Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript

Daily Lesson Plan Template Analytical Geometry following J. Dempsey Day & Date: Monday, October 20 Standard:. MCC9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: MCC9-12.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. MCC9-12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar MCC9-12.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. MCC9-12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Understand congruence in terms of rigid motions MCC9-12.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. MCC9-12.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. MCC9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems MCC9-12.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. MCC9-12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. MCC9-12.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. Essential Question/Learning Goal: What do I remember about the material studied so far this year? Lesson Opener: (10 min.) Procedures/Strategies: (40 min.) review topics of study and look at examples Lesson Summarizer: (5 min.) MOST IMPORTANT THING Assessment/Evaluation: Student answers to the questions presented Materials Needed:, Smart board 1 Day & Date: Tuesday, October 21 Standard: MCC9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: MCC9-12.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. MCC9-12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar MCC9-12.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. MCC9-12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Understand congruence in terms of rigid motions MCC9-12.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. MCC9-12.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. MCC9-12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems MCC9-12.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. MCC9-12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. MCC9-12.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. Essential Question/Learning Goal: What do I remember about the material studied so far this year? Lesson Opener: (10 min.) Answer any questions students have prior to the test Procedures/Strategies: (30 min.) Take benchmark test Lesson Summarizer: (10 min.) Think about areas of study that you still need help. Email me with those areas so that I can adjust the future lessons Assessment/Evaluation: Benchmark test Materials Needed: clickers, iPad 2 Day & Date: Wednesday, October 22 Standard: MCC9‐12.G.SRT.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. Essential Question/Learning Goal: What do similar triangles have in common with right triangles? Lesson Opener: (7 min.) 3 clicker questions ACTIVATOR WATCH VIDEO GETTING TRIGGY WIT IT Procedures/Strategies: (40min.) Begin deconstructing the standard Review using the definition of similar triangles to determine missing sides of the triangles Demonstrate how to create right triangles with a specific angle measure. Use created triangle to determine the length of a ramp using similar triangle relationships Use similar triangles and Geogebra to find measurement with other applied problems Lesson Summarizer: (5 min.) Assessment/Evaluation: questions, Constructing task, summarizer Materials Needed:. smart board, iPad, hard copy of guided notes for homework 3 Day & Date: Thursday, October 23 Standard: MCC9‐12.G.SRT.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. Essential Question/Learning Goal: How do you label the parts of a right triangle? Lesson Opener: (10 min.) 3 clicker questions Procedures/Strategies: (40 min.) Draw a right triangle and label the vertices with your initials. Identify theta and label the opposite, adjacent and hypotenuse of your triangle. Post a picture of your labeled triangle on the class tagboard. #mrswomackRHS Discuss student post on tagboard. Lesson Summarizer: (5 min.) Assessment/Evaluation: clicker questions, created triangle, post, discussion, summarizer, homeworkibrainstorm Materials Needed: smart board, iPad, paper copy of guided notes for homework 4 Day & Date: Friday, October 24 Standard: MCC9‐12.G.SRT.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. Essential Question/Learning Goal: How are the sides and angles of right triangles related to each other? Lesson Opener: (10 min.) 3 clicker questions Procedures/Strategies: (40 min.) Complete document on setting up trig functions Post ibrainstorm to #mrswomackRHS Watch video on Relationships of Sine and Cosine of Complementary angles, take notes Lesson Summarizer: (5 min.) Create your own acronym for the trig functions Assessment/Evaluation: questions, worksheet, acronym, video on complementary angles Materials Needed: questions, iPad, guided notes 5

Document related concepts

Euclidean geometry wikipedia, lookup

Pythagorean theorem wikipedia, lookup

History of geometry wikipedia, lookup

Rational trigonometry wikipedia, lookup

Integer triangle wikipedia, lookup

Trigonometric functions wikipedia, lookup

Multilateration wikipedia, lookup

Technical drawing wikipedia, lookup

Anatomical terms of location wikipedia, lookup

History of trigonometry wikipedia, lookup

Dessin d'enfant wikipedia, lookup

Golden ratio wikipedia, lookup

Euler angles wikipedia, lookup

Reuleaux triangle wikipedia, lookup