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Curriculum Map – Unit 1: Basics of Geometry Teacher: Month / Year Aug Sept SAUSEDA Department: MATH Essential Question(s) How do I make predictions from patterns? How do I make conjectures using Inductive Reasoning? How do I sketch a point, line, plane, segment and angle? How do I draw the intersection of two geometric figures? How do I measure a segment? How do I use the Segment Addition Postulate? How do I classify angles by their measures? How do I use a protractor to draw & measure an angle? How do I use the Angle Addition Postulate? How do I use symbols to write the name of a point, line, Content Patterns Inductive Reasoning Points, Lines, Planes Intersection s Segments Angles Skills Identify patterns and use them to make predictions. Apply Inductive Reasoning to make conjectures. Understand the basic concept of a point, line, and plane and the relationship between them. Understand the intersection between geometric figures. Sketch figures and their intersections. Measure segments. Understand and apply the Segment Addition Postulate. Classify angles by the measures. Draw and measure angles using a protractor. Understand and apply the Angle Addition Postulate. Recognize and use correctly symbols for naming points, lines, planes, segments, and angles. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments Video lesson Draw and measure angles worksheet Partner Activity: Points, Lines, Planes, etc. Table Matching Group Activity: Points, Lines, Planes, etc. Multiple Choice/Short Answer Questions SUMMATIVE Quiz at end of every two to three lessons Extra Practice over unit End of Unit Test Standards PASS 1.1, 2.2, 5.1 CC G.CO.1 Resources Textbo ok Math’s Cool Video Lesson over Langua ge of Geom etry plane, segment and angle? Curriculum Map – Unit 2: Segments and Angles Teacher: SAUSEDA Month / Year Sept Department: MATH Essential Question(s) How to I bisect a segment? How do I find midpoint coordinates of a segment? How do I bisect and angle? How do I find measures of complementary and supplementary angles? How do I find measures of angles formed by intersecting lines? How do I use ifthen statements? How do I apply the Law of Detachment and Law of Syllogism? How do I use properties of equality and congruence? Content Segment Bisectors Angle Bisectors Compleme ntary and Supplement ary Angles Vertical Angles Linear Pairs If-then Statements Deductive Reasoning Properties of Equality and Congruence Skills Analyze segment bisectors and know how to bisect a segment. Apply the midpoint formula to find the coordinates of the midpoint of a segment. Analyze angle bisectors and know how to bisect an angle. Identify complementary angles, supplementary angles, vertical angles and linear pairs. Find measures of complementary and supplementary angles. Find measures of angles formed by intersecting lines (i.e., vertical angles and linear pairs) Use if-then statements Apply the Laws of Logic (Law of Detachment and Law of Syllogism) Use properties of equality and congruence to justify mathematical statements Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments Extra practice worksheets SUMMATIVE Standards Quiz at end of every two to three lessons End of Unit Test Vocabulary Test over Units 1 and 2 PASS 2.1, 2.2c, 5.1 CC Resources Textbo ok Power Presen tations Disc Board works power points Disc Curriculum Map – Unit 3: Parallel and Perpendicular Lines Teacher: SAUSEDA Month / Year Oct Department: MATH Essential Question(s) How do I identify the relationships between lines? How do I identify the relationship between perpendicularity and right angles? How do I classify angles formed by 2 lines and a transversal? What is the relationship between angles formed by 2 “parallel” lines cut by a transversal? What information about angles do I need in order to conclude that lines forming them with a transversal are parallel? How do I write the inverse, converse, and contrapositive of an if-then statement? Content Parallel lines Perpendicul ar lines Skew lines Parallel planes Lines perpendicul ar to planes Transversal s Correspond ing Angles Alternate Interior Angles Alternate Exterior Angles Same-Side Interior Angles Inverse Converse Contraposit ive Skills Identify relationships between parallel, perpendicular, and skew lines. Understand and apply theorems about perpendicular lines. Identify the special angles pairs formed by two lines and a transversal. Identify congruent angles formed when a transversal cuts parallel lines. Identify supplementary angles formed when a transversal cuts parallel lines. Write the inverse, converse, and contrapositive of if-then statements. Explain whether lines are parallel or not based on the angles formed by a transversal. Explain the various ways to show that two lines are parallel. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments Extra practice over identifying special angle pairs Enrichment over special angle pairs SUMMATIVE Quiz over every two lessons End of Unit Test Standards PASS 2.2, 2.2a CC G-CO.1 and G-CO.9 Resources Textbo ok Power point Presen tations Disk Usatest prep videos Curriculum Map – Unit 4: Slope of Parallel and Perpendicular Lines Teacher: SAUSEDA Month / Year Oct Nov Department: MATH Essential Question(s) How do I find the slope of a line? How do I use slope to determine parallel and perpendicular lines in a coordinate plane? How do I write equations of parallel lines? How do I write equations of perpendicular lines? Content Slope Parallel lines Perpendicul ar lines Equations of parallel and perpendicul ar lines Skills Use slope formula to find the slope of a line Use rise and run to find the slope of a line Use slope to determine if lines are parallel or perpendicular Write equations of parallel and perpendicular lines. Course: GEOMETRY Activities & Assessments FORMATIVE Worksheets SUMMATIVE End of Unit Test Standards PASS 5.1 CC G.CO.9 Resources Textbo ok Power point present ations disk Usatest prep videos Curriculum Map – Unit 5: Triangle Relationships Teacher: SAUSEDA Month / Year Nov Dec Department: MATH Essential Question(s) How do I classify triangles by their angles? How do I classify triangles by their sides? How do I find interior and exterior angle measures of a triangle? How do I find side lengths and angle measures of an isosceles triangle? How do I use Pythagorean Theorem to find missing side of a right triangle? How do I use Distance Formula to find distance between two points? How do I use side lengths of a triangle to determine if it is acute, right, or obtuse? How do I use centroid of a triangle to find segment lengths related to the Content Triangles Interior angles Exterior angles Isosceles triangles Equilateral triangles Pythagorea n Theorem Distance Formula Right Triangles Converse of Pythagorea n Theorem Median of a triangle Centroid of a triangle Skills Classify triangles according to number of congruent sides. Classify triangle by their angle measures. Apply the Triangle Sum Theorem to find interior angle measures of a triangle. Apply the Exterior Angle Theorem to find exterior angle measures of a triangle. Use properties of Isosceles and Equilateral triangles. Apply the Pythagorean Theorem to find missing side of a right triangle. Apply the Distance Formula to find the distance between two points on the coordinate plane. Apply the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle. Use side lengths of a triangle to classify it as acute, right or obtuse. Identify medians in triangles. Use the notion of centroid to find segment lengths related to the median. Use the angle measures in a triangle to determine longest and shortest sides. Use the side lengths of a triangles to determine largest and smallest angles Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments from textbook or worksheets SUMMATIVE Quiz at end of every two to three lessons Extra practice of unit End of Unit Test Standards PASS 2.3b, 3.1, 5.1 CC G-CO.10, G-SRT.8 Resources Textbo ok Power point present ations disk Usatest prep videos for Distan ce Formu la and Pythag orean Theore m median? How do I use angle measures to determine shortest and longest sides of a triangle? How do I use side lengths to determine smallest and largest angles of a triangle? Curriculum Map – Unit 6: Congruent Triangles Teacher: SAUSEDA Month / Year Dec Jan Department: MATH Essential Question(s) How do I identify congruent triangles? How do I identify corresponding parts? How do I use the shortcut methods to show triangles are congruent? How do I show that corresponding parts of congruent triangles are congruent? Content Correspond ing parts Congruent figures SSS, SAS, ASA, AAS, HL Distance from a point to a line Equidistant Perpendicul ar Bisector Skills Identify congruent triangles and corresponding parts. Show triangles are congruent using SSS, SAS, ASA, AAS, and HL. Write congruence statements for congruent triangles correctly. Show corresponding parts of congruent triangles are congruent. Use angle bisectors and perpendicular bisectors. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments Extra practice over SSS, SAS, ASA, AAS SUMMATIVE Quiz after every two lessons End of Unit Test Congruent Triangles Project Standards PASS 2.5a, 2.5b CC G-CO.7, G-CO.8, G-CO.9, G-CO.12 Resources Textbo ok Power point Presen tations disk Curriculum Map – Unit 7: Transformations Teacher: SAUSEDA Month / Year Dec Jan Department: MATH Essential Question(s) How do I identify a translation? How do I identify a reflection? How do I identify a rotation? How do I identify a dilation? How do I find the scale factor of a dilation? How do I describe transformations using words? How do I describe transformations using coordinate notation or motion rule? How do I draw the image of a translation, reflection or rotation? How do I determine if a figure has line or rotational symmetry? Content Transforma tions Image Translation Reflection Rotation Dilation Scale Factor of Dilation Coordinate Notation or Motion Rule Line Symmetry Rotational Symmetry Line of Symmetry Angles of Rotation Skills Identify whether a transformation is a translation, a reflection or a rotation? Describe transformations using words. Describe transformations using Coordinate Notation or Motion Rules. Draw the image of a figure given the rule for a translation, reflection or rotation. Determine whether figures have line symmetry or rotational symmetry. Determine angles of rotation about a given center of rotation. Determine angles of rotation that map a figure onto itself. Determine whether the dilation of a figure is a reduction or an enlargement. Determine the scale factor of a dilation. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments Video lessons SUMMATIVE Extra practice worksheets End of Unit Test End of Unit Transformations Writing Assignment (Honors Geometry) Standards PASS 5.2b CC G-CO.2 through G-CO.5 CC G-SRT.1 Resources Textbo ok Math’s Cool Video Lesson s Usatest prep videos Kutaso ftware worksh eets Curriculum Map – Unit 8: Quadrilaterals Teacher: SAUSEDA Month / Year Jan Feb Department: MATH Essential Question(s) How do I identify figures that are polygons? How do I classify polygons by the number of sides they have? How do I find angle measures of quadrilaterals? How do use properties of parallelograms, rhombuses, rectangles, squares, and trapezoids to find their side lengths and angle measures? How do I show that a quadrilateral is a parallelogram? How do I identify a quadrilateral as one of the special quadrilaterals? Content Polygons Parallelogra ms Rhombuses Rectangles Squares Trapezoids Isosceles trapezoids Properties of all special Quadrilater als Skills Identify whether a figure is a polygon. Classify the most common types of polygons according to the number of sides. Apply the Quadrilateral Interior Angles Theorem to find angle measures in quadrilaterals. Identify parallelograms, rectangles, rhombuses, squares and trapezoids. Use properties of parallelograms, rectangles, rhombuses, squares and trapezoids. Explore ways to determine whether a quadrilateral is a parallelogram, rectangle, rhombus, or square. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments SUMMATIVE Quizzes after every two to three lessons Extra practice worksheets End of unit test Properties of Quadrilaterals Test Quadrilaterals Project (Honors Geometry) Standards PASS 2.3a, 2.3b, 2.3c CC G-CO.11 Resources Textbo ok Curriculum Map – Unit 9: Similarity Teacher: SAUSEDA Month / Year Feb Department: MATH Essential Question(s) How do I write a proportion? How do I solve proportions? How do I determine similar polygons? How do I find the scale factor of similar polygons? How do I write a similarity statement? How do I write a statement of proportionality? How do I find the ratio of the perimeters for similar polygons? How do I use AA, SSS, and SAS to determine if two triangles are similar? How do I use the Triangle Proportionality Theorem to determine segment lengths? How do I use the Converse of Content Ratios Proportions Means Extremes Cross Product Property Similar Polygons Scale Factor AA Similarity Postulate SSS Similarity Theorem SAS Similarity Theorem Perimeters of Similar Polygons Midsegmen t of a Triangle Skills Use ratios to determine segment lengths and side lengths of rectangles. Use Cross Product Property to solve proportions. Understand how to write proportions. Identify all pairs of congruent angles and proportional sides of congruent polygons. Write a similarity statement. Write a statement of proportionality. Find the scale factor of similar polygons. Find the ratio of perimeters of similar polygons. Show triangles are similar using the AA Similarity Postulate. Show triangles are similar using the SSS and SAS Similarity Theorems. Understand and apply the Triangle Proportionality Theorem and its converse. Use the Midsegment Theorem to find the length of a midsegment of a triangle. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments. Math’s Cool Video lesson over Similarity SUMMATIVE End of Unit Quiz or Test Plan-to-Pass EOI review worksheets. Standards PASS 2.4b CC Resources Textbo ok Math’s Cool video the Triangle Proportionality Theorem to determine if segments are parallel? How do I find the length of a midsegment of a triangle? Curriculum Map – Unit 10: Polygons and Area Teacher: SAUSEDA Month / Year Feb. Department: MATH Essential Question(s) How do I classify polygons as convex or concave? How do I classify polygons as equilateral, equiangular, or regular? How do I find the sum of the interior angles of a polygon? How do I find the sum of the exterior angles of a polygon? How do I find the area of a parallelogram? How do I find the area of a square? How do I find the area of a rectangle? How do I find the area of a triangle? How do I find the area of a rhombus? How do I find the area of a trapezoid? How do I find the circumference Content Polygons Convex Concave Equilateral Equiangular Regular Interior angle Exterior angle Area Height Base Circle Center of Circle Radius Diameter Circumfere nce Central Angle Sector Area of Similar Polygons Skills Classify polygons as convex or concave Classify polygons as equilateral, equiangular, or regular. Find the sum of the measures of the interior angles of a convex polygon. Find the sum of the measures of the exterior angles of a convex polygon. Find the measure of an interior angle of a regular polygon. Find the area of squares and rectangles. Find the area of complex polygons. Find the area of triangles. Find the ratio of areas of similar polygons. Find the area of parallelograms and rhombuses. Find the area of trapezoids. Given the area of a polygon, find the missing dimensions. Find the circumference of a circle. Find the area of a circle. Find the area of a sector of a circle. Apply area formulas for polygons and circles to solve real-life situation word problems. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments. SUMMATIVE End of Unit Test Area of Irregular Shapes worksheet Properties of 2dimensional figures (Plan-toPassworksheet) Standards PASS 2.3a, 2.3b, 2.3d CC Resources Textbo ok of a circle? How do I find the area of a circle? How do I find the area of a sector of a circle? Curriculum Map – Unit 11: Surface Area and Volume Teacher: SAUSEDA Month / Year March Department: MATH Essential Question(s) How do I identify solids? How do I determine if a solid is a polyhedral? How do I name a prism? How do I name a pyramid? How do determine faces, edges, and vertices of a solid? How do I determine the net of a solid? How do I find surface area of prisms and cylinders? How do I find lateral area of prisms and cylinders? How do I find surface area of pyramids and cones? How do I determine the slant height or height of pyramids and cones? How do I find the volume of Content Solid Polyhedra Platonic Solids Base Face Edge Vertices Prism Surface Area Lateral face Lateral area Cylinder Pyramid Height of Pyramid Slant height of pyramid Cone Height of Cone Slant height of cone Volume Sphere Hemisphere Skills Identify solids Name solids Identify solids that are Polyhedra Identify the Platonic Solids Determine bases, faces, edges and vertices of a solid Determine the net of a solid Find the Surface Area of prisms, cylinders, pyramids, cones, spheres and hemispheres Find the lateral area of solids Determine the height or slant height of pyramids and cones Find the Volume of prisms, cylinders, pyramids, cones, spheres and hemispheres Apply surface area and volume formulas to solve real-life situation word problems Course: GEOMETRY Activities & Assessments FORMATIVE Math’s Cool Video lesson over 3dimensional shapes Do Math’s Cool Video Guided Practice worksheets together Assign Daily worksheets for independent practice SUMMATIVE End of Unit Test Additional practice worksheets with more challenging problems involving solids Standards PASS 4.1a, 4.1b CC G-CMD.3 Resources Textbo ok Models of solids Usatest prep videos prisms and cylinders? How do I find the volume of pyramids and cones? How do I find surface area and volume of spheres and hemispheres? Curriculum Map – Unit 12: Right Triangles and Trigonometry Teacher: SAUSEDA Month / Year Mar April Department: MATH Essential Question(s) How do I simplify radicals without a calculator? How do I use a calculator to find square roots? How do I multiply radicals without a calculator? How do I determine if a triangle is a special right triangle? How do I find side lengths of 45-45-90 triangles? How do I determine the shorter leg and longer leg of a 30-60-90 triangles? How do I find side lengths of a 30-60-90 triangle? How do I determine the tangent, sine and cosine ratios of an acute angle of a right triangle? How do I use Content Radical Radicand 45-45-90 triangles Shorter leg Longer leg 30-60-90 triangles Trigonomet ric ratios Opposite leg Adjacent leg Tangent Sine Cosine Inverse Tan Inverse Sin Inverse Cos Angles of Elevation Angles of Depression Law of Sines Law of Cosines Skills Simplify radicals Use a calculator to find square roots Multiply radicals Determine whether a right triangle is a special 45-45-90 or 30-60-90 triangle. Use the 45-45-90 Triangle Theorem to find side lengths of a right triangle. Use the 30-60-90 Triangle Theorem to find side lenths of a right triangle. Find the tangent, sine, and cosine ratios of an acute angle of a right triangle. Use SIN, COS, and TAN functions on a calculator to approximate the trig ratios of an angle. Use inverse TAN, inverse SIN and inverse COS functions on a calculator to approximate angle measures of a right triangle. Understand how to set up proportions using trig ratios to find missing side lengths and angles of a right triangle. Solve a right triangle. Apply trig ratios to solve real-life situation word problems. Solve problems involving angles of elevation and angles of depression. Understand under what cases the Laws of Sines and Law of Cosines can be used. Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments. SUMMATIVE End of Unit Test Extra Practice worksheets over trig ratios Standards PASS 3.2, 3.3 CC G-STR.6, G-STR.7, G-SRT.11 Resources Textbo ok Scienti fic calcula tor the SIN, COS, and TAN functions on a calculator? How do I use trig ratios to find missing side lengths of a right triangle? How do I use inverse trig ratios to determine the acute angles of a right triangle? How do I solve a right triangle? When and how do I use the Law of Sines to find missing sides or angles of a triangle? When and how do I use the Law of Cosines to find missing sides or angles of a triangle? Use the Law of Sines and or Law of Cosines to solve a triangle. Curriculum Map – Unit 13: Circles Teacher: SAUSEDA Month / Year April Department: MATH Essential Question(s) How do I identify a chord, secant, and tangent of a circle? How do I find the measure of a central angle? How do I find the measure of a minor arc? How do I find the measure of a major arc? How do I find the length of an arc? How do I determine if two arcs are congruent? How do I find the measure of an inscribed angle? How do I determine if a line is tangent to a circle? How do I determine measures of angles formed by intersecting chords? How do I determine measures of Content Chord Secant Tangent Point of Tangency Radius Diameter Center of Circle Central Angle Major Arc Minor Arc Semicircle Arc measure Arc length Inscribed Polygon Circumscrib ed Circle Inscribed Angle Circumscrib ed Polygon Equations of Circles Skills Name the term that best describes a given line, segment and point in a circle. Find the measures of minor arcs, major arcs, and semicircles. Understand and apply the Arc Addition Postulate to determine the measure of an arc formed by two adjacent arcs. Find the length of an arc. Understand and apply different properties used to determine if two arcs are congruent. Determine measures of arcs formed by inscribed polygons. Determine arc and chord lengths formed by diameters perpendicular to a chord. Find the measure of an inscribed angle. Determine measures of angles of inscribed polygons. Understand and apply relationships involving tangents to find segment lengths. Understand properties of circumscribed polygons to find segment lengths. Find measures of angles formed by secants and tangents. Find measures of segments formed when two chords intersect in a circle. Find measures of segments formed when tangents intersect outside a circle. Find equations of circles on the Course: GEOMETRY Activities & Assessments FORMATIVE Daily homework assignments. SUMMATIVE End of Unit Test Extra Practice worksheets. Standards PASS 2.6 CC G-C.2, CC G-C.4, CC G-CO.13 CC G-GPE.1 Resources Textbo ok Study Guide Packet from Glenco e textbo ok segments of intersecting chords? How do I determine measures of angles formed by intersecting secants and tangents? How do I determine segment lengths formed by secants and tangent? How do I find the equation for a circle on the coordinate plane? How do I graph a circle on a coordinate plane given an equation? coordinate plane. Graph circles on the coordinate plane.