Livingston American School 4TH Quarter Lesson Plan

Transcription

1 Livingston American School 4TH Quarter Lesson Plan Week 27 Week 28 Week 29 Week 30 Concept / Topic To Teach: Find the distance between two points and find the midpoint of the line segment Use the distance and the midpoint formulas in real life situations Graph and write equations of parabolas Use parabolas to solve real-life problems. Graph and write equations of ellipses Use ellipses in real-life situations. Graph and write hyperbola Use hyperbola to solve real life problem Graph and write circle Use circle to solve real life problems Write and graph of equation of a parabola with its vertex (h,k) and an equation of a circle, ellipse or hyperbola with its center (h,k) Classify conics Solve systems of quadratic equations Use quadratic system to solve real life problems Assess/Review Use and write sequences Use summation notation to write series and find sums of series Write the rules of arithmetic sequences and find sums of arithmetic series Use arithmetic series in real-life problems Standards Addressed: Expressing Geometric Properties with Equations G-GPE Expressing Geometric Properties with Equations G-GPE Expressing Geometric Properties with Equations G-GPE Interpreting Functions F-IF Building Functions F-BF Specific Objectives: Translate between the geometric description and the equation for a conic section Derive the equation of a parabola given a focus and directrix. Use coordinates to compute perimeters of polygons and Translate between the geometric description and the equation for a conic section (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of Translate between the geometric description and the equation for a conic section Understand the concept of a function and use function notation Build a function that models a relationship between two quantities

2 areas of triangles and rectangles, e.g., using the distance formula. distances from the foci is constant. General Goal(s): Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Use coordinates to prove simple geometric theorems algebraically Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Classify the conic section and writing equation in standard form Solving quadratic equations algebraically and find their point lo intersections Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to

3 model situations, and translate between the two forms. Assessment Based On Objectives: Core Values

4 Week 31 Week32 Week 33 Week 34 Concept / Topic To Teach: Write rules for geometric sequences and find sum of geometric series Use geometric series to model real life problems Find the sum of infinite series Use infinite geometric series as models to reallife problems Evaluate and write recursive rules for sequences Review/Assess Use the fundamental counting principle to count the number of ways an event can happen Use permutations to count the number of ways an event can happen Use combinations to count the number of ways the even can happen. Use binomial theorem to expand a binomial that is raised to a power. Find theoretical and experimental probabilities Find geometric probabilities Find the probabilities of unions and intersections of two events Use complements to find the probability of the events Find the probability of independent events Find the probability of dependent events Find the binomial probabilities and analyze binomial distributions Test a hypothesis Calculate probabilities using normal distributions. Use normal distributions to approximate binomial distributions. Find expected values of collections and outcomes. Standards Addressed: Interpreting Functions F-IF Building Functions F- BF Making Inferences and Justifying Conclusions S-IC Conditional Probability and the Rules of Probability S-CP Conditional Probability and the Rules of Probability S-CP Specific Objectives: Understand the concept of a function and use function notation Build a function that models a relationship between two quantities Understand and evaluate random processes underlying statistical Experiments Use the rules of probability to compute probabilities of compound Understand independence and conditional probability and use them to interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Use probability to evaluate outcomes of decisions events in a uniform probability

5 model General Goal(s): Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) f(n-1) for n 1. Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? 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. 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. (+) Apply the general Multiplication Rule in a uniform probability Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or, and, not ). Understand 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. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret 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. (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant. Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

6 model, P(A and B) = P(A)P(B A) = P(B)P(A B), and interpret the answer in terms of the model. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. probability of B given A is the same as the probability of B. Assessment Based On Objectives: Core Values

7 Week 35 Week36 Week 37 Concept / Topic To Teach: Use trigonometric relationships to evaluate trigonometric functions Use trigonometric functions to solve reallife problems. Review/ Assessment Finals Measure angles in standard position using algebra measure Calculate arc length and areas of sectors Evaluate trigonometric functions of any angles Using trigonometric functions to solve reallife problems Standards Addressed: Similarity, Right Triangles, and Trigonometry G-SRT Specific Objectives: Define trigonometric ratios and solve problems involving right triangles Apply trigonometry to general triangles

8 General Goal(s): (+) Derive the formula A = 1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (+) Prove the Laws of Sines and Cosines and use them to solve problems. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Assessment Based On Objectives: Core Values

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