Addison Community Schools



Mathematics Pacing Guide

Time Frame: 6 Weeks – September/October High School Geometry

Unit 1: Congruence

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

| |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

|2. Reason abstractly and quantitatively | |

| |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

|3. Construct viable arguments and critique the reasoning of others |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

| |equation) into words. |

|4. Model with mathematics | |

| |WHST 10.2d Use precise language and domain-specific vocabulary to manage the complexity of the topic and |

|5. Use appropriate tools strategically |convey a style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

|6. Attend to precision |WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |

| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|

|7. Look for and make use of structure | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

|8. Look for and express regularity in repeated reasoning |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|G.CO.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). | | | | |

|G.CO.3 Given a rectangle, parallelogram, trapezoid, or | | | | |

|regular polygon, describe the rotations and reflections that | | | | |

|carry it onto itself. | | | | |

| | | | | |

|G.CO.4 Develop definitions of rotations, reflections, and | | | | |

|translations in terms of angles, circles, perpendicular | | | | |

|lines, parallel lines, and line segments. | | | | |

| | | | | |

|G.CO.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. | | | | |

| | | | | |

|Understand congruence in terms of rigid motions | | | | |

|G.CO.6 Use geometric descriptions of rigid motions to | | | | |

|transform figures and to predict the effect of a given rigid | | | | |

|motion on a given figure; given two figures, use the | | | | |

|definition of congruence in terms of rigid motions to decide | | | | |

|if they are congruent. | | | | |

|Prove geometric theorems | | | | |

|G.CO.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. | | | | |

| | | | | |

|Make geometric constructions | | | | |

|G.CO.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. | | | | |

| | | | | |

|G.CO.13 Construct an equilateral triangle, a square, and a | | | | |

|regular hexagon inscribed in a circle. | | | | |

| | | | | |

|Use coordinates to prove simple geometric theorems | | | | |

|algebraically | | | | |

|G.GPE.4 Use coordinates to prove simple geometric theorems | | | | |

|algebraically. For example, prove or disprove that a figure | | | | |

|defined by four given points in the coordinate plane is a | | | | |

|rectangle; prove or disprove that the point (1, √3) lies on | | | | |

|the circle centered at the origin and containing the point | | | | |

|(0, 2). | | | | |

| | | | | |

|G.GPE.6 Find the point on a directed line segment between two| | | | |

|given points that partitions the segment in a given ratio. | | | | |

Mathematics Pacing Guide

Time Frame: 3 Weeks – October High School Geometry

Unit 2: Congruence (continued)

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the|

| |precise details of explanations or descriptions. |

|2. Reason abstractly and quantitatively | |

| |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

| | |

|4. Model with mathematics |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

| |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

|5. Use appropriate tools strategically |equation) into words. |

| | |

|6. Attend to precision |RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a |

| |recommendation for solving a scientific or technical problem. |

|7. Look for and make use of structure | |

| |WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared |

|8. Look for and express regularity in repeated reasoning |writing products, taking advantage of technology’s capacity to link to other information and to display |

| |information flexibly and dynamically. |

| | |

| |WHST 10.7 Conduct short as well as more sustained research projects to answer a question (including a |

| |self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize |

| |multiple sources on the subject, demonstrating understanding of the subject under investigation. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Prove geometric theorems |How do you prove geometric |Before |acute |Right Triangle Solver: |

|G.CO.10 Prove theorems about triangles. Theorems include: |theorems? |Draw examples of interior angles of a |altitude | |

|measures of interior angles of a triangle sum to 180 | |triangle, base angels of isosceles triangles,|diagonal | |

|degrees; base angles of isosceles triangles are congruent;| |and the segment joining midpoints of two |equilateral |Also use Resources from Unit 1 |

|the segment joining midpoints of two sides of a triangle | |sides. |exterior angles | |

|is parallel to the third side and half the length; the | | |hypotenuse | |

|medians of a triangle meet at a point. | |During |interior angles | |

| | |Write a proof demonstrating that the base |isosceles | |

| | |angles of an isosceles triangle are |leg | |

| | |congruent. |median | |

| | | |midpoint | |

| | |Write a proof demonstrating that the |mid-segment | |

| | |diagonals of a rhombus are perpendicular. |obtuse | |

| | | |opposite | |

| | |After |parallelogram | |

| | |Give a cumulative assessment test that asks |rhombus | |

| | |students to prove theorems about |right | |

| | |parallelograms. |scalene | |

| | | |triangles | |

|G.CO.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. | | | | |

Mathematics Pacing Guide

Time Frame: 3 Weeks – November High School Geometry

Unit 3: Expressing Geometric Properties with Equations

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

| |or performing technical tasks, attending to special cases or exceptions defined in the text. |

|2. Reason abstractly and quantitatively | |

| |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

| | |

|4. Model with mathematics |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

| |procedures/ experiments, or technical processes. |

|5. Use appropriate tools strategically |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

|6. Attend to precision |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

|7. Look for and make use of structure |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

|8. Look for and express regularity in repeated reasoning |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Translate between the geometric description and the equation|How do you use coordinates to |Before |plane |Geoboard x,y coordinate: |

|for a conic section |prove geometric theorems |Use slope to prove that two lines are | | |

|G.GPE.2 Derive the equation of a parabola give focus and |algebraically? |parallel/ perpendicular. | | |

|directrix. | | | | |

| | |During | | |

|Use coordinates to prove simple geometric theorems | |Use slope to prove that the diagonals of a | | |

|algebraically. | |rhombus are perpendicular. | | |

|G.GPE.5 Prove the slope criteria for parallel and | | | | |

|perpendicular lines and use them to solve geometric problems| |After | | |

|(e.g., find the equation of a line parallel or perpendicular| |Disprove that a figure defined by four | | |

|to a given line that passes through a given point). | |given points in the coordinate plane is a | | |

| | |rectangle. | | |

Mathematics Pacing Guide

Time Frame: 4 Weeks – November/December High School Geometry

Unit 4: Circles

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the|

| |precise details of explanations or descriptions. |

|2. Reason abstractly and quantitatively | |

| |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

|3. Construct viable arguments and critique the reasoning of others |or performing technical tasks, attending to special cases or exceptions defined in the text. |

| | |

|4. Model with mathematics |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

| |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

|5. Use appropriate tools strategically | |

| |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

|6. Attend to precision |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

| |equation) into words. |

|7. Look for and make use of structure | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

|8. Look for and express regularity in repeated reasoning |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Understand and apply theorems about circles |How do you apply theorems to |Before |arc |Virtual Manipulatives: |

|G.C.1 Prove that all circles are similar. |circles? |Use a compass and straightedge to draw chords,|center | |

| | |inscribed angles, and radii and describe their|central angle | |

|G.C.2 Identify and describe relationships among inscribed | |relationships. |chord |Radian Measure: |

|angles, radii, and chords. Include the relationship | | |circle |

|between central, inscribed, and circumscribed angles; | |During |circumference |_1.pdf |

|inscribed angles on a diameter are right angles; the | |Give students a construction problem using a |circumscribed |Chords, Radii, Tangents, Secants, and Arcs: |

|radius of a circle is perpendicular to the tangent where | |compass and straightedge to show that all |concentric |

|the radius intersects the circle. | |circles are similar. |diameter |MA_LP_S03_BC_L10_I10_01.pdf |

| | | |inscribe |Circle Conjectures:  |

|G.C.3 Construct the inscribed and circumscribed circles of| |Use a compass and straightedge to construct |major | |

|a triangle, and prove properties of angles for a | |inscribed, circumscribed figures and tangent |minor |Lessons/5.1CircleConjectures.pdf |

|quadrilateral inscribed in a circle. | |lines in and around circles. |radian measure | |

| | | |radius |​Texas Instruments |

|G.C.4 (+) Understand and apply theorems about circles. | |After |right angle |

|Construct a tangent line from a point outside a given | |Ask students to demonstrate the relationship |secant |ivities/Detail?id=3888 |

|circle to the circle. | |between degree and radian measure. |sector | |

| | | |tangent line |Exploring the Equation of a Circle (TI-Nspire):   |

|Find arc lengths and areas of sectors of circles | | | |

|G.C.5 Derive using similarity the fact that the length of | | | |/Activities/Detail?sa=5024&t=5047&id=13173 |

|the arc intercepted by an angle is proportional to the | | | |  |

|radius, and define the radian measure of the angle as the | | | |​Secants, Tangents, and Arc​​s (TI-Nspire):  ​ |

|constant of proportionality; derive the formula for the | | | |

|area of a sector. | | | |/Activities/Detail?sa=5024&t=5047&id=13176 |

| | | | |  |

| | | | |​Tangents to a Circle​ (TI-Nspire):  |

| | | | |

| | | | |/Activities/Detail?sa=5024&t=5047&id=13174 |

| | | | |  |

| | | | |​Constructing Circles (Ti-84+):  . |

| | | | |

| | | | |ivities/Detail?id=4063 |

| | | | |  |

| | | | |​Angles Formed by Intersecting Chords, Secants, and |

| | | | |Tangents (TI-84+):   |

| | | | |

| | | | |ivities/Detail?id=4065 |

| | | | |  |

| | | | |NUMB3RS - Season 1 - "Pilot" - The Center of it |

| | | | |All (TI-84+):   ​ |

| | | | |

| | | | |ivities/Detail?id=7719 |

| | | | |  |

| | | | |NUMB3RS - Season 2 - "Harvest" - Meltdown (TI-84+): |

| | | | |  ​ |

| | | | |

| | | | |ivities/Detail?id=6521 |

| | | | |  |

| | | | |NCTM Illuminations  |

| | | | | |

| | | | |Power of Points:  |

| | | | |

| | | | |700 |

| | | | |Circle Packing: |

| | | | |

| | | | |175 |

| | | | |​Equations of Circles 1:  |

| | | | |

| | | | |d=406&subpage=concept |

| | | | |  |

| | | | |Equations of Circles 2:  |

| | | | |

| | | | |d=425&subpage=concept |

| | | | | |

| | | | |Modeling:  Rolling Cups:  |

| | | | |

| | | | |id=1254 |

| | | | | |

| | | | |Articles from National Council of Teachers of |

| | | | |Mathematics ()    |

| | | | |

| | | | |21 |

| | | | |

| | | | |91 |

| | | | |Temple Geometry: |

| | | | |

| | | | |261&subpage=apprentice |

| | | | | |

| | | | |Circles in Triangles: |

| | | | |

| | | | |256&subpage=apprentice |

| | | | | |

| | | | |Sectors of Circles:  |

| | | | |

| | | | |d=441&subpage=concept |

| | | | |Equations of Circles 1:  |

| | | | |

| | | | |d=406&subpage=concept |

| | | | |Equations of Circles 2:  |

| | | | |

| | | | |d=425&subpage=concept |

Mathematics Pacing Guide

Time Frame: 5 Weeks – January/February High School Geometry

Unit 5: Geometric Measurement and Dimension

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the|

| |precise details of explanations or descriptions. |

|2. Reason abstractly and quantitatively | |

| |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

|3. Construct viable arguments and critique the reasoning of others |or performing technical tasks, attending to special cases or exceptions defined in the text. |

| | |

|4. Model with mathematics |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

| |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

|5. Use appropriate tools strategically | |

| |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

|6. Attend to precision |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

| |equation) into words. |

|7. Look for and make use of structure | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

|8. Look for and express regularity in repeated reasoning |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Explain volume formulas and use them to solve problems |How do you solve problems using|Before |apothem |ACT Prep Materials: |

|G.GMD.1 Give an informal argument for the formulas for the |volume formulas? |Give students a bell ringer that assesses |area | |

|circumference of a circle, area of a circle, volume of a | |their comprehension of volume formulas. |cone | |

|cylinder, pyramid, and cone. Use dissection arguments, | | |cross section |NCTM Illuminations |

|Cavalieri’s principle, and informal limit arguments. | |During |cylinder | |

| | |Have a class discussion on the formulas |lateral area | |

| | |for circles. |polyhedron |Using Cubes and Isometric Drawings: |

| | | |prism |

| | |Have a class discussion on the formulas |pyramid |x?ID=U166 |

| | |for spheres. |rotation | |

| | | |sphere |​Popcorn, Anyone?:  |

| | |After |surface area |

| | |Give students a comprehensive test on |three-dimensional |x?id=L797 |

| | |volumes of prisms, cylinders, pyramids, |two-dimensional |​Texas Instruments​

| | |cones, and spheres. Stress use of |volume |lators/timath/ |

| | |Pythagorean Theorem, Special Triangles and| |Exploring Cavalieri's Principle(TI-84+):   |

| | |Pythagorean Triples to find lengths of the| |

| | |parts of the figures. Use coordinate axis | |US/Activities/Detail?ID=12581 |

| | |to help students create three dimensional | |NUMB3RS - Season 2 - "Rampage" - Tesseract​ |

| | |figures through rotation. | |(TI-84+):   |

| | | | |

| | | | |US/Activities/Detail?ID=6899 |

| | | | |Making Hay While the Sun Shines & Not Losing |

| | | | |It in the Rain(The Geometry of the Big Round |

| | | | |Bale) (TI-Nspire):   |

| | | | |

| | | | |US/Activities/Detail?ID=10559 |

| | | | |​Paint Can Dimensions ​(TI-Nspire):   |

| | | | |

| | | | |US/Activities/Detail?ID=10586 |

| | | | |​Volume (TI-Nspire):   |

| | | | |

| | | | |US/Activities/Detail?ID=9689 |

| | | | | |

| | | | |​CPMP-Tools   |

| | | | | |

| | | | | |

| | | | |Shodor Interactivate |

| | | | | |

| | | | | |

| | | | |Surface Area of a Rectangular Prism: |

| | | | |

| | | | |rfaceAreaRectangular/ |

| | | | | |

| | | | |Surface Area of Prisms: |

| | | | |

| | | | |rfaceAreaPrisms/ |

| | | | | |

| | | | |Volume of Rectangular Prisms: |

| | | | |

| | | | |lumeRectangular/ |

| | | | | |

| | | | |Volume of Prisms: |

| | | | |

| | | | |lumePrisms/ |

| | | | | |

| | | | |Surface Area and Volume: |

| | | | |

| | | | |rfaceAreaAndVolume/  |

| | | | | |

| | | | |​Interactives, Geometry 3D Shapes:   |

| | | | |

| | | | |ndex.html |

| | | | | |

| | | | |GeoGebra |

| | | | | |

| | | | |​Unwrapping a Prism:   |

| | | | |

| | | | |m.html |

| | | | | |

| | | | |​Rotating Pyramid:  ​ |

| | | | |

| | | | |mid.html |

| | | | | |

| | | | |GEOGEBRA 3D:  ​ |

| | | | |

| | | | |/Espace.htm |

| | | | | |

| | | | |MARS Dead or Alive:  ​ |

| | | | |

| | | | |es/3101_mars.html#standards |

| | | | |​Using Spheres to Examine Changes in Volume and|

| | | | |Surface Area: |

| | | | |

| | | | |Algebra1/Algebra1.htm |

| | | | |​Dan Meyer Blog Archive: Popcorn Picker:  ​ |

| | | | |

| | | | |3 |

| | | | |Evaluating Statements About Enlargements |

| | | | |(2D and 3D):   |

| | | | |

| | | | |?taskid=213 |

| | | | |  |

| | | | |Calculating Volumes of Compound Objects:   |

| | | | |

| | | | |?taskid=216  |

| | | | |Focus in High School Mathematics: Reasoning |

| | | | |and Sense Making:  |

| | | | |

| | | | |494 |

| | | | |Focus in High School Mathematics: Reasoning |

| | | | |and Sense Making In Geometry: |

| | | | |

| | | | |525  |

| | | | |​MAP Assessment Tasks |

| | | | |​Funsize Cans:   |

| | | | |

| | | | |askid=252 |

| | | | | |

| | | | |​Glasses:   |

| | | | |

| | | | |askid=259 |

| | | | | |

| | | | |​Fruit Boxes:   |

| | | | |

| | | | |askid=275 |

| | | | | |

| | | | |​Fearless Frames:   |

| | | | |

| | | | |askid=277 |

| | | | | |

| | | | |​Bestsize Cans:  |

| | | | |

| | | | |askid=284 |

| | | | | |

| | | | |​Propane Tanks:   |

| | | | |

| | | | |askid=288 |

| | | | | |

| | | | |Security Camera:   |

| | | | |

| | | | |askid=273&subpage=expert |

|G.GMD.2 Give an informal argument using Cavalieri’s principle | | | | |

|for the formulas for the volume of a sphere and other solid | | | | |

|figures. | | | | |

| | | | | |

|G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and | | | | |

|spheres to solve problems.* | | | | |

|Visualize relationships between two-dimensional and | | | | |

|three-dimensional objects | | | | |

|G.GMD.4 Identify the shapes of two-dimensional cross-sections of| | | | |

|three-dimensional objects, and identify three-dimensional | | | | |

|objects generated by rotations of two-dimensional objects. | | | | |

Mathematics Pacing Guide

Time Frame: 5 Weeks – February/March High School Geometry

Unit 6: Similarity, Right Triangles, and Trigonometry

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the|

| |precise details of explanations or descriptions. |

|2. Reason abstractly and quantitatively | |

| |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

|3. Construct viable arguments and critique the reasoning of others |or performing technical tasks, attending to special cases or exceptions defined in the text. |

| | |

|4. Model with mathematics |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

| |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

|5. Use appropriate tools strategically | |

| |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

|6. Attend to precision |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

| |equation) into words. |

|7. Look for and make use of structure | |

| |RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a |

|8. Look for and express regularity in repeated reasoning |recommendation for solving a scientific or technical problem. |

| | |

| |RST 10.9 Compare and contrast findings presented in a text to those from other sources (including their own |

| |experiments), noting when the findings support or contradict previous explanations or accounts. |

| | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

| |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Understand similarity in terms of similarity transformations | | | | |

|G.SRT.1 Verify experimentally the properties of dilations | | | | |

|given by a center and a scale factor: | | | | |

|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. | | | | |

|b. The dilation of a line segment is longer or shorter in the| | | | |

|ratio given by the scale factor. | | | | |

| | | | | |

|G.SRT.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. | | | | |

| | | | | |

|G.SRT.3 Use the properties of similarity transformations to | | | | |

|establish the AA criterion for two triangles to be similar. | | | | |

| | | | | |

|Prove theorems involving similarity | | | | |

|G.SRT.4 Prove theorems about triangles. Theorems include: a | | | | |

|line parallel to one side of a triangle divides the other two | | | | |

|proportionally, and conversely; the Pythagorean Theorem proved| | | | |

|using triangle similarity. | | | | |

| | | | | |

|G.SRT.5 Use congruence and similarity criteria for triangles | | | | |

|to solve problems and to prove relationships in geometric | | | | |

|figures. | | | | |

Mathematics Pacing Guide

Time Frame: 4 Weeks – March/April High School Geometry

Unit 7: Expressing Geometric Properties with Equations

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

| |or performing technical tasks, attending to special cases or exceptions defined in the text. |

|2. Reason abstractly and quantitatively | |

| |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

| | |

|4. Model with mathematics |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

| |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

|5. Use appropriate tools strategically |equation) into words. |

| | |

|6. Attend to precision |RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a |

| |recommendation for solving a scientific or technical problem. |

|7. Look for and make use of structure | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

|8. Look for and express regularity in repeated reasoning |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|Use coordinates to prove simple geometric theorems algebraically| | | | |

|G.GPE.4 Use coordinates to prove simple geometric theorems | | | | |

|algebraically. For example, prove or disprove that a figure | | | | |

|defined by four given points in the coordinate plane is a | | | | |

|rectangle; prove or disprove that the point (1, √3) lies on the | | | | |

|circle centered at the origin and containing the point (0, 2). | | | | |

| | | | | |

|G.GPE.7 Use coordinates to compute perimeters of polygons and | | | | |

|areas of triangles and rectangles, e.g., using the distance | | | | |

|formula.* | | | | |

Mathematics Pacing Guide

Time Frame: 3 Weeks – April/May High School Geometry

Unit 8: Right Triangles

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

| |or performing technical tasks, attending to special cases or exceptions defined in the text. |

|2. Reason abstractly and quantitatively | |

| |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

|3. Construct viable arguments and critique the reasoning of others |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

| | |

|4. Model with mathematics |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

| |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

|5. Use appropriate tools strategically |equation) into words. |

| | |

|6. Attend to precision |RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a |

| |recommendation for solving a scientific or technical problem. |

|7. Look for and make use of structure | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

|8. Look for and express regularity in repeated reasoning |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |WHST 10.4 Produce clear and coherent writing in which the development, organization, and style are |

| |appropriate to task, purpose, and audience. |

| | |

| |WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared |

| |writing products, taking advantage of technology’s capacity to link to other information and to display |

| |information flexibly and dynamically. |

| | |

| |WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |

| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

Mathematics Pacing Guide

Time Frame: 4 Weeks – May/June High School Geometry

Unit 9: Modeling with Geometry

|Standards for Mathematical Practice |Literacy Standards |

|1. Make sense of problems and persevere in solving them |RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the|

| |precise details of explanations or descriptions. |

|2. Reason abstractly and quantitatively | |

| |RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, |

|3. Construct viable arguments and critique the reasoning of others |or performing technical tasks, attending to special cases or exceptions defined in the text. |

| | |

|4. Model with mathematics |RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they |

| |are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. |

|5. Use appropriate tools strategically | |

| |RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form |

|6. Attend to precision |(e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an |

| |equation) into words. |

|7. Look for and make use of structure | |

| |RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a |

|8. Look for and express regularity in repeated reasoning |recommendation for solving a scientific or technical problem. |

| | |

| |RST 10.9 Compare and contrast findings presented in a text to those from other sources (including their own |

| |experiments), noting when the findings support or contradict previous explanations or accounts. |

| | |

| |WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific |

| |procedures/ experiments, or technical processes. |

| |a. Introduce a topic and organize ideas, concepts, and information to make important connections and |

| |distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when |

| |useful to aiding comprehension. |

| |c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, |

| |and clarify the relationships among ideas and concepts. |

| |d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a |

| |style appropriate to the discipline and context as well as to the expertise of likely readers. |

| | |

| |WHST 10.4 Produce clear and coherent writing in which the development, organization, and style are |

| |appropriate to task, purpose, and audience. |

| | |

| |WHST 10.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a |

| |new approach, focusing on addressing what is most significant for a specific purpose and audience. |

| | |

| |WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared |

| |writing products, taking advantage of technology’s capacity to link to other information and to display |

| |information flexibly and dynamically. |

| | |

| |WHST 10.7 Conduct short as well as more sustained research projects to answer a question (including a |

| |self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize |

| |multiple sources on the subject, demonstrating understanding of the subject under investigation. |

| | |

| |WHST 10.8 Gather relevant information from multiple authoritative print and digital sources, using advanced |

| |searches effectively; assess the usefulness of each source in answering the research question; integrate |

| |information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a |

| |standard format for citation. |

| | |

| |WHST 10.9 Draw evidence from informational texts to support analysis, reflection, and research. |

| | |

| |WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time |

| |frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.|

| | |

| |SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive |

| |elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add |

| |interest. |

|Common Core |Essential Questions |Assessment |Vocabulary |Resources |

|G.MG.2 Apply concepts of density based on area and volume in| | | | |

|modeling situations (e.g., persons per square mile, BTUs per| | | | |

|cubic foot).* | | | | |

|G.MG.3. Apply geometric methods to solve design problems | | | | |

|(e.g., designing an object or structure to satisfy physical | | | | |

|constraints or minimize cost; working with typographic grid | | | | |

|systems based on ratios).* | | | | |

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