4.0 independently go beyond the classroom to design a real-world connection with polygons that represents a situation in its context.

Transcription

1 ANDERSON Lesson plans!!! Intro to Polygons to Level SCALE Intro to Polygons Evidence 4.0 independently go beyond the classroom to design a real-world connection with polygons that represents a situation in its context. 3.0 use geometric shapes, their measures, and their properties to describe objects. (MAFS.912.G-MG.1.1 use coordinates to compute perimeters of polygons and areas of triangles and rectangles. (MAFS.912.G-GPE.2.7 prove theorems about triangles; use theorems about triangles to solve problems. (MAFS.912.G-CO.3.10 verify experimentally the properties of dilations given by a center and a scale factor. 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. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. (MAFS.912.G-SRT.1.1a,b; draw the transformed figure, given a geometric figure and a rotation, reflection, or translation.(mafs.912.g-co.1.5; use the definition of similarity in terms of similarity transformations to decide if two given figures 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. (MAFS.912.G- SRT.1.2 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. (MAFS.912.G-CO.2.6;

2 Level SCALE Intro to Polygons Evidence 2.0 understand geometric shapes, their measures, and their properties to describe objects. (G-MG.1.1) compute perimeters and areas of triangles or rectangles. (G-GPE.2.7) understand and use theorems about triangles to solve problems. (G-CO.3.10) use properties of dilations given by a center and a scale factor. (G-SRT.1.1a,b) use rotation, reflection, or translation to transform a figure. (G-CO.1.5) describe the rotations and reflections, given a rectangle, parallelogram, trapezoid, or regular polygon, that carry it onto itself. (G-CO.1.3) understand the meaning of similarity in terms of similarity transformations for triangles. (G-SRT.1.2) recall the definition of congruence in terms of rigid motions. (G-CO.2.6)

3 Level SCALE Intro to Polygons Evidence 1.0 recall properties of geometric shapes. (G-MG.1.1) remember area and perimeter formulas. (G-GPE.2.7) recall triangle theorems. (G-CO.3.10) recall properties of dilations, center, and a scale factor. (G-SRT.1.1a,b) remember rotation, reflection, and translation definitions. (G-CO.1.5) recognize rotations and reflections, given a rectangle, parallelogram, trapezoid, or regular polygon. (G-CO.1.3) recall the meaning of similarity in terms of similarity transformations for triangles. (G-SRT.1.2) recognize rigid motion transformations used with congruency. (G-CO.2.6) 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. (G-CO.2.7) recall properties of geometric shapes. (G-MG.1.1) remember area and perimeter formulas. (G-GPE.2.7) recall triangle theorems. (G-CO.3.10) recall properties of dilations, center, and a scale factor. (G-SRT.1.1a,b) remember rotation, reflection, and translation definitions. (G-CO.1.5) recognize rotations and reflections, given a rectangle, parallelogram, trapezoid, or regular polygon. (G-CO.1.3) recall the meaning of similarity in terms of similarity transformations for triangles. (G-SRT.1.2) recognize rigid motion transformations used with congruency. (G-CO.2.6) 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. (G-CO.2.7)

4 ESSENTIAL STANDARDS 10/17/16-11/4/16 Duration of MTP/Unit MAFS.912.G-MG.1.1 Students will use geometric shapes to describe objects found in the real world. Students will use measures of geometric shapes to find the area, volume, surface area, perimeter, or circumference of a shape found in the real world. Students will apply properties of geometric shapes to solve real-world problems. MAFS.912.G-GPE.2.7 Students will use coordinate geometry to find a perimeter of a polygon. Students will use coordinate geometry to find the area of triangles and rectangles. Students will use the distance formula. MAFS.912.G-CO.3.10 Students will prove theorems about triangles. Students will use theorems about triangles to solve problems. MAFS.912.G-SRT.1.1a,b Students will verify that the dilated line is parallel, when dilating a line that does not pass through the center of dilation. Students will verify that the line is unchanged, when dilating a line that passes through the center of dilation. Students will verify that the dilated line segment is longer or shorter with respect to the scale factor, when dilating a line segment. MAFS.912.G-CO.1.5 (also assesses MAFS.912.G-CO.1.3) Students will apply two or more transformations to a given figure to draw a transformed figure. Students will specify a sequence of transformations that will carry a figure onto another. Students will describe rotations and reflections that carry a geometric figure onto itself. Students will use graph paper, tracing paper, or geometry software to draw transformed figures. MAFS.912.G-SRT.1.2 Students will use the definition of similarity in terms of similarity transformations to decide if two figures are similar. Students will explain using the definition of similarity in terms of similarity transformations that corresponding angles of two figures are congruent and that corresponding sides of two figures are proportional. MAFS.912.G-CO.2.6 (also assesses MAFS.912.G-CO.2.7) Students will use rigid motions to transform figures. Students will predict the effect of a given rigid motion on a given figure. Students will use the definition of congruence in terms of rigid motions to determine if two figures are congruent. Students will apply congruence to solve problems. Students will use congruence to justify steps within the context of a proof.

5 Assessed Standards: MAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects. (SAT Standard) MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. (SAT Standard) MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. (SAT Standard) MAFS.912.G-SRT.1.1a,b: Verify experimentally the properties of dilations given by a center and a scale factor. 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. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. (SAT Standard) MAFS.912.G-CO.1.5: Draw the transformed figure, given a geometric figure and a rotation, reflection, or translation. (SAT Standard) MAFS.912.G-SRT.1.2: Use the definition of similarity in terms of similarity transformations to decide if two given figures 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. (SAT Standard) MAFS.912.G-CO.2.6: 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. (SAT Standard)

6 DAY Lesson 1 Properties- Activity 2 MAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects Video (Mathematical Patterns and Folds in the Brain (CPALMS)) Activity ( computer activity ) 6-1 Polygon Textbook Angle-Sum Theorems 3 Pg 364 Textbook (9-27, 33-35) 4 MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. 5 6 MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems. 7 8 MAFS.912.G-SRT.1.1a,b: Verify experimentally the properties of dilations given by a center and a scale factor. 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. The dilation of a line segment is longer or shorter in the ratio given by the scale factor MAFS.912.G-CO.1.5: Draw the transformed figure, given a geometric figure and a rotation, reflection, or translation MAFS.912.G-SRT.1.2: Use the definition of similarity in terms of similarity transformations to decide if two given figures 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. 13

7 DAY Lesson 14 MAFS.912.G-CO.2.6: Use geometric descriptions of rigid motions to 15 EXTRA CREDIT 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. Vocabulary area formula center congruence corresponding dilation perimeter formula reflection regular polygon rigid motion rotation scale factor similarity transformation translation triangle theorems Homework 6.1 student workbook page 374 (7-12;22-24;32-34) page 379 (9-14;28-37;58-61) Page 394 (7-36 all) Mid Chapter 6 Quiz page 399 (1-15) page 404 (5-15 odd: odd) page 410 (7-14: 17, 19,23,24,28) page 417 (4-5;6-10; 21,22 ; 33-40) page 419 TEAM (1-3) Quiz B Ch 6 (concepts 6.7 to 6.9 Textbook) Review two days Unit THREE Assessment Nov 4th

8 Concept Bites 6.1 The sum of the measures of the angles of an n-gon is (n-2)180. The measures of one of the angles is (n-2)180/n. The sum of the measure of the exterior angles of a polygon, one at each vertex, is 360 degrees. 6.2 OPPOSITE SIDES and OPPOSITE ANGLES of a PARALLELOGRAM are congruent. CONSECUTIVE ANGLES in a parallelogram are supplementary. The diagonals of a parallelogram bisect each other. If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every segment DEF of Quadrilateral is a parallelogram if any one of the following is true. Both pairs of opposite sides are parallel Both pair of opposite sides are congruent. Consecutive angles are supplementary Both pairs of opposite angles are congruent The diagonals bisect each other One pair of opposite sides is both congruent and parallel 6.4 Rhombus is a parallelogram with four congruent sides Rectangle is a parallelogram with four rt angles Square is a parallelogram four congruent sides and four right angles The diagonals of a rhombus are perpendicular Each diagonal bisects a pair of opposite sites The diagonals of a rectangle are congruent 6.5 If one diagonal of a parallelogram bisects two angles of the parallel, then the parallelogram is a rhombus. If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If the diagonals are congruent then the parallelogram is a rectangle.

9 Concept Bites 6.6 The parallel sides of a trapezoid are its bases and the nonparallel sides are its legs. Two angles that share a base of a trapezoid are the base angles. the mid-segment of a trapezoid joins the midpoints of its legs. the base angles of an isosceles trapezoid are congruent. the diagonals of a trapezoid are congruent. the diagonal of a kite are perpendicular 6.7 To determine whether sides or diagonals are congruent, use the Distance Formula. To determine the coordinate of the midpoint of a side, or whether the diagonals bisect, use the Mid point Formula. To determine whether opposite sides are parallel, or whether diagonals or sides are perpendicular, use Slope Formula. 6.8 and 6.9 When placing a figure in the coordinate plane, it is usually helpful to place at least one side on an axis. Use variables when naming the coordinates of a figure in order to show that the relationship are true for general case.