic Vocabulary parallel lines perpendicular lines skew lines corresponding angles consecutive interior angles alternate interior angles alternate exterior angles transversal corresponding angles postulate corresponding angles converse consecutive interior angles theorem consecutive interior angles converse alternate interior angles theorem alternate interior angles converse alternate exterior angles theorem alternate exterior angles converse transitive property of parallel lines lines perpendicular to a line theorem distance from a point to a line Materials and Resources protractor ruler poster board Technology Integration smart board Summative Assessment Unit test - part multiple choice, part performance event which will include proofs Topic: Special Angle Relationships Formed from Intersecting Lines Duration: 4 Week(s) Duration: 4 Day(s) Students will look at lines being intersected by a transversal and identify names of angle pairs. They will also look at the impact parallel lines have on angle measures. transversal parallel lines skew lines corresponding angles alternate exterior angles alternate interior angles Page 6
Students will take Chapter 3 Quiz #1 over angle relationships and parallel lines. I can use parallel lines and transversals to define special angle relationships. I can determine if a line is parallel or perpendicular to another line. linked to Power Standard = Topic: Slopes of Parallel and Perpendicular Lines Student will learn how to calculate slope and compare the slopes of parallel and perpendicular lines. slope parallel perpendicular lines Students will be able answer 3 multiple choice questions using the CPS clicker system. I can write the equation of a line in slope intercept form. linked to Power Standard = Topic: Graphing and Writing Equations of Lines Duration: 5 Day(s) Students can write equations of lines given different information and graph linear equations. slope-intercept form Short quiz over writing equations given parallel or perpendicular slopes along with a point. I can determine if a line is parallel or perpendicular to another line. I can write the equation of a line in slope intercept form. linked to Power Standard = Topic: Proofs of Parallel Lines Duration: 2 Day(s) Students will use angle relationships to prove lines are parallel. corresponding alternate interior angles consecutive interior angles remote interior angles alternate exterior angles vertical angles supplementary angles complementary angles Page 7
Parallel Line Proof Practice worksheet - has 12 proofs, students must complete each one correctly. I can determine if a line is parallel or perpendicular to another line. DOK Level 4 I can use parallel lines and transversals to define special angle relationships. DOK Level 4 I can write the equation of a line in slope intercept form. linked to Power Standard = Unit: Congruent & Similar Triangles Unit Description I can determine if triangles are similar using side and angle properties. I can use ratios and proportions to find missing lengths of similar or congruent triangles. I can determine if triangles are congruent using side and angle properties. Essential Questions How can you classify triangles? How do you find measures of angles of triangle? How can you understand what constructs a congruent figure? How can you prove triangles are congruent? Academic Vocabulary acute triangles obtuse triangles right triangles scalene triangles isosceles triangles equilateral triangles equiangular triangles Materials and Resources compass Technology Integration online geometer's sketchpad Summative Assessment Test will contain some multiple choice with about 5 proofs involving triangles and congruence. Topic: Apply Triangle Sum Properties Duration: 5 Week(s) Students will focus on classifying triangles and finding measures of their angles. scalene triangle isosceles triangle equilateral triangle acute triangle right triangle obtuse triangle quadrangular triangle triangle sum theorem exit slip I can use ratios and proportions to find missing lengths of similar or congruent triangles. Page 8 linked to Power Standard =
Topic: Apply Congruence and Triangles Students will identify congruent figures. congruent figures corresponding parts of congruent figures Triangle Proofs I can determine if triangles are congruent using side and angle properties. linked to Power Standard = Topic: Prove Triangles Congruent using shortcuts Duration: 6 Day(s) We will prove triangles congruent by SSS, SAS, ASA, AAS, and HL. side-side-side side-angle-side angle-side-angle angle-angle-side hypotenuse-leg Triangle Proofs Packet I can determine if triangles are congruent using side and angle properties. DOK Level 4 linked to Power Standard = Topic: Use Congruent Triangles Duration: 4 Day(s) Students will focus on performing congruence transformations and using congruent triangles to prove corresponding parts congruent. congruent triangles adjacent prove triangles workbook I can determine if triangles are congruent using side and angle properties. DOK Level 4 linked to Power Standard = Topic: Use Isosceles and Equilateral Triangles Students' focus will be on using theorems regarding isosceles and equilateral triangles. ratios proportions similar Page 9
congruent triangles sides angles buried treasure (attached) I can use ratios and proportions to find missing lengths of similar or congruent triangles. I can determine if triangles are congruent using side and angle properties. DOK Level 4 linked to Power Standard = Topic: Apply Similarity and Triangles Duration: 4 Day(s) Students will determine if triangles are similar, congruent, or neither using properties they have learned so far. sides angles ratios proportions similar congruent triangles 6.7 practice page I can determine if triangles are similar using side and angle properties. I can use ratios and proportions to find missing lengths of similar or congruent triangles. linked to Power Standard = Unit: Points of Concurrency Unit Description Students will be able to use a protractor and compass to find points of concurrency and will know what their uses are. Essential Questions How are measurements within triangles related to lengths of the bases and sides? How can you draw a circle around a triangle or inside of a triangle? What relationships within triangles show up in everyday triangles you might find? Academic Vocabulary incenter circumcenter orthocenter centroid medians altitude concurrency Materials and Resources compass ruler protractor Technology Integration Duration: 2 Week(s) Page 10
Geometers Sketchpad Summative Assessment Performance event concurrent constructions Topic: Midsegments of Shapes Duration: 2 Day(s) Students will find the middle of a segment and connect the mid segments to form 4 congruent triangles. midsegments bisector midsegment quiz I can find points of concurrency. linked to Power Standard = Topic: Perpendicular & Angle Bisectors Students will use angle measures to bisect angles and draw perpendicular lines through angles and sides. perpendicular bisector perpendicular and angle bisectors quiz I can find points of concurrency. linked to Power Standard = Topic: Use Medians and Altitudes Students will construct medians and altitudes and use them to break apart triangles, find the height of triangles, and find points of concurrencies within triangles. medians altitudes medians and altitudes quiz I can find points of concurrency. linked to Power Standard = Topic: Triangle Inequalities Duration: 2 Day(s) Students will determine if side lengths of a triangle actually form a triangle and they will use those lengths to determine if a triangle is obtuse, right, or acute using the converse of the Pythagorean theorem. inequality greater than Page 11
less than triangle inequality quiz I can find points of concurrency. linked to Power Standard = Unit: Right Triangles & Trigonometry Unit Description I can use Pythagorean Theorem to find missing sides of right triangles. I can use trigonometric ratios to find missing sides and angles of right triangles. I can use trigonometry in real life situations. Essential Questions How can I find height of objects using right triangles? How can triangles be constructed and why are they constructed that way? Academic Vocabulary Pythagorean Theorem leg hypotenuse opposite adjacent tangent sine cosine slant height Materials and Resources notecard paper clip string protractor straw Technology Integration Make your own Clinometer Summative Assessment Multiple choice test and performance event. Topic: Pythagorean Theorem Duration: 3 Week(s) Duration: 2 Day(s) Students will use Pythagorean Theorem to determine missing sides of right triangles. hypotenuse legs big horn sheep project (attached) I can use Pythagorean Theorem to find missing sides of right triangles. linked to Power Standard = Topic: Converse of Pythagorean Theorem Duration: 2 Day(s) Students will use Pythagorean Theorem to determine whether a triangle is acute, obtuse, or right, when given all side lengths in the triangle. hypotenuse Page 12
legs Baseball problem (attached) I can use Pythagorean Theorem to find missing sides of right triangles. linked to Power Standard = Topic: Special Right Triangles Students will use 30-60-90 and 45-45-90 triangles to find missing side lengths in simplified radical form. 30-60-90 45-45-90 adjacent opposite hypotenuse remote interior exterior right angle special triangle practice worksheet (attached) I can use Pythagorean Theorem to find missing sides of right triangles. linked to Power Standard = Topic: Right Triangle Trigonometry Duration: 8 Day(s) Students will use Sine, Cosine, and Tangent to find missing sides and angles within triangles. sine cosine tangent hypotenuse adjacent opposite build your own clinometer and use it to find heights of objects around the school I can use trigonometric ratios to find missing sides and angles of right triangles. I can use trigonometry in real life situations. DOK Level 4 Unit: Properties of Shapes, Area, & Volume linked to Power Standard = Duration: 8 Week(s) Unit Description Students will use properties of shapes and methods of finding lengths and parallel / perpendicular lines to determine what type of shape they have. Students will find the area and volume of 2D and 3D shapes. Page 13
Students will explore lengths within these polygons such as altitudes and apothems, as well as chords, secants, and tangents within circles. Essential Questions How can I use area and volume to help solve problems in real life? What determines a shape's makeup and how is it related to other shapes? What relationships occur within shapes based on length and measurement? Academic Vocabulary polygon regular square rectangle parallelogram rhombus trapezoid kite quadrilateral pentagon hexagon octagon decagon circle diameter base radius pi parallel perpendicular right Angle circumference perimeter Materials and Resources nets glue scissors play doh Technology Integration korthalsaltes.com Summative Assessment Multiple choice test with build a shape performance event. Topic: Polygon Angle Measures I can classify shapes and figures based on their properties. Duration: 4 Day(s) Students will explore to find a formula that will give them the interior angle sum of any polygon. They will use this to find the apothem later on regular polygons. regular polygon interior angles exterior angles polygon interior angle sum theorem stop sign activity linked to Power Standard = Topic: Properties of Shapes Duration: 10 Day(s) Students will learn what properties make up specific shapes and how to find if those properties hold true or not on a coordinate plane or in a proof. Page 14
parallel perpendicular opposite sides congruent adjacent properties of shapes table I can define properties of specific shapes. I can classify shapes and figures based on their properties. linked to Power Standard = Topic: Properties of Circles Duration: 7 Day(s) Students will explore chords, secants, and tangents of circles as well as arcs and sectors. circle radius diameter circumference chord secant tangent sector circle exercises worksheet I can graph a circle. I can write the equation of a circle. I can use properties of circles to find angles and line segment lengths. linked to Power Standard = Topic: Area and Perimeter Duration: 8 Day(s) Students will find the area and perimeter of shapes area perimeter rectangle square rhombus trapezoid parallelogram distance magnitude area investigation packet Page 15
I can find the area of a polygon. I can classify shapes and figures based on their properties. linked to Power Standard = Topic: Volume of Polyhedra Duration: 10 Day(s) Students will find volume of shapes and explore different solids found in the real world. volume polyhedron faces vertices edges base slant height height antiprism prism cube stellated truncated cone sphere semi challenge practice for volume I can classify shapes and figures based on their properties. I can find the volume of a polyhedron. linked to Power Standard = Page 16