Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade


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1 Content Area: GEOMETRY Grade 9 th Quarter 1 st Curso Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources Recursos Algebra Review Students will be able to use variables to represent unknown quantities. Write and solve equations. Calculate distance and midpoint of segments on a number line and a coordinate grid. variable, coefficient, quantity, expression, equation, distance, midpoint, slope Geometric Logic, Reasoning, and Language Students will be able to write conditional statements to understand geometric truths and define new terms. Students will be able to write converse, inverse, and contrapositive statements and use logical reasoning to prove True or False. Research and present Properties of Equality. conditional statements, conjectures, counterexamples, converse, inverse, contrapositive Building Blocks of Geometry Students will be able to define and construct the basic building blocks of geometry; points, lines, angles, planes. Identify how to properly name geometric terms. Classify types of angles. Point, line, ray, segment, angle, plane, acute, obtuse, right, straight, linear, intersection, colinear, coplanar, parallel, perpendicular,
2 Content Area: GEOMETRY Grade 9 th Quarter 1 st Serie Serie Unidade Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources Recursos Angle Relationships Students will be able to illustrate and define the relationships between pairs of angles. missing angle measures using new concepts. complementary, supplementary, vertical, transversal, adjacent, linear pair, alternate interior, alternate exterior, corresponding Students will be able to use angle relationships to write and solve equations.
3 Content Area: GEOMETRY Grade 9 th Quarter 2 nd _ Serie Serie Unidade Classify Polygons (Triangles) Students will be able to classify and construct triangles based on sides and on angles. and write conjectures based on characteristics. acute, obtuse, right, scalene, isosceles, equilateral, equiangular, legs, base, vertex angle, perpendicular bisector, missing measurements using new concepts. Classify Polygons (Quadrilaterals) Students will be able to use relationships to write and solve equations. Students will be able to classify & construct quadrilaterals based on characteristics. Students will be able to analyze differences in categories. and write conjectures based on characteristics. parallelogram, rectangle, square, trapezoid, rhombus, opposite, consecutive, diagonal, bases, midsegment missing measurements using new concepts. Students will be able to use relationships to write and solve equations.
4 Students will be able to use slope to prove types of quadrilaterals. Standards/Content Padrões / Conteúdo Learning Objectives Objetivos de Aprendizado Vocabulary Vocabulário Assessments Avaliações Resources Recursos Triangle Congruency the range of possible side lengths to construct triangles. Students will be able to prove triangles are congruent using limited measurements. included side, included angle, proofs, CPCTC and write conjectures that can be used. Students will be able to disprove what is NOT always true with counterexamples. Students will be able to write proofs and justify mathematical statements. special theorems for right triangles. Students will calculate side lengths of right triangles in real world situations using Pythagorean legs, hypotenuse, irrational number, radical, altitude
5 Special Right Triangles Theorem. Students will simplify irrational numbers in radical form. Students will identify special right triangle situations. Students will use and rules to calculate side lengths in radical in decimal form. Perimeter & Area Students will calculate the perimeter (circumference) and area of polygons and circles. Students will explain the meanings of area formulas from corresponding shapes. base, height, legs, apothems, radius, diameter, composite figure Students will differentiate between forms of answers in terms of π or when rounded. Students will deconstruct composite figures into sections to calculate perimeter and area. Circles Arcs & Angles Students will define and construct circles. Students will define, identify, and compare *parts of circles. Students will construct circles containing specific parts to write * chords, secants, tangents, central angles, inscribed angles, minor arcs, major arcs, semicircle
6 conjectures. Students will use conjectures to calculate unknown lengths, angles, and arcs. Students will through circumference, use arc length to calculate arc measure and vice versa. Surface Area & Volume Students will define and classify 3d figures as prisms or pyramids and identify them by nets. Students will draw nets of 3d figures. dimensions, surface area, volume, base vs Base, faces, lateral faces, vertices, edges, slant height vs height Students will construct nets to calculate surface area and lateral surface area. Students will explain the significance of terms in surface area and volume formulas. Students will use formulas to calculate the surface area and volume of 3d figures. Similar Figures Students will use scale factor to calculate missing sides and construct similar figures. Students will identify the two scale factors between similar figures. similar figures, corresponding, ratio, scale factor, dimensions
7 Students will explain how perimeter, area, and volume are affected differently by scale factor. Students will students will calculate new perimeters, areas, and volumes of similar figures using scale factor. Drawing Conclusions Introduction to Trigonometry Students will use conditional statements and logical reasoning to draw conclusions or disprove statements. Students will write proofs using logical reasoning. Students will identify trigonometric ratios of a right triangle. Students will calculate side lengths and angle measures of right triangles using trigonometry. Sine, Cosine, Tangent, radians **3 rd and 4 th quarter are under revision
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