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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 Arcs (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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