Access Points Scope & Sequence Focus Calendar Geometry Overview Focus Access Points Assessed Weekly Assignments OVERVIEW: Students will apply geometric concepts in modeling situations. Students will explore geometric theories and related vocabulary. Students will investigate, model, and practice different geometric concepts involving triangles, circles, 2D and 3D shapes. Essential Understanding: (Concrete) Students will construct and manipulate line segments. Students will categorize and classify shapes, such as triangles and parallelograms. Congruence MAFS.912.G-CO.1.AP.1a Identify 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. MAFS.912.G-CO.3.AP.9a Measure lengths of line segments and angles to establish the about the angles created when parallel lines are cut by a transversal and the points on a perpendicular bisector. MAFS.912.G-CO.4.AP.12a Copy a segment. MAFS.912.G-CO.4.AP.12c Bisect a segment. MAFS.912.G-CO.4.AP.12e Construct perpendicular lines, including the perpendicular bisector of a line segment. MAFS.912.G-CO.4.AP.12f Construct a line parallel to a line through a point not on the line. Geometric Properties with Equations MAFS.912.G-GPE.2.AP.6a Given two points, find the point on the line segment between the two points that divides the segment into a given ratio. Unit 1 Line Segment Weekly Assignment 1: Create a line segment using two points. (MAFS.912.G.-CO.4.AP.12a) Weekly Assignment 2: Indicate point ratios on a line segment (1/2, ¾). (MAFS.912.G-GPE.2.AP.6a) Weekly Assignment 3: Construct a bisector of a segment using paper folding. (MAFS.912.G-CO.4.AP.12c)
Essential Questions How can you use the tools of geometry to solve real-world problems? How can you use concepts of congruency or translation to solve real-world problems? How can you use properties of triangles or quadrilaterals to solve real-world problems? How can you use similarity and transformations to solve real-world problems? How can you use volume formulas to solve real-world problems? How can you use modeling to solve problems? Similarity, Right Triangles & Trigonometry MAFS.912.G-SRT.1.AP.2a Determine if two figures are similar. MAFS.912.G-SRT.1.AP.2b Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides. Congruence MAFS.912.G-CO.2.AP.7a Use definitions to demonstrate congruency and similarity in figures. MAFS.912.G-CO.3.AP.11a Measure the angles and sides of parallelograms to establish facts about parallelograms. Circles MAFS.912.G-C.1.AP.1a Compare the ratio of diameter to circumference for several circles to establish all circles are similar. Unit 3 Shapes Weekly Assignment 6: Classify shapes that are similar. (MAFS.912.G-SRT.1.AP.2a) Weekly Assignment 7: Recognize shapes that are congruent. (MAFS.912.G-CO.2.AP.7a) Weekly Assignment 8: List characteristics of parallelograms. (MAFS.912.G.CO.3.AP.11a)
Geometric Properties with Equations MAFS.912.G-GPE.1.AP.1a Given the center and the radius of a circle, use the Pythagorean Theorem to find the equation of the circle. MAFS.912.G-GPE.1.AP.1b Given the equation, find the center and the radius of a circle. Circles MAFS.912.G-C.1.AP.1a Compare the ratio of diameter to circumference for several circles to establish all circles are similar. MAFS.912.G-C.1.AP.5a Find the arc length of a circle. Geometric Measurement and Dimension MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection. Unit 7 Geometric Properties Weekly Assignment 25: Distinguish between the center, radius, diameter, and circumference of a circle. (MAFS.912.G-GPE.1.AP.1b) Weekly Assignment 26: a string, measure the arc length of a circle. (MAFS.912.G-C.1.AP.5a) Weekly Assignment 27: Connect at least three diameter measurements to different sized circles they belong with. (MAFS.912.G-C.1.AP.1a)
Circles MAFS.912.G-C.1.AP.3a Construct the inscribed and circumscribed circles of a triangle. Congruence MAFS.912.G-CO.4.AP.13a Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle. Geometric Measurement and Dimension MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection. Unit 8 Circles Weekly Assignments 28 & 29: Create different shapes inscribed in a circle. (MAFS.912.G-CO.4.AP.13.a)
Circles MAFS.912.G-C.2.AP.5c Apply the formula to the area of a sector (e.g., area of a slice of pie). Geometric Properties with Equations MAFS.912.G-GPE.1.AP.1a the center and the radius of a circle, use the Pythagorean Theorem to find the equation of the circle. Geometric Measurement & Dimension MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection. MAFS.912.G-GMD.1.AP.3a Use appropriate formulas to calculate volume for cylinders, pyramids, and MAFS.912.G-GMD.2.AP.4a Identify shapes created by cross sections of two-dimensional and three-dimensional figures. Modeling with Geometry MAFS.912.G-MG.1.AP.1a Describe the relationship between the attributes of a figure and the changes in the area or volume when one attribute is changed. MAFS.912.G-MG.1.AP.2a Recognize the relationship between density and area; density and volume using models. MAFS.912.G-MG.1.AP.3a the formula of geometric figures to solve design problems (e.g., designing an object or structure to satisfy physical restraints or minimize cost). Unit 10 2D & 3D Area Weekly Assignment 32: Sequence the steps needed to solve the area of a sector. (MAFS.912.G-C.2.AP.5c) Weekly Assignment 33: Calculate the volume to a three dimensional shape following a formula model. (MAFS.912.G-GMD.1.AP.3a) Weekly Assignment 34: Explore how changes in one attribute will affect volume. (MAFS.912.G-GMD.1.AP.1a) Weekly Assignment 35: Explore the density of set items in containers of different sizes. (MAFS.912.G-MG.1.AP.2a) Weekly Assignment 36: Apply the knowledge of area to calculate measurement in real life scenarios. (MAFS.912.G-MG.1.AP.3a)