HADDONFIELD PUBLIC SCHOOLS Discovering Geometry Curriculum Map Chapter 1 September Targeted Standard(s): G-CO.1, G-CO.9, G-MG.1 Geometry can be broken down into three basic figures: points, lines and planes What are the building blocks of geometry? What are the definitions of polygons and what are their properties? How do we properly denote angles, segments, lines, rays, etc? Chapter 1 Introducing Geometry 1.1 Building Blocks of Geometry 1.2 Poolroom Math - Use correct terminology and notation of points, segments, lines, rays, planes, angles, and - Vocabulary packet - Kiezzo review game - Group jigsaw with triangle 1.1 1.3 Quiz 1.4 1.5 Quiz Chapter 1 Test
- Measure an angle - Angle bisectors 1.3 What s a Widget - Angle definitions 1.4 Polygons 1.5 Triangles & Special Quads 1.6 Circles Powerpoint, Protractors, Rulers collinear and coplanar points. - Use measurement tools. - Define special angle relationships. - Define and classify polygons and circles and their related terms. and quadrilateral definitions Chapter 2 October/November Targeted Standard(s): A-SSE.1, A-REI.1, A-REI.3, G-CO.9 Patterns can be interpreted by using inductive and deductive reasoning skills How do we find the next term in a number or picture pattern? How do we find the nth term in a numeric sequence?
What are the relationships between special angle pairs? Chapter 2 Reasoning in Geometry 2.1 Inductive reasoning 2.3 Finding the nth term 2.4 Mathematical Modeling 2.5 Angle Relationships 2.6 Special Angles on Parallel Lines - Alternate Interior/Exterior - Same Side Interior/Exterior - Corresponding Powerpoint, Geometer s Sketchpad - Use inductive reasoning the find the next term in a pattern. - Find the nth term in a linear number sequence. - Discover relationships between special pairs of angles - Write a two-column proof involving parallel lines - Note packet - Indiana Jones reference for parallel line activity 2.1 2.3 Quiz Angle Town Chapter 2 Test Chapter 3 November/December Targeted Standard(s): G-CO.9, G-CO.10, G-CO.12
There are many methods for finding the center of a triangle, including angle bisectors, perpendicular bisectors, medians, and altitudes How do we bisect an angle? a segment? How many centers does a triangle have? Which point is the center of gravity in a triangle? Chapter 3 Using Tools of Geometry 3.2 Constructing Perpendicular Bisectors 3.4 Constructing Angle Bisectors 3.7 Constructing Points of Concurrency - Centroid - Orthocenter - Circumcenter - Incenter Powerpoint, Geometer s Sketchpad, Rulers, Protractors - Construct perpendicular Bisectors, angle bisectors, and midpoints. - Discover the points of congruency of angle bisectors, perpendicular bisectors, altitudes, and medians. - Identify the center of gravity in a triangle. - Triangle center stations - Triangle center packet 3.2 3.4 Quiz Chapter 3 Test
Chapter 4 January/February Targeted Standard(s): A-SSE.1, G-CO.7, G-CO.8, G-CO.9, G-CO.10, G-CO.12 In order to prove two triangles are congruent we need three pieces of information: SSS, SAS, ASA or SAA What special properties can be found in triangles? What makes triangles congruent? How can we prove triangle congruency? Chapter 4 Discovering and Proving Triangle Properties 4.1 Triangle Sum Conjecture 4.2 Properties of Special Triangles 4.3 Triangle Inequalities 4.4 Are There Congruence - Discover and explain the sum of the measures of the angles of a triangle. - Discover a relationship between the base angles of an isosceles triangle. - Construct triangles with ribbon, tape, scissors 4.1 4.3 Quiz 4.4 4.5 Quiz Chapter 4 Test
Shortcuts 4.5 Are There Other Congruence Shortcuts 4.6 CPCTC 4.8 Proving Isosceles Triangle Conjectures - Investigate inequalities among sides and angles in triangles. - Apply the SSS, SAS, AAS, ASA congruency shortcuts and CPCTC. Powerpoint, Geometer s Sketchpad, Rulers, Protractors, Scissors, Ribbon, Tape Chapter 5 February/March Targeted Standard(s): A-SSE.1, G-CO.9, G-CO.10, G-CO.11 The interior angle sum of any polygon can be found by breaking the polygon into triangles and using calculations based on 180 What special properties can be found in polygons? How do we find the interior angle sum of any given polygon?
What are the properties of midsegments in triangles and in trapezoids? Chapter 5 Discovering and Proving Polygon Properties 5.1 Polygon Sum Conjecture 5.2 Exterior Angles of a Polygon 5.3 Kite and Trapezoid Properties 5.4 Properties of Midsegments 5.5 Properties of Parallelograms 5.6 Properties of Special Parallelograms 5.7 Proving Quadrilateral Properties - Discover the sum of the interior and exterior angle measures in a polygon. - Discover properties of kites, trapezoids, parallelograms, rectangles, rhombuses, and squares. - Define and discover properties of midsegments in triangles and trapezoids. Powerpoint, Geometer s Sketchpad, Rulers, Protractors - Break polygons into triangles to find the interior angle sum. - Jigsaw with new conjectures 5.1 5.2 Quiz 5.3 5.4 Quiz 5.5 5.6 Quiz Chapter 5 Test Chapter 6 April/May Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-REI.1, A-REI.3, G-C.1, G-C.2, G-C.4, G-C.5
The length and the measure of an arc of a circle, the diameter and the circumference of a circle, and the radius and the area of a circle can be related by setting up a proportion What are the relationships among chords, arcs, angles, and tangent lines? How do we calculate the length of an arc? What are the formulas for area and circumference of a circle? Chapter 6 Discovering and Proving Circle Properties 6.1 Chord Properties 6.2 Tangent Properties 6.3 Arcs and Angles 6.5 The Circumference/Diameter Ratio 6.6 Around the World 6.7 Arc Length - Understand basic properties of a circle. - Discover properties of chords and tangents. - Discover relationships between inscribed angles and their intercepted arcs. - Calculate area, circumference, and arc length/measure of a circle. Powerpoint, Geometer s Sketchpad, Youtube, Rulers, Protractors - Circle song 6.1 6.2 Quiz 6.3 Quiz 6.5 6.6 Quiz 6.7 Quiz Chapter 6 Test
Chapter 8 May Targeted Standard(s): N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-REI.1, A-REI.3 The formula for area of a given polygon can be used to solve for a missing value What are the formulas for area of rectangles, parallelograms, triangles. Trapezoids, and kites? Chapter 8 Area 8.1 Areas of Rectangles and Parallelograms 8.2 Areas of Triangles, Trapezoids, and Kites - Use the formulas to find the area of the given polygons. - Algebraic review Area Test
Powerpoint, Rulers, Protractors Special Right Triangles Ratios June Targeted Standard(s): A-SSE.1, A-REI.1, A-REI.3, G-SRT.2, G-SRT.5 All 45-45-90 triangles will have the same ratio among their side lengths 1 1 2 All 30-60-90 triangle will have the same ratio among their side lengths 1 3 2 What are the ratios between side lengths of a 45-45-90 triangle? What are the ratios between side lengths of a 30-60-90 triangle? Special Right Triangle Ratios 45-45-90 Ratios - Use the ratios to find missing side lengths of special right - Ratio review packet Right Triangle Test
30-60-90 Ratios Powerpoint, Rulers, Protractors triangles. - Use the Pythagorean Theorem to find missing side lengths of any right triangle.