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Curriculum Map UNIT NAME Unit 1 Lines and Angles Chapters 1 and 3 STANDARDS OBJECTIVES I can… CRS CCS BOA: 13-15 ■ model a variety of problem situations with expressions and/or equations ■ locate and describe objects in terms of their position on the number line and on a grid ■ Estimate or calculate the length of a line segment based on other lengths given on a geometric Figure CCSS.MATH.CONTENT.7.G. B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. CCSS.MATH.CONTENT.8.G. B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. BOA:20-23 ■ Compute the perimeter of polygons when all side lengths are given ■ Locate points in the coordinate plane ■ Comprehend the concept of length on the number line* ■ Find the measure of an angle using properties of parallel lines ■ Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) BOA: 24 – 27 ■ Determine the slope of a line from points or equations* ■ Match linear graphs with their equations* ■ graph linear equations and inequalities, determine slopes of CCSS.MATH.CONTENT.HS G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CCSS.MATH.CONTENT.HS G.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CCSS.MATH.CONTENT.HS G.GPE.B.7 Identify and model points, lines and planes Identify collinear and coplanar points and intersecting lines and planes in space Compute with measures Find the distance between two points Find the midpoint of a segment Measure and classify angles Identify and use congruent angles and the bisector of an angle Identify and use special pairs of angles Identify perpendicular lines Identify and name polygons Find perimeters of a polygons Identify the relationships between two lines or two planes Name angles formed by a pair of lines and transversal Use the properties of parallel lines to determine congruent angles Use algebra to find angle measure Find the slope of the line Use slope to identify parallel and perpendicular lines Write an equation of a line given information Solve problems by writing equations ASSESSMENTS BOY Exam Mid Chapter Exam ( Chapter 1 ) Chapter 1 Exam Mid Chapter Exam ( Chapter 3 ) Chapter 3 Exam Midterm Exam Projects: PortfolioAssessments Throughout Construction Copy a segment and angle Construct perpendicular/angle bisector Construct an isosceles and regular triangle Construct various regular polygons Discovering angle relationship when two parallel lines are intersected by a transversal Discover the relationship between the slopes of parallel and perpendicular lines lines, identify parallel and perpendicular lines, and find distances ■ Find the midpoint of a line segment* ■ Use several angle properties to find an unknown angle measure BOA: 33-36 ■ Use the Distance Formula ■ Use the Pythagorean theorem Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* CCSS.MATH.CONTENT.HS G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. CCSS.MATH.CONTENT.HS G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CCSS.MATH.CONTENT.HS G.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Curriculum Map UNIT NAME Unit 2 Triangles, Proof, Similarity, and Trigonometry. Chapters 2 (proof) 4, 5 (triangles), 6 (similarity) and 7 (Trig) STANDARDS CRS CCS BOA: 13- 15 ■ Estimate or calculate the length of a line segment based on other lengths given on a geometric figure CCSS.MATH.CONTENT.8.G. A.4 Understand that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. BOA: 16- 19 ■ identify the basic trigonometric ratios† BOA: 20- 23 ■ Exhibit some knowledge of the angles associated with parallel lines ■ describe angles and triangles using mathematical terminology and apply their properties ■ recognize what geometric properties and relationships for parallel lines to apply to find unknown angle measures ■ recognize when to apply geometric properties and relationships of triangles to find unknown angle measures BOA: 24- 27 ■ Use properties of isosceles triangles* ■ Recognize Pythagorean triples* ■ Apply special right triangle properties and the Pythagorean Theorem to solve congruent and similar shape problems CCSS.MATH.CONTENT.8.G. A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. OBJECTIVES I can… CCSS.MATH.CONTENT.8.G. B.6 Explain a proof of the Pythagorean Theorem and its converse. CCSS.MATH.CONTENT.8.G. B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real- Identify and classify triangles by angles and sides Apply the Angle Sum Theorem and the Exterior angle Theorem Name and label corresponding parts of congruent triangles Identify congruence transformations Use SSS and SAS Postulate to test for triangle congruence Use ASA and AAS Postulates to test for triangle congruence Use properties of Isosceles and Equilateral triangles Identify and use perpendicular and angle bisectors in triangles Identify and use medians and altitudes in triangles Recognize and apply properties of inequalities to the measures of angles of a triangle Recognize and apply properties of inequalities to the relationship between angles and sides of a triangle Apply the Triangle Inequality Theorem Write ratios and use properties of proportions Identify similar figures and solve problems involving scale factors Identify similar triangles and use such to solve problems Use proportional parts of triangles Divide a segment into parts Use the Pythagorean Theorem and its converse Use properties of 45-45-90 ASSESSMENTS Mid Chapter Exam ( Chapter 4 ) Chapter 4 Exam Mid Chapter Exam ( Chapter 5 ) Chapter 5 Exam Mid Chapter Exam ( Chapter 6 ) Chapter 6 Exam Final Exam Mid Chapter Exam ( Chapter 7 ) Chapter 7 Exam Projects Ongoing Portfolio Assessments Student construct Sextants for Trig Application Project ■ Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths† ■ use basic trigonometric ratios to solve problems involving indirect measurement† BOA: 33- 36 ■ Draw conclusions based on a set of conditions ■ Solve multi step geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas ■ Write expressions, equations, and inequalities for common algebra settings ■ Solve linear inequalities that require reversing the inequality sign ■ examine and compare a variety of methods to find areas of composite figures and construct scale drawings ■ Use scale factors to determine the magnitude of a size change ■Apply properties of 30°60°-90°, 45°-45°-90°, similar, and congruent triangles ■ Use the Pythagorean Theorem ■ Apply basic Trigonometric to solve right triangle problems world and mathematical problems in two and three dimensions. CCSS.MATH.CONTENT.HS G.CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. CCSS.MATH.CONTENT.HS G.CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. CCSS.MATH.CONTENT.HS G.CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. CCSS.MATH.CONTENT.HS G.CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. CCSS.MATH.CONTENT.HS G.SRT.A.1 Verify experimentally the and 30-60-90 triangles Find trigonometric ratios using right triangles Solve problems using trigonometric ratios Solve problems using angles of elevation and depression properties of dilations given by a center and a scale factor: CCSS.MATH.CONTENT.HS G.SRT.A.1.A A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. CCSS.MATH.CONTENT.HS G.SRT.A.1.B The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CCSS.MATH.CONTENT.HS G.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. CCSS.MATH.CONTENT.HS G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CCSS.MATH.CONTENT.HS G.SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. CCSS.MATH.CONTENT.HS G.SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. CCSS.MATH.CONTENT.HS G.SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Curriculum Map UNIT NAME Unit 3 Quadrilaterals And Circles Chapters 8, 9 and 10 STANDARDS CRS BOA: 13 – 15 ■ locate and describe objects in terms of their position on the number line and on a grid ■ describe, compare, and contrast plane and solid figures using their attributes ■ Estimate or calculate the length of a line segment based on other lengths given on a geometric figure BOA: 16-19 ■Locate points in the coordinate plane ■ represent and interpret relationships defined by equations and formulas; translate between representations as ordered pairs, graphs, and equations; and investigate symmetry and transformations (e.g., reflections, translations, rotations) ■ Compute the area of rectangles when whole number dimensions are given ■ find area and perimeter of a variety of polygons by substituting given values into standard geometric formulas ■ Use geometric formulas when all necessary information is given ■ apply a variety of strategies to determine the circumference or perimeter and the area for circles, OBJECTIVES I can… CCS CCSS.MATH.CONTENT.8.G. A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using CCSS.MATH.CONTENT.HS G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. CCSS.MATH.CONTENT.HS G.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). CCSS.MATH.CONTENT.HS G.CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Find the sum of the measures of the interior/exterior angles of a polygon Recognize and apply properties of the sides, angles and diagonals of parallelograms Recognize the conditions that assure quadrilateral is a parallelogram Recognize and apply properties of rectangles and determine whether parallelogram is a rectangle Recognize and apply the properties of rhombi and squares Recognize and apply the properties of trapezoids Solve problems involving the medians of trapezoids Draw reflected images and recognize and draw lines of symmetry Draw translated images using coordinates Identify figures with rotational symmetry Determine whether the dilation is enlargement, a reduction or congruence transformation Determine the scale factor for a given polygon Solve problems involving the circumference of a circle Find arc length Recognize and use relationships between arcs ASSESSMENTS Mid Chapter Exam ( Chapter 8 ) Chapter 8 Exam Chapter 9 Exam Chapter 10 Exam Midterm Exam Projects Ongoing Portfolio Assessments triangles, rectangles, and composite geometric figures BOA: 20- 23 ■ Compute the perimeter of simple composite geometric figures with unknown side lengths* BOA: 33-36 ■ investigate angle and arc relationships for circles ■ Use relationships among angles, arcs, and distances in a circle CCSS.MATH.CONTENT.HS G.CO.C.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. CCSS.MATH.CONTENT.HS G.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. and chords Curriculum Map UNIT NAME Unit 4 Area, Surface Area and Volume Chapters 11,12 and 13 STANDARDS CRS CCS BOA: 13- 15 ■ describe, compare, and contrast plane and solid figures using their attributes ■ distinguish between area and perimeter, and find the area or perimeter when all relevant dimensions are given CCSS.MATH.CONTENT.7.G. B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. BOA: 16-19 ■ Find area and perimeter of a variety of polygons by substituting given values into standard geometric formulas ■ Compute the area and perimeter of triangles and rectangles in simple problems ■ Use geometric formulas when all necessary information is given ■ apply a variety of strategies to determine the circumference or perimeter and the area for circles, triangles, rectangles, and composite geometric figures BOA: 20- 23 ■ Compute the area of triangles and rectangles when one or more additional simple steps are required ■ Compute the area and circumference of circles after identifying necessary information ■ Compute the perimeter of simple composite geometric figures with unknown side lengths* CCSS.MATH.CONTENT.7.G. B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. CCSS.MATH.CONTENT.7.G. B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. CCSS.MATH.CONTENT.8.G. C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. CCSS.MATH.CONTENT.HS OBJECTIVES I can… Find perimeters and areas of parallelograms Find areas of triangles and trapezoids Calculate areas of regular polygons and circles Find areas of irregular figures Identify and use threedimensional figures Draw two-dimensional models for three-dimensional figures Calculate surface areas of three-dimensional figures Find lateral and surface areas of prisms, cylinders, pyramids and cones Calculate surface area of sphere Find volumes of prisms, cylinders, cones, pyramids and spheres ASSESSMENTS Mid Chapter Exam ( Chapter 11) Chapter 11 Exam Mid Chapter Exam ( Chapter 12 ) Chapter 12 Exam Mid Chapter Exam ( Chapter 13 ) Chapter 13 Exam Final Exam EOY Exam Projects Group Research and Presentation Project Concludes the last month of school year. BOA: 24 – 27 ■ Use relationships involving area, perimeter, and volume of geometric figures to compute another measure ■ examine and compare a variety of methods to find areas of composite figures and construct scale drawings ■ Compute the area of composite geometric figures when planning or visualization is required G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. CCSS.MATH.CONTENT.HS G.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*