CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide. CRLS Mathematics Department Geometry Curriculum Map/Pacing Guide

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1 Curriculum Map/Pacing Guide page of Unit : Tools of 5 9 Totals Always Include 2 blocks for Review & Test Activity binder, District Google How do you find length, area? 2 What are the basic tools and concepts of geometry? ow do we measure line segments and angles? How do we use the Distance Formula? ow do we use the Midpoint Formula? How do we identify parallel and perpendicular lines? find area/perimeter of rectangles, triangles, circles, composites. identify and define the basic tools of geometry (Line, point, plane, etc.) measure & construct segments, angles, triangles, bisectors measure figures, and find midpoint and distance on the coordinate plane identify and define parallel and perpendicular lines use slope to determine whether lines are parallel or perpendicular.7.2,.3.4, , 3.6 Curriculum Map/Pacing Guide page 2 of 6

2 Unit : Tools of (continued) How do we prove that lines are parallel? How do we determine angle measure when parallel lines are cut by a transversal? plan and write paragraph, flow chart and two column proofs, distinguishing between properties, postulates and theorems write conditional statements & their converses write proofs using the Alternate Interior Angles, Alternate Exterior Angles, & Corresponding 3.2, 3.2 Angle Theorems determine angle measure when parallel lines 3., 3.2 are cut by a transversal explain the relationship between the types of angles created when parallel lines are cut by a transversal Curriculum Map/Pacing Guide page 3 of 6 Unit 2: Triangles 25 0 Totals Always Include 2 blocks for Review & Test How do we classify triangles by sides and angle? What are the relationships between the sides and angles of a triangle? What is the Triangle Inequality define, identify, and classify triangles by sides (scalene, isosceles, equilateral) and angles 3.3 (acute, equiangular, obtuse). understand the Side-Angle Postulate 0.5 justify the Side-Angle Postulate in informal proofs solve problems involving the Triangle Inequality Postulate 5.5 Activity binder, District Google

3 postulate? What are the special segments within a triangle? What are the relationships between the special segments within triangles? How do we determine if triangles are congruent? justify the Triangle Inequality Postulate in informal proofs identify and solve problems involving midsegments, altitudes, and medians identify and solve problems involving incenter, orthocenter, circumcenter, and centroid. (Centroid-CP, all else Honors) understand the shortcuts for determining congruency in triangles (ASA/SAA/SAS) , 4.6 Curriculum Map/Pacing Guide page 4 of 6 Unit 2: Triangles (continued) How do we prove that triangles are congruent? How do we determine if triangles are similar? 3 2 write proofs using the congruency postulates 7 identify similar triangles, and solve problems involving proportion identify minimum information to know if triangles are similar (AA, SSS~, SAS~) 4.4, 4.5, Curriculum Map/Pacing Guide page 5 of 6

4 Unit 3: Similarity & Trigonometry 3 9 Totals Always Include 2 blocks for Review & Test Activity binder, District Google What are the special properties of right triangles? How can we use the Pythagorean Theorem & its converse? 4 2 use geometric mean/similarity to solve problems 8.4 solve with Pythagorean Theorem deduce obtuse,acute,right with Pythagorean Thoerem 7.2 GSP Demos Ch 09 use 3,4,5 and 5,2,3 Pythagorean Triples What are special right triangles? What are the 3 Trigonometric Ratios? solve problems involving and triangles apply the properties of special right & similar triangles to determine the missing side of a given triangle solve problems with trigonometry & use trig tables & calculators for ratios connect tangent ratio to slope of lines Trig Ratio Tables p73 IMP : Return of the Tree page 95 EGwGSP Curriculum Map/Pacing Guide page 6 of 6 Unit 4: Polygons 6 0 Totals Always Include 2 blocks for Review & Test Activity binder, District Google How can a polygon be classified? How can the sum of a polygon's classify polygons based on number of sides (quadrilateral, triangle, etc.) concave/convex, regular/irregular determine the sum of the interior and exterior angles of a polygon 3.4 Ch5 Discovering 3.4 GSP Demos Ch 5

5 How can the sum of a polygon's interior angles be determined when only the number of sides is known? How can it be determined if two polygons are similar? How can quadrilaterals be classified using properties of sides, angles and diagonals? 2 4 decompose polygon into triangles solve problems using the formulas for interior and exterior angles of polygons to determine the measure of missing angles apply properties of similar figures to determine if two polygons are similar apply properties of similar figures to determine the length of missing sides and the measure of missing angles in similar polygons using proportions use knowledge of angles, sides and diagonals in order to classify quadrilaterals , EGwGSP page 2-3 Golden Ratio applies to credit cards, business cards GSP Demos Ch 0 CH 4 of EGwGSP page EGwGSP, Curriculum Map/Pacing Guide page 7 of 6 Unit 4: Polygons (continued) What makes a good definition? 0.5 use properties of quadrilaterals (sides, diagonals, angles, and diagonals) to solve problems involving squares, rectangles, parallelograms, etc. define classes of quadrilaterals with biconditionals justify postulates about the special quadrilaterals using informal proof

6 How do we prove a conjecture? 2 2 write proofs of quadrilateral theorems using the properties of congruence, and angle postulates 6.3 Midterm Review 2 blocks What are the essential elements of? 4 3 complete practice review problems that summarize the terms work Curriculum Map/Pacing Guide page 8 of 6 Unit 5: Circles Totals Always Include 2 blocks for Review & Test Activity binder, District Google What types of lines and line segments are associated with circles? classify special segments of circles (radius, diameter, chord, secant, tangent, arc) 7.6 What are the special ratios of circles? What relationships exist among the measures of central and inscribed angles and arcs? demonstrate an understanding of circle ratios: radius-diameter, diameter-circumference, pi solve problems for the circumference, diameter, and radii of circles solve problems relating inscribed angles, intercepted arcs, radii, tangent segments, secant segments, chords* apply proportions to chords, tangents, secants,radii* demonstrate understanding of the relationships between the measures of central and inscribed angles and arcs

7 apply mean to vertical angles between intercepted arcs. -.4 Curriculum Map/Pacing Guide page 9 of 6 Unit 5: Circles (continued) How can the relationship between arcs and angles be used to find the length or measure of arcs? 2 solve problems for the measurements of central and inscribed angles, arc angles, the measurements of angles and arcs formed by secants and tangents. -.4 How do we prove circle conjectures? 2 write indirect proofs in paragraph and twocolumn format to prove theorems of circles, involving conjectures, tangents, inscribed angles, and parallel lines. -.4 Curriculum Map/Pacing Guide page 0 of 6 Unit 6: Measuring 2D Figures 8 7 Totals Always Include 2 blocks for Review & Test 2 differentiate between perimeter and area Activity binder, District Google

8 How are triangles measured using properties to deduce missing information? How are quadrilaterals measured using properties to deduce missing information? How are perimeter and/or area of regular polygons found? How are circles measured using properties to deduce missing information? Curriculum Map/Pacing Guide deduce altitude of equilateral triangle solve for the perimeter and area of triangles using triangle formulas (i.e. area, Pythagoras, Special Right Triangles, Trig) differentiate between perimeter and area solve for the perimeter and area of quadrilaterals (parallelograms vs. trapezoids) using area formulas connect mean to trapezoid area formula 7.4 solve problems using the lengths of segments 0.5 and apothems to solve for the perimeter and/or 7.5 area of regular polygons solve problems for the circumference and area 0.5 of circles andcalculate the arc length and area of 7.6, 7.7 sectors with proportions page of 6 Unit 7: Measurement in Space 0 6 Totals Always Include 2 blocks for Review & Test What does 3-D mean? differentiate between 2D and 3D figures. identify appropriate measurement units (i.e. 0., 0.2 units², units³) How can polyhedrons be named? 0.5 differentiate between bases and faces of prisms explore net diagrams Activity binder, District Google

9 How is the lateral surface area of an object found? What are the formulas used to solve for it? How is the total surface area of an object found? What are the formulas used to solve for it? Curriculum Map/Pacing Guide demonstrate understanding of lateral surface area as total surface area minus the base area(s) solve for 0.3, 0.4 the total lateral area of objects in space using lateral surface area formulas complete real-world modeling problems 0.7 differentiate between total surface area and lateral surface area of an object solve for the total surface area of objects in space using surface area formulas identify and calculate slant height 0.3, 0.4 complete real-world modeling problems 0.7 page 2 of 6 Unit 7: Measurement in Space (continued) demonstrate understanding of volume as a How does one measure the space measurement in cubic units select 0.5, 0.6 inside 3D figures? and differentiate between the volume formulas necessary to solve problems What is volume? complete real-world modeling problems 0.7 What are the relationships between perimeter scale factors and area/volume ratios? identify scale factors for given polyhedrons based on perimeter calculations (units) use the scale factor to calculate the area and volume ratios (units², units³) 0.8

10 Curriculum Map/Pacing Guide page 3 of 6 Unit 8: Transformations 7 5 Totals Always Include 2 blocks for Review & Test Activity binder, District Google What is a transformation? What is an isometry? 0.5 When do we use dilation? 0.5 understand the basic concepts of transformations, including image/pre-image, isometry identify and define translation, reflection, and rotation on and off the coordinate plane understand dilation and apply the concept of scale factor to figures complete real-world modeling problems ******MCAS Review****** , How are composite transformations created? 0.5 understand the concept of composition 2.4 identify multiply transformations, including glide reflections, reflections over parallel lines (translation), and reflections over intersecting lines (rotations) Curriculum Map/Pacing Guide page 4 of 6

11 Unit 8: Transformations (continued) When are tessellations useful? identify when tessellations are used in the real world create tessellations using chosen transformation 2.6 identify the vertex arrangements of tessellations, note sum of degrees ************NOTE: Alternative Assessment: Tessellation Drawing Project, Geometer's Sketchpad Kaleidoscope (pg 66)*************** Curriculum Map/Pacing Guide page 5 of 6 Unit 9: Statistics & Geometric Probability 8 6 Totals Always Include 2 blocks for Review & Test Activity binder, District Google Why do we look at data? How can it best be represented? classify different methods of data collection and 7.6 Skills Handbook

12 What are some of the ways quantitative data can be represented? classify different methods of data collection and graphic representation such as frequency tables, box-and-whisker, and stem-leaf plots, scatterplots pp How can one interpret quantitative data? 2 demonstrate understanding of mean, median, mode, and range of data by solving central tendency problems select appropriate measures of central tendency to adequately interpret data 8.4 What is a measure of central tendency? What generalizations can you draw from a given set of data? 0.5 demonstrate understanding of weighted frequency and line-of-best-fit with graphic representations 3.5 Curriculum Map/Pacing Guide page 6 of 6 Unit 9: Statistics & Geometric Probability (continued) What is the likelihood that an outcome will occur? 2.5 use lengths, areas to calculate probability pp

13 Final Review What are the essential elements of? 5 4 find P(dart in bull's eye) 7.8 solve problems for the probability of an event occurring complete practice review problems that summarize the year/semesters work