Download Geometry, 1st 4.5 weeks 2016

Geometry, 1st 4.5 weeks 2016-­‐‑2017 1 The following practice standards will be used throughout 4.5 weeks: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. TN Academic Standards Student Friendly “I Can” Statements Prerequisite Knowledge ACT Readiness ACT Readiness Expected of students UPON ENTERING Geometry. Instruction
al Time TN Ready Questions/ Resources ACT Questions/ Resources 1 day G.203, G.302, G.303, G.304, G.406, G.504 ONGOING Readiness: G.504, G.704, G.705 G.CO.1 Know precise definitions of angle, circle, perpendicular I can describe and name the undefined notions of points, lines, Properties of Plane Figures: *Exhibit some knowledge of the angles associated with Geometry, 1st 4.5 weeks 2016-­‐‑2017 2 line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. (Distance around a circular arc will be taught in Quarter 4 with Circles.) and planes. 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 I can draw transformations of reflections, rotations, translations, and combinations of these using graph paper, transparencies, and patty paper, both on and off the coordinate plane. parallel lines Find the measure of an angle using properties of parallel lines **Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) I can precisely define angles, including supplementary, complementary, adjacent, and linear pairs and describe their characteristics. G.201, G.202, G.402, G.403, G.405, G.501 I can determine the coordinates for the image of a figure when a transformation rule is applied to the pre-­‐‑
Graphical Representations: 3 days Interpret and use information from graphs in the coordinate plane Properties of Plane Figures: **Apply properties of 30°-­‐‑
60°-­‐‑90°, 45°-­‐‑45°-­‐‑90°, similar, and congruent triangles G.407, G.512 Geometry, 1st 4.5 weeks 2016-­‐‑2017 3 not (e.g., translation versus horizontal stretch). image. I can explain rigid motion as motion that preserves distance and angle measure. I can distinguish between congruence transformations that are rigid (reflections, rotations, translations) and those that are not (dilations or rigid motions followed by dilations). 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 I can correctly interpret geometric diagrams by identifying what can and cannot be assumed. I can identify and use the properties of congruence and equality (reflexive, Properties of Plane Figures: 1 day *Find the measure of an angle using properties of parallel lines **Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) **Use several angle properties to find an unknown angle measure Geometry, 1st 4.5 weeks 2016-­‐‑2017 4 on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. symmetric, transitive) in proofs. Draw conclusions based on a set of conditions ***Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections to other content I can explore inductive and deductive reasoning. G.301, G.401, G.407, G.512, G.607, G.608 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 I can determine if a figure has rotational symmetry (maps on to itself), and if so, determine the angle of rotation. Properties of Plane Figures: 1 day ***Apply properties of 30°-­‐‑
60°-­‐‑90°, 45°-­‐‑45°-­‐‑90°, similar, and congruent triangles G.407, G.502, G.512 I can determine if a figure has line symmetry, and if so, find all the lines of symmetry. I can define and describe transformations in terms of angles, circles, Graphical Representations: ***Identify characteristics of graphs based on a set of conditions or on a general 4 days Geometry, 1st 4.5 weeks 2016-­‐‑2017 5 angles, circles, perpendicular lines, parallel lines, and line segments. lines, and line segments (i.e. reflecting a figure over a line or parallel lines, rotating a figure 180°, etc.). equation such as y = ax² + c Solve problems integrating multiple algebraic and/or geometric concepts Properties of Plane Figures: Draw conclusions based on a set of conditions Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas I can use a rule to define reflections, rotations, and translations on the coordinate plane (i.e. ( , ) → (− , ) when rotating 90° counterclockwise about the origin, etc.) G.407, G.512, G.607, G.608 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 I can predict and verify the sequence of transformations (a composition) that will map a figure onto another. Graphical Representations: Interpret and use information from graphs in the coordinate plane Properties of Plane Figures: ***Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas 4 days Geometry, 1st 4.5 weeks 2016-­‐‑2017 6 onto another. G.407, G.512, G.607, G.608 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. I can define congruent figures as figures that have the same shape and size and state the composition of rigid motions (reflections, rotations, translations, and combinations of these) that will map one congruent figure onto the other. Graphical Representations: 4 days Interpret and use information from graphs in the coordinate plane Properties of Plane Figures: ***Apply properties of 30°-­‐‑
60°-­‐‑90°, 45°-­‐‑45°-­‐‑90°, similar, and congruent triangles G.407, G.512, G.607, G.608 G.CO.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. I can determine if two figures are congruent by determining if rigid motions will turn one figure onto the other (preserving distance and angle measure). I can explain and prove that in a pair of congruent triangles, corresponding sides Properties of Plane Figures: 2 days ***Apply properties of 30°-­‐‑
60°-­‐‑90°, 45°-­‐‑45°-­‐‑90°, similar, and congruent triangles Draw conclusions based on a set of conditions G.407, G.512, G.607, G.608 Geometry, 1st 4.5 weeks 2016-­‐‑2017 7 are congruent and corresponding angles are congruent. 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. I can prove vertical angles are congruent. I can prove and apply theorems about the angles formed by parallel lines and a transversal (corresponding, alternate interior, same-­‐‑side interior). I can prove points on a perpendicular bisector of a line segment are exactly equidistant from the segment’s endpoints. Properties of Plane Figures: 1 day ***Find the measure of an angle using properties of parallel lines **Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) **Use several angle properties to find an unknown angle measure Draw conclusions based on a set of conditions ***Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas G.GPE.4 Use coordinates to prove simple geometric I can use coordinate geometry to prove theorems algebraically. Graphical Representations: 1 day Use properties of parallel and perpendicular lines to Geometry, 1st 4.5 weeks 2016-­‐‑2017 8 theorems algebraically. determine an equation of a line or coordinates of a point G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses 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). I can use slope to prove lines are parallel or perpendicular. I can find the equation of a line parallel or perpendicular to a given line that passes through a given point. Graphical Representations: 1 day Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point G.510, G.605