Geometry Unit & Lesson Overviews Mathematics. Unit: 1.1 Foundations of Geometry Days : 8

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1 Unit: 1.1 Foundations of Geometry Days : 8 How do you use undefined terms as the basic elements of Geometry? What tools and methods can you use to construct and bisect segments and angles? How can you use angle pairs to solve problems? How can you find midpoints of segments and distances on the coordinate plane? Students will learn the vocabulary and symbols for the basic elements of geometry Students will construct and bisect segments and angles Students will use angle pairs to solve problems Students will find midpoints of segments and distances on the coordinate plane There are 2 assessments planned for this unit Using a protractor to measure angles Using a compass to construct segments and angles Using angle relationships to write and solve equations to find unknown angles Using midpoint and distance formulas CC.9-12.G.CO.1 CO.5 CO.9 CO.12 CC.9-12.A.CED.4 CC.9-12.G.GPE.4 Sections 1-1, 1-2, 1-3, 1-4, 1-6 in the CoreMath Text Explorations in CoreMath

2 Unit: 1.2 Geometric Reasoning Days : 6 What kinds of justifications can you use in writing algebraic and geometric proofs? How can you organize the deductive reasoning of a geometric proof? What are some formats you can use to organize geometric proofs? Students will learn the different types of justifications that can be used when writing proofs Students will learn how to organize a proof Students will discover the different formats that can be used to organize proofs There is one assessment planned for this unit Differentiating between theorems and postulates Justifying geometric statements CC.9-12.G.CO.9 Sections 2-5, 2-6, and 2-7 in CoreMath Text Explorations in CoreMath

3 Unit: 1.3 Parallel and Perpendicular Lines Days : 9 How many distinct angle measures are formed when three lines in a plane intersect in different ways? How can you construct perpendicular lines and prove theorems about perpendicular bisectors? How do you find the point on a line segment that partitions the segment in a given ratio? How can you use slope to write equations of lines that are parallel or perpendicular? Students will learn the types of angles that are formed by a parallel line and its transversals Students will learn the properties of the angles formed by parallel lines and its transversals Students will learn the relationship of the slopes of parallel and perpendicular lines There are two assessments scheduled for this unit Sections 3-1, 3-2, 3-4, 3-5 and 3-6 in the CoreMath Text Determining the slope of a line parallel or perpendicular to a given line Determining missing measures of angles formed by parallel lines and their transversals CC.9-12.G.CO.9 CC.9-12.G.CO.12 CC.9-12.G.GPE.5 CC.9-12.G.GPE.6

4 Unit: 1.4 Transformations Days : 9 How do you draw the image of a figure under a translation, reflection, rotation and/or dilation? How can you use more than one transformation to map one figure onto another? How do you identify transformations that are rigid motions? Students will be able to draw the image of a figure under a translation, reflection, rotation and/or dilation Students will be able to identify which transformations are rigid motions Students will use more than one transformation to map one figure onto another One assessment to be given at the end of the unit Draw figures using translations, reflections, rotations and/or dilations Identifying rigid motion transformations Predict effects of a given rigid motion on a figure CC.9-12.G.CO.2, CC.9-12.G.CO.4, CC.9-12.G.CO.5, CC.9-12.G.CO.6 Ch. 1.7, 9.2, 9.1, 9.3, 9.4 and 9.7 in the Explorations in CoreMath

5 Unit: 2.1 Properties of Triangles Days : 15 How can you classify triangles in the coordinate plane? What are some theorems about angle measures in triangles? What special relationships exist among the sides and angles of isosceles triangles? What can you conclude about the medians of a triangle? What must be true about the segment that connects the midpoints of two sides of a triangle? How are side lengths and angle measures of triangles related? Students will classify triangles on the coordinate plane Students will identify special relationships related to isosceles triangles Students will make conclusions using the medians of a triangle Students will explore the segment that connects the midpoints of two sides of a triangle Students will determine how side lengths and angle measures of triangles are related Two assessments one midway through the unit, one at the end of the unit Calculating distance and midpoint on the coordinate plane Identifying relationships in isosceles triangles Making conclusions about the medians of a triangle Determining how side lengths and angle measures in triangles are related CC.9-12.G.GPE.4, CC.9-12.G.GPE.7, CC.9-12.G.CO.10 Ch. 4-2, 4-3, 4-9, 5-3, 5-1, 5-4 and 5-5 in the Explorations in COREMath textbook

6 Unit: 2.2 Triangle Congruence Days : 9 How can you use properties of rigid motions to draw conclusions about corresponding sides and angles in congruent triangles? How can you establish the SSS, SAS, ASA, AAS, and HL triangle congruence criteria? How can CPCTC be used to in proofs? Students wil use properties of rigid motions to draw conclusions about corresponding sides and angles in congruent triangles Students will use SSS, SAS, ASA, AAS, and HL triangle congruence criteria to prove triangles are congruent Students will use CPCTC to establish proofs One assessment given at the end of the unit Ch 4-4, 4-5, 4-6 and 4-7 in the Explorations in COREMath Using SSS, SAS, ASA, AAS, HL triangle congruence criteria and CPCTC in proofs CC.9-12.G.CO.7 CC.9-12.G.CO.8 CC.9-12.G.CO.10 CC.9-12.G.SRT.5

7 Unit: 2.3 Triangle Similarity Days : 10 How can you use ratios of corresponding side lengths to solve problems involving similar polygons? How can dilations be used to show figures are similar? Students will use scale factor and proportions to solve for missing side lengths of similar polygons Students will use ratios and angle measures to identify whether figures are similar Students will solve problems by applying the Triangle Proportionality Theorem Two assessments throughout the unit Sections 7-6, 7-3, 7-1, and 7-4 in the CoreMath text Write and use proportions to solve problems with similar figures. G.SRT.2 G.SRT.5 MG.1

8 Unit: 3.1 Right Triangles Days : 15 How can you apply the Pythagorean Theorem? How do you find the tangent, sine and cosine ratios for the acute angles in a right triangle? How can you use trigonometric ratios to solve problems involving angles of elevation and depression? What can you say about the side lengths associated with special right triangles? Students will be able to find missing side lengths of right triangles using the Pythagorean Theorem and Special Right triangles Students will be able to apply trigonometric ratios to find missing sides and/or angles Two assessments and a Common Task (Cranston Marina) Explorations in COREMath : Use different right triangle properties to solve problems G.SRT.6 G.SRT.7 G.SRT.8

9 Unit: 3.2 Quadrilaterals Days : 8 What can you conclude about the sides, angles, and diagonals of a parallelogram? What are the properties of rectangles and rhombi? How can you use slope in coordinate proofs? Students will learn the properties of different types of quadrilaterals (ie, parallelograms, rectangles, rhombi, etc.) Students will use the properties of quadrilaterals as well as slope, distance, and midpoint in coordinate proofs Students will solve problems using the properties of quadrilaterals There is one assessment planned for this unit Sections 6-2, 6-3, 6-4, 6-5, and 6-6 in the CoreMath Text Using the slope, distance and midpoint formulas Using properties of parallel lines and transversals G.CO.9 G.CO.11 G.GPE.4 G.SRT.5 Explorations in Core Math

10 Unit: 4.1 Circles Days : 13 How are arcs and chords of circles associated with central angles? What is the relationship between central angles and inscribed angles in a circle? What is the relationship between a tangent line to a circle and the radius drawn from the center to the point of tangency? When two tangents are drawn to a circle, how do you find the measure of the angle formed at their intersection? How can you write and use equations of circles in the coordinate plane? Students will be able to name and find the measures of arcs, angles and segments on and in a circle. Students will be able to write the equation of a circle and graph a circle on the coordinate plane. Two assessments, one mid-unit and one end of unit Exploration in CORE Math: 12-2, 12-4, 12-1, 12-5, 12-6, 12-7 Finding angle, segment and arc measure in a circle. Writing equations of a circle Graphing circles on the coordinate plane G.C.2 G.C.3 G.CO.9 G.GPE.1

11 Unit: 4.2 Extending Perimeter, Circumference and Area Days : 6 How can you find areas of irregular shapes? How do you find the area of a sector of a circle? How do you calculate arc length in a circle? Students will remember how to find the area and perimeter (circumference) of polygons and circles. Students will be able to find the areas of composite figures. Students will be able to find the area of a sector of a circle. Students will be able to find arc length of a circle. One assessment at the end of the unit Explorations in CoreMath text: 10-2 and 12-3 Finding area of triangles, parallelograms, trapezoids and circles. Using areas of polygons and circles to find area of composite figures. Using proportional reasoning to fins the area of a sector and arc length on a circle. G.MG.1 G.MG.3 G.CO.1 G.C.5 G.GMD.1

12 Unit: 4.3 Volume Days : 11 How do you calculate the volume of a prism or cylinder? How do you calculate the volume of a pyramid or cone and use volume formulas to solve problems? How do you calculate the volume of a sphere? How do you calculate the volume of composite figures? Students will be able to find the volume of prisms, cylinders, pyramids, cones and spheres. Students will solve problems involving volume. Students will be able to find the volume of composite figures. Two assessments, one mid-unit and one end of unit Explorations in CoreMath: 11-2, 11-3, and 11-4 Finding volume of different figures G.GMD.1 G.GMD.3 G.MG.1 G.MG.2

13 Unit: 4.4 Probability Days : 9 What are permutations and combinations and how can you use them to calculate probabilities? How can you use probabilities to help you make fair decisions? How can you use geometric probability to solve problems? How do you find the probability of independent and dependent events? How do you find the probability of mutually exclusive events and overlapping events? Students will be able to use permutations and combinations to calculate probability. Students will make educated decisions based on probability. Students will be able to calculate theoretical probabilities. Students will be able to use the multiplication rule and find the probability of independent and dependent events. Students will find the probability of mutually exclusive events and overlapping events and apply the addition rule. One assessment at the end of the unit Exploration in CORE Math: 13-1, 13-2, 10-6, 13-3, 13-5 Calculating factorials Applying the formulas for permutations and combinations appropriately Decision making problems Probability of an event and its complement Independent and dependent events Conditional probability Mutually exclusive and overlapping events Addition rule S.CP.9 S.MD.6 S.CP.1-5,7 (Also see Glencoe Geometry 2005 section 11-5 for geometric probability)