Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome 2. Concepts of similarity are foundational to geometry and its applications a.Understand similarity in terms of similarity transformations. (CCSS: GSRT) i. ii. iii. 2. Concepts of similarity are foundational to geometry and its applications Student-Friendly Learning Objective We will identify similar polygons and apply properties similar polygons in problem solving Level of Thinking Resource Correlation Comp Apply 7.2 Ratios in Similar Polygons Verify experimentally the properties of dilations given by a center and a scale factor. (CCSS: G-SRT.1) b. Prove theorems involving similarity. (CCSS: G-SRT) Academic Vocabulary Similar Similar Polygons Similarity Ratio 7.2 Tech Lab- Explore the Golden Ratio pg 460 V Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. (CCSS: GSRT.2) 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. (CCSS: G-SRT.2) a. Understand similarity in terms of similarity transformations. (CCSS: GSRT) i. TIMELINE: 3rd Quarter GRADE: High School (NOTE in CC Edition this is section 7.1 pg 466) (Note: 7.1 Ratios and Proportions in original edition is not aligned with new state standards. It may need to be presented as a review at the beginning of this lesson.) We will draw and describe similarity transformations in a coordinate plane. We will apply properties of similarity transformations to determine whether polygons are similar and to prove that all circles are similar. Apply Evaluate Synthesis 7.2 Similarity and transformations Similarity Transformation IN CC Edition Only pg 472 ii. Prove that all circles are similar. (CCSS: G-C.1) © Learning Keys, 800.927.0478, www.learningkeys.org Page 1 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome 2. Concepts of similarity are foundational to geometry and its applications a.Understand similarity in terms of similarity transformations. (CCSS: GSRT). ii. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. (CCSS: G-SRT.2) TIMELINE: 3rd Quarter GRADE: High School Student-Friendly Learning Objective We will prove triangles are similar by applying AA, SSS and SAS and apply in problem solving Level of Thinking Apply Analysis Evaluate Resource Correlation Academic Vocabulary 7.3 Triangle Similarity AA, SSS and SAS pg 470 (pg 482 in CC Edition) 7.3 Tech Lab- Predict Triangle Similarity Relationships pg 468 iii. 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. (CCSS: G-SRT.2) iv. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (CCSS: G-SRT.3) a. Prove theorems involving similarity. (CCSS: G-SRT) iii. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS: GSRT.5) © Learning Keys, 800.927.0478, www.learningkeys.org Page 2 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome 2. Concepts of similarity are foundational to geometry and its applications a.Understand similarity in terms of similarity transformations. (CCSS: GSRT) ii.Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. (CCSS: G-SRT.2) iii. 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. (CCSS: G-SRT.2) TIMELINE: 3rd Quarter GRADE: High School Student-Friendly Learning Objective We will apply properties of similar triangles to find segment lengths and apply proportionality and triangle angle bisector theorems in problem solving. Level of Thinking Apply Resource Correlation Academic Vocabulary 7.4- Applying Properties of Similar Triangles pg 481 (CC edition pg 495) 7.4 Technology Lab – Investigate Angle Bisectors of a triangle pg 480 (CC Edition pg 494) b. Prove theorems involving similarity. (CCSS: G-SRT) i. Prove theorems about triangles.9 (CCSS: G-SRT.4) iii. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS: GSRT.5) © Learning Keys, 800.927.0478, www.learningkeys.org Page 3 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome 2. Concepts of similarity are foundational to geometry and its applications b. Prove theorems involving similarity. (CCSS: G-SRT) 1. Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically a. Experiment with transformations in the plane. (CCSS: G-CO) iii. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. (CCSS: G-SRT.5) i. ii. iii. iv. TIMELINE: 3rd Quarter GRADE: High School S Represent transformations in the plane using1 appropriate tools. (CCSS: G-CO.2) Describe transformations as functions that take points in the plane as inputs and give other points as outputs. (CCSS: G-CO.2) Compare transformations that preserve distance and angle to those that do not.2 (CCSS: G-CO.2) © Learning Keys, 800.927.0478, www.learningkeys.org Student-Friendly Learning Objective Level of Thinking We will apply ratios to make indirect measurements and apply scale drawing in problem solving Apply We will apply Similarity properties in the coordinate plane (dilations) and write coordinate proofs to prove figures similar Apply Synthesis Resource Correlation 7.5 Using Proportional Relationships pg 488 Academic Vocabulary Indirect Measurement Scale Drawing Scale (CC Edition pg 502) 7.6 Dilations and Similarity in the coordinate Plane pg 495 Dilation Scale Factor (CC edition pg 509) Connecting Geometry to Algebra- Direct Variation pg 501 (CC edition pg 517) Page 4 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome 2. Concepts of similarity are foundational to geometry and its applications c. Define trigonometric ratios and solve problems involving right triangles. (CCSS: G-SRT) i. 2. Concepts of similarity are foundational to geometry and its applications 2. Concepts of similarity are foundational to geometry and its applications TIMELINE: 3rd Quarter GRADE: High School Explain 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. (CCSS: G-SRT.6) c. Define trigonometric ratios and solve problems involving right triangles. (CCSS: G-SRT) i. Explain 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. (CCSS: G-SRT.6) c. Define trigonometric ratios and solve problems involving right triangles. (CCSS: G-SRT) ii. Explain and use Student-Friendly Learning Objective Level of Thinking Resource Correlation We will apply geometric means to find segment lengths in right triangles and apply similarity relationships in right triangles to solve problems Apply 8.1 Similarity in Right Triangles pg 518 We will find sine, cosine and tangent of acute angles. We will apply trigonometric ratios to find side lengths in right triangles and apply in problem solving Apply We will apply the relationship between the sine and cosine of complementary angles Apply Academic Vocabulary Geometric Mean (CC edition pg 534) 8.2 Trigonometric Ratios pg 525 (CC Edition pg 540) Trigonometric Ratios Sine Cosine Tangent 8.2 Technology LabExplore Trigonometric Ratios pg 524 Trigonometric Ratios and Complementary Angles CC Edition ONLY pg 549 the relationship between the sine and cosine of complementary angles. (CCSS: GSRT.7) © Learning Keys, 800.927.0478, www.learningkeys.org Page 5 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation 2. Concepts of similarity are foundational to geometry and its applications TIMELINE: 3rd Quarter GRADE: High School Evidence Outcome a. Define trigonometric ratios and solve problems involving right triangles. (CCSS: GSRT) Student-Friendly Learning Objective Level of Thinking We will apply inverse trigonometric ratios to find angle measures in right triangles and apply in problem solving Apply a. Define trigonometric ratios and solve problems involving right triangles. (CCSS: GSRT) We will solve problems involving angles of elevation and angles of depression Apply b. Use the rules of probability to compute probabilities of compound events in a uniform probability model. (CCSS: S-CP) iv.Use permutations and combinations to compute probabilities and solve problems (CCSS: S-CP.9) © Learning Keys, 800.927.0478, www.learningkeys.org 8.3- Solving Right Triangles pg 534 8.4 Angles of Elevation and Depression pg 544 Angle of Elevation Angle of Depression (CC edition pg 562) 8.4 Geometry LabIndirect Measurement Using Trigonometry pg 550 iii. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* (CCSS: GSRT.8) 3. Probability models outcomes for situations in which there is inherent randomness Academic Vocabulary (CC Edition pg 552) Connecting Geometry to Algebra – Inverse Functions pg 533 iii. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* (CCSS: GSRT.8) 2. Concepts of similarity are foundational to geometry and its applications Resource Correlation NOTE 8.5 and 8.6 not in Colorado Standards We will solve problems involving the Fundamental Counting Principal, permutations and combinations Apply 13.1 Permutations and Combinations pg 870 CC edition (NOTE this whole chapter is in CC Edition only) Fundamental Counting Principal Permutation Factorial Combination Page 6 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation 3. Probability models outcomes for situations in which there is inherent randomness 3. Probability models outcomes for situations in which there is inherent randomness Evidence Outcome b. Use the rules of probability to compute probabilities of compound events in a uniform probability model. (CCSS: S-CP) iv.Use permutations and combinations to compute probabilities and solve problems (CCSS: S-CP.9) a.Understand independence and conditional probability and use them to interpret data. (CCSS: S-CP) i. Describe events as subsets of a sample space5 using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events.6(CCSS: S-CP.1) TIMELINE: 3rd Quarter GRADE: High School Student-Friendly Learning Objective Level of Thinking We will compare theoretical and experimental probability, find the probability of theoretical and experimental probability and apply in geometric probability problems Apply Analysis We will determine whether events are independent or dependant. We find the probability of independent and dependant events. Apply Analysis Evaluate Resource Correlation 13.2 Theoretical and Experimental Probability pg 878 CC edition 13.2 Technology Lab Explore Simulations pg 886 CC Edition 13.3 Independent and Dependant Events pg 887 CC Edition Academic Vocabulary Probability Outcome Sample Space Event Equally likely outcomes Favorable outcomes Theoretical probability Complement Geometric Probability Experiment Trial Experimental probability Independent Events Dependant Events Conditional probability ii. Explain that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. (CCSS: SCP.2) iii. Using the conditional probability of A given B as P(A and B)/P(B), © Learning Keys, 800.927.0478, www.learningkeys.org Page 7 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry Grade Level Expectation Evidence Outcome TIMELINE: 3rd Quarter GRADE: High School Student-Friendly Learning Objective Level of Thinking Resource Correlation Academic Vocabulary interpret the independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. (CCSS: S-CP.3) v. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.8 (CCSS: S-CP.5) 3. Probability models outcomes for situations in which there is inherent randomness a. Understand independence and conditional probability and use them to interpret data. (CCSS: S-CP) Iv .Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities.7 (CCSS: S-CP.4) © Learning Keys, 800.927.0478, www.learningkeys.org We will construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Apply Evaluate Synthesis 13.4 Two way tables pg 899 CC Edition Joint Relative Frequency Marginal relative frequency Conditional relative frequency Page 8 ROCKY FORD CURRICULUM GUIDE SUBJECT: Geometry TIMELINE: 3rd Quarter GRADE: High School Grade Level Expectation Evidence Outcome 3. Probability models outcomes for situations in which there is inherent randomness b. Use the rules of probability to compute probabilities of compound events in a uniform probability model. (CCSS: S-CP) i. ii. Student-Friendly Learning Objective We will find the probability of mutually exclusive events and inclusive events and apply in problem solving Level of Thinking Apply Resource Correlation 13.5 Compound Events pg 907 CC Edition Academic Vocabulary Simple Event Compound Event Mutually Exclusive Events Inclusive Events Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. (CCSS: S-CP.6) Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (CCSS: S-CP.7) © Learning Keys, 800.927.0478, www.learningkeys.org Page 9