HWM Geometry Curriculum Overview 2017€¦ · HWM Geometry Curriculum Overview 2017 Overview Standards for Mathematical Content Unit Focus Standards for Mathematical Practice Unit

HWM Geometry Curriculum Overview 2017

Overview Standards for Mathematical Content Unit Focus

Standards for

Mathematical

Practice

Unit I Basic of Geometry

September

● G-CO.A.1

● G-CO.D.12 ● G-GPE.B.7 ● G-MG.A.1

● Experiment with transformations in the plane

● Make geometric constructions ● Use coordinates to prove simple geometric theorems

algebraically ● Apply geometric concepts in modeling situation

MP.1 Make

sense of

problems and

persevere in

solving them.

MP.2 Reason

abstractly and

quantitatively.

MP.3

Construct

viable

arguments &

critique the

reasoning of

others.

Unit 2 Reasoning and Proof

October

(Preparing for) ● G-CO.C.9 ● G-CO.C .10 ● G-CO.C .11

● Prove geometric theorems

Unit 3 Parallel and Perpendicular lines

October

● G-CO.A.1

● G-CO.C.9 ● G-CO.D.12 ● G-GPE.B.5 ● G-GPE.B.6


● Prove geometric theorems ● Make geometric constructions ● Use coordinates to prove simple geometric theorems

algebraically

Unit 4 Transformations

November

● G-CO.A.2

● G-CO.A.3 ● G-CO.A.4 ● G-CO.A.5 ● G-CO.B.6 ● G-SRT.A.1 ● G-SRT.A.2


● Understand congruence in terms of rigid motions ● Understand similarity in terms of similarity

transformations

Unit 5 Congruent Triangles

December

● G-CO.C.10

● G-CO.B.7 ● G-CO.B.8 ● G-CO.B.10 ● G-CO.D ● G-SRT.B.5 ● G-GPE.B.4


● Understand congruence in terms of rigid motions ● Make geometric constructions ● Prove theorems involving similarity

Unit 6 Relationships with Triangles

January

● G-CO.C.9

● G-CO.C.10 ● G-MG.A.1 ● G-CO.D.12

● Prove Geometric theorems

● Apply geometric concepts in modeling situations ● Make geometric constructions

MP.4 Model

with

mathematics.

MP.5 Use

appropriate

tools

strategically.

MP.6 Attend to

precision.

MP.7 Look for

and make use

of structure.

MP.8 Look for

and express

regularity in

repeated

reasoning

Unit 7 Quadrilaterals and Other Polygons

February

● G-CO.C.11

● G-SRT.B.5 ● G-MG.A.1 ● G-MG.A.3


● Prove theorems involving similarity ● Apply geometric concepts in modeling situations

Unit 8 Similarity

March

● G- SRT.A.2

● G- SRT.A.3 ● G-MG.A.3 ● G-MG.A.1 ● G-SRT.B.5 ● G-SRT.B.4 ● G-GPE.B.5

● Understand similarity in terms of similarity transformations

● Apply geometric concepts in modeling situations ● Prove theorems involving similarity ● Use coordinates to prove simple geometric theorems

algebraically

Unit 9 Right Triangles and Trigonometry

April

● G-SRT.B.4

● G-SRT.B.5 ● G-SRT.C.7 ● G-SRT.C.6 ● G-SRT.C.8 ● G-SRT.D.9 ● G-SRT.D.10 ● G-SRT.D.11

● Prove theorems involving similarity

● Define trigonometric ratios and solve problems involving right triangles

● Apply trigonometry to general triangles

Unit 10 Circles

May

● G-CO.A.1

● G-C.A.1 ● G-C.A.2 ● G-C.A.3 ● G-C.A.4 ● G-CO.D.13 ● G-GPE.A.1 ● G-GPE.B.4


● Understand and apply theorems about circles ● Make geometric constructions ● Translate between the geometric description and the

equation for a conic section ● Use coordinates to prove simple geometric theorems

algebraically

Unit 11 Circumference, Area

and Volume

● G-GMD.A.1

● G-GMD.A.2 ● G-GMD.A.3

● Explain volume formulas and use them to solve problems

● Find arc lengths and areas of sectors of circles

June

● G-C.B.5 ● G-GMD.B.4 ● G-MG.A.1 ● G-MG.A.2 ● G-MG.A.3

● Visualize relationships between two-dimensional and three-dimensional objects

● Apply geometric concepts in modeling situations

HWM Geometry Curriculum 2017

Unit 1 Basic of Geometry

Content Standards Suggested Standards for

Mathematical Practice

Critical Knowledge & Skills

G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc

Mathematical practices

addressed throughout the

unit

MP.1 Make sense of problems

and persevere in solving them.

MP.2 Reason abstractly and

quantitatively.

MP.3 Construct viable

arguments & critique the

reasoning of others.

MP.4 Model with mathematics.

MP.5 Use appropriate tools

strategically

MP.6 Attend to precision.

MP.7 Look for and make use

of structure.

MP.8 Look for and express

regularity in repeated

reasoning

Students are able to:

● Name points, lines and planes ● Name segments and rays ● Sketch intersections of lines and planes ● Solve real life problems involving lines and planes ● Use ruler postulate ● Use segment addition postulate ● Name angles ● Measure and classify angles ● Identify congruent angles ● Identify complementary and supplementary angles ● Identify linear pairs and vertical angles

G-CO.D.12 Make formal geometric constructions with a variety of tools and methods


● Copy segments and compare segments for congruence ● Find segment lengths using midpoints and segment bisectors ● Bisect angles

G-GPE.B .7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent


● Use midpoint formula ● Use distance formula ● Find perimeters and areas of polygons in the coordinate plane

G-MG.A. 1 Use geometric shapes, their measures, and their properties to describe objects


● Classify Polygons

Unit 1 Geometry

District/School Formative Assessment Plan District/School Summative Assessment Plan

Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test

District/School Primary and Supplementary Resources

Big Ideas, Dynamic Classroom, Warm Up, Cumulative Review, Answer Presentation Tool , Big Idea’s Laurie’s Notes, Khan Academy

Accommodations and Modifications ELL, Special Education, Gifted and Talented

Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth

21st Century Skills Technology and Interdisciplinary skills

● Students compare different ways of approaching traditional mathematical problems and find innovative solutions, using practical examples where appropriate.

● Students listen to and evaluate others’ reasoning and offer improvements and corrections, with supporting arguments. They listen to others’ feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems

● Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require

Graphing calculator activities Khan academy Geogebra Google classroom Financial, Economic and Business Literacy

working effectively in a climate of ambiguity and changing priorities. ● Students articulate mathematical thoughts and ideas using oral and

written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others’ reasoning.

● Students identify and ask significant questions about mathematics and engage in analyzing each other’s answers

Unit 2 Reasoning and Proof




(Preparing for) G-CO.C.9 Prove theorems about lines and angles. G-CO.C.10 Prove theorems about triangles. G-CO.C.11 Prove theorems about parallelograms



unit




quantitatively.






strategically



Student will be able to:

● Write conditional statements ● use definitions written as conditional statements ● Write biconditional statements ● make truth tables ● Use inductive reasoning ● use deductive reasoning ● identifying postulates using diagrams ● Sketch and interpret diagrams ● Justify steps on solving an equation ● Write two-column proofs ● Name and prove properties of congruence ● Write flowchart proofs to prove geometric constructions ● write paragraph proofs to prove geometric relationships

of structure.



reasoning

Unit 2 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test








● Students work in pairs and small groups to address mathematical challenges that involve varied roles and responsibilities, and require working effectively in a climate of ambiguity and changing priorities.

● Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning with attention to precision, they construct viable arguments and analyze others’ reasoning.



Unit 3 Parallel and Perpendicular lines




G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc



unit




quantitatively.



Students will be able to:

● Identify lines and planes ● identify parallel and perpendicular lines ● Identify pairs of angles formed by transversals

G-CO.C.9 Prove theorems about lines and angles.


● Use properties of parallel lines ● Prove theorems about parallel lines ● Use corresponding angles converse ● Use transitive property of parallel lines ● find distance from a point to a line ● prove theorems about perpendicular lines





strategically



of structure.



reasoning


● construct parallel lines ● construct perpendicular lines

G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).


● Use slope to partition directed line segments ● use slope to find the distance from a point to a line

G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio


● Use slope to partition directed line segments ● Write equations of parallel and perpendicular lines

Unit 3 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












Unit 4 Transformations




G-CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments G-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another



unit




quantitatively.






strategically



of structure.



reasoning


● perform translations ● perform compositions ● Perform reflections ● perform glide reflections ● identify lines of symmetry ● perform rotations ● perform compositions with rotations ● identify rotational symmetry ● identify congruent figures ● Describe congruence transformations

G-CO.B.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.


● perform translations ● perform compositions ● Perform reflections ● perform glide reflections ● identify lines of symmetry ● perform compositions with rotations ● identify rotational symmetry ● identify congruent figures ● Describe congruence transformations

G-SRT.A.1a - A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a


● Identify and perform dilations

line passing through the center unchanged. G-SRT.A.1b - The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

● Solve real life problems involving scale factors and dilation ● perform similarity transformations ● Describe similarity transformations ● prove that figures are similar

Unit 4 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test




Follow learning strategies and modifications as stated in IEP or 504 plan Differentiated instruction

Small group instruction Teacher support Varying the length of time a student may take to complete a task in order to provide additional support for a struggling learning or to encourage an advanced learner to pursue a topic in greater depth








Unit 5 Congruent Triangles




G-CO.C.10 Prove theorems about triangles



unit




● classify triangles by sides and angles ● find interior and exterior angle measures

G-CO.B.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding


● Identify and use corresponding parts ● Use Third angle Theorem

pairs of sides and corresponding pairs of angles are congruent. G-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-CO.C.10 - Prove theorems about triangles.


quantitatively.






strategically



of structure.



reasoning

● Use SAS congruence theorem ● Use base angles theorem ● use isosceles and equilateral triangles ● Use SSS congruence theorem ● Use ASA congruence theorem ● Use AAS congruence theorem

G-CO.D.12 Make formal geometric

constructions with a variety of tools

and methods


● construct equilateral triangle ● construct triangle using SAS ● construct triangles using SSS ● construct triangles using ASA

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.


● Use congruent triangles ● prove constructions

G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically


● Place figures in a coordinate plane ● Write coordinate proof

Unit 5 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












Unit 6 Relationships with Triangles




G-CO.C.9 Prove theorems about lines and angles G-CO.C.10 Prove theorems about triangles.



unit




quantitatively.






strategically



of structure.



reasoning


● Use perpendicular bisectors to find measures ● Use angle bisectors to find measures and direct relationships ● Write equations to perpendicular bisectors ● Use medians and fin centroids of triangles ● Use altitudes and find orthocenters of triangles ● Use midsegments of triangles in the coordinate plane ● Use the triangle midsegment theorem to find distances ● Write indirect proofs ● List sides and angles of triangle in order by size ● Use Triangle Inequality Theorem to find possible side lengths ● Compare measures in Triangles ● Solve problems using the Hinge Theorem

G-MG.A.1 Use geometric shapes,

their measures, and their properties to

describe objects


● Use geometric shapes, their measures, and their properties to describe objects ● Use and find the circumcenter of a triangle ● use and find the incenter of a triangle



● Circumscribe a circle about a triangle

Unit 6 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test









● Students articulate mathematical thoughts and ideas using oral and written communication skills. Using abstract and quantitative reasoning


with attention to precision, they construct viable arguments and analyze others’ reasoning.


Unit 7 Quadrilaterals and Other Polygons




G-CO.C.11 Prove theorems about parallelograms.



unit




quantitatively.






strategically



of structure.




● Use interior angle measures of polygons ● Use the exterior angles measures of polygons ● Use properties to find side lengths and angles of parallelograms ● Use parallelograms in the coordinate plane ● Identify and verify parallelograms ● Show that a quadrilateral is a parallelogram in the coordinate plane ● Use properties of special parallelograms ● use properties of diagonals of special parallelograms ● use coordinate geometry to identify special types of parallelograms

G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures


● Use properties of trapezoids ● Use the Trapezoid Midsegment theorem to find distances ● Use properties of kites ● Identify quadrilaterals

G-MG.A.1Use geometric shapes, their measures, and their properties to describe objects G-MG.A.3 Apply geometric methods to solve design problems


● Use geometric shapes, their measures, and their properties to describe objects ● Apply geometric methods to solve design problems

reasoning

Unit 7 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test







● Students listen to and evaluate others’ reasoning and offer improvements and corrections, with supporting arguments. They listen


to others’ feedback and modify their own arguments as needed. They learn from mistakes, and make repeated attempts at solving problems




Unit 8 Similarity




G- SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.



unit




quantitatively.







● Use similarity statements ● Find corresponding lengths in similar polygons ● Find perimeters and areas of similar polygons ● Decide whether polygons are similar ● Use angle angle similarity theorems ● Use SSS Similarity Theorem ● Use SAS similarity theorem

G-MG.A.1Use geometric shapes, their measures, and their properties to describe objects G-MG.A.3 Apply geometric methods to solve design problems


● Apply geometric methods to solve design problems ● Use geometric shapes, their measures, and their properties to describe objects

G-SRT.B.4 Prove theorems about triangles G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

strategically



of structure.



reasoning


● Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

● Use triangle Proportionality Theorem and its converse ● Use other proportionality theorems

G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems


● Prove slope criteria using similar triangles

Unit 8 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












Unit 9 Right Triangles and Trigonometry




G-SRT.B.4 Prove theorems about triangles. G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures



unit





● Use Pythagorean theorem ● Use converse of the Pythagorean theorem ● Classify triangles ● Identify similar triangles ● use geometric means

G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied


problems. G-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.

quantitatively.






strategically



of structure.



reasoning

● Use Pythagorean theorem ● Use converse of the Pythagorean theorem ● Find side lengths in special right triangles ● use tangent ratio ● Us inverse trigonometric ratios ● solve right triangles ● use tangent ratio ● Use sine and cosine ratios ● Find the sine and cosine measures in special right triangles ● Use sine and cosine ratios ● Find the sine and cosine measures in special right triangles

G-SRT.D.9 Derive the formula for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.D.10 Prove the Laws of Sines and Cosines and use them to solve problems. G-SRT.D.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).


● Find areas of triangles ● Use law of sines and cosines to solve problems ● Use law of sines and cosines to solve problems

Unit 9 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












Unit 10 Circles




G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.



unit




quantitatively.






strategically



of structure.



reasoning


● identify special segments and lines ● draw and identify common tangents ● use properties of tangents

G-C.A.1 Prove that all circles are similar G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle G-C.A.4 Construct a tangent line from a point outside a given circle to the circle.


● Prove that all circles are similar ● Identify and describe relationships among inscribed angles, radii, and chords. ● identify special segments and lines ● draw and identify common tangents ● use properties of tangents ● identify congruent arcs ● find arc measures ● Use chords of circles to find lengths and arc measures ● Find angle and arc measures ● Use circumscribed angles ● Use segments of chords, tangents and secants ● Construct the inscribed and circumscribed circles of a triangle, and prove properties

of angles for a quadrilateral inscribed in a circle ● Use inscribed angles ● Use inscribed polygons ● Construct a tangent line from a point outside a given circle to the circle. ● identify special segments and lines ● draw and identify common tangents ● use properties of tangents

G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle


● Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

G-GPE.A.1 Derive the equation of a circle


● Derive the equation of a circle of given center and radius using the Pythagorean

Theorem; complete the square to find the center and radius of a circle given by an equation.

● Write and graph equations of circles

G-GPE.B.4 Use coordinates to prove simple geometric theorems algebraically


● Use coordinates to prove simple geometric theorems algebraically. ● Write coordinate proofs involving circles

Unit 10 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












Unit 11 Circumference, Area and Volume




G-GMD.A.1Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G-GMD.A.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.



unit




quantitatively.




Students will be able to:.

● Use formula for circumference ● use arc length to find measures ● Use formula for area of a circle ● use formula for population density ● Find surface areas of right cones ● Find and use volumes of cones ● Find surface areas of spheres ● Find volume of spheres ● Find areas of rhombuses and kites ● find angle measures in regular polygons ● Find area of regular polygons ● Find volume of spheres ● Find and use volumes of pyramids ● Find and use volumes of prisms and cylinders

G-C.B.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector



strategically



of structure.



reasoning


● Measure angles in radians ● Find and use areas of sectors

G-GMD.B.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.


● classify solids ● describe cross sections ● sketch and describe solids of revolution

G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects G-MG.A.2 Apply concepts of density based on area and volume in modeling situations G-MG.A.3 Apply geometric methods to solve design problems.


● Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

● Apply concepts of density based on area and volume in modeling situation ● Use formula for density ● Apply geometric methods to solve design problems

Unit 11 Geometry


Teacher check in

Student questioning

Homework

Classwork

Exit cards

Unit quizzes

Unit test












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HWM Geometry Curriculum Overview 2017€¦ · HWM Geometry Curriculum Overview 2017 Overview Standards for Mathematical Content Unit Focus Standards for Mathematical Practice Unit