WOODLAND HILLS HIGH SCHOOL LESSON PLAN

SAS and Understanding By Design Template

Name Melissa Broadwater Date 2/4/14 Length of Lesson 12 days Content Area Intro to Calculus Edline was updated this week:

My Class website was updated this week:

STAGE I – DESIRED RESULTS
LESSON TOPIC:
Sequences and Probability / BIG IDEAS:
(Content standards, assessment anchors, eligible content) objectives, and skill focus)
M11.E.1.1 Appropriately display and/or use data in problem-solving settings
M11.E.2.1 Use measures of central tendency to describe a set of data.
M11.E.3.1 Apply probability and/or odds to practical situations
M11.E.3.2 Apply counting techniques in problem-solving settings
M11.E.4.1 Make predictions using data displays and probability.
M11.E.4.2 Analyze and/or interpret data on a scatter plot and/or use a scatter plot to make predictions.
UNDERSTANDING GOALS (CONCEPTS):
Students will understand: Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms).
Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. Measure and compare angles in degrees and radians
Demonstrate mathematical solutions to problems (e.g., in the physical sciences).
Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. Present mathematical procedures and results clearly, systematically, succinctly and correctly. Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. Represent functional relationships in tables, charts and graphs
Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Model situations geometrically to formulate and solve problems. Use graphing calculators to display periodic and circular functions; describe properties of the graphs.
Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. / ESSENTIAL QUESTIONS:
How do you tell whether a sequence is geometric or algebraic?
What is meant by coterminal angles?
In what ways can the unit circle be used?
How do you determine the domain, range, and period of the sine and cosine functions using the unit circle?
How do you sketch a graph of a sin, cos, tan, cot, sec, or csc?

VOCABULARY: arc length, coterminal angles, radian, unit circle, odd function, even function, trigonometric identities

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STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES):

Students will be able to:
1. Find the first n terms of a given sequence; find the nth term of a given sequence
2. Use summation notation ( ) to find or write the sum.
3. Determine if a sequence is arithmetic. Find the nth term of an arithmetic sequence.
4. Find the sum of an arithmetic sequence.
5. Solve problems using arithmetic sequences.
6. Determine if a sequence is geometric. Find the nth term of a geometric sequence.
7. Find the sum of a geometric sequence.
8. Solve problems using geometric sequences.
9. Apply the Principle of Mathematical Induction to prove formulas. (optional)
10. Apply the Binomial Theorem to find binomial coefficients of a polynomial.
11. Apply Pascal’s Triangle to evaluate or find coefficients of a polynomial. (1 day)
12. Expand a binomial using Binomial Theorem or Pascal’s Triangle. (1 day)
13. Use the Fundamental Counting Principle to determine the total number of outcomes of 2 or more events. (1 day)
14. Solve problems involving permutations and combinations. (2 days)
15. Find the probability of an event, mutually exclusive events, union of two events, independent events, and complements of events. (2 days)
16. Review and test on skills above. (2 days)
STAGE II – ASSESSMENT EVIDENCE
PERFORMANCE TASK:Students will actively participate in class examples, discussion, and group work. / FORMATIVE ASSESSMENTS:
#1. Choose assessments:Graphic OrganizersExit TicketsSummarizing Main IdeasPre-AssessmentOpen Ended QuestionsThink-Pair-ShareThumbs UpResponse CardsBrief in Class Writing PrompPortfolios
#2. Choose assessments:Graphic OrganizersExit TicketsSummarizing Main IdeasPre-AssessmentOpen Ended QuestionsThink-Pair-ShareThumbs UpResponse CardsBrief in Class Writing PrompPortfolios
#3. Choose assessments:Graphic OrganizersExit TicketsSummarizing Main IdeasPre-AssessmentOpen Ended QuestionsThink-Pair-ShareThumbs UpResponse CardsBrief in Class Writing PrompPortfolios
Others: Summarizing Main Idea
STAGE III: LEARNING PLAN
INSTRUCTIONAL PROCEDURES:
Active Engagements used:
#1. Choose Active EngagementsNote-TakingGraphic OrganizersSummarizingHigher Level Thinking SkillsCooperative EducationPartneringWhole Class ResponseThink-Pair-ShareCompare & ContrastRandom Reporter
#2. Choose Active EngagementsNote-TakingGraphic OrganizersSummarizingHigher Level Thinking SkillsCooperative EducationPartneringWhole Class ResponseThink-Pair-ShareCompare & ContrastRandom Reporter
Others: Graphic Organziers, Summarizing, Cooperative Education, Partnering
Describe usage: See below for Compare/Contrast, Graphic Organizers, Cooperative Education, Partnering, Note-Taking. Check for understanding and summarizing using warm up, homework, formative assessment questioning or exit tickets to determine whether to continue lesson or do interventions as needed. (model, spiral scaffolding, instruct/ reteach as needed)
Scaffolding used:
#1. Choose Technique:Graphic OrganizersGuided NotesBuild VocabularyBuild on Prior KnowledgeChunkingProvide Visual SupportTeacher PrompingK-W-L
#2 . Choose Technique:Graphic OrganizersGuided NotesBuild VocabularyBuild on Prior KnowledgeChunkingProvide Visual SupportTeacher PrompingK-W-L
Others: Graphic Organizers, Build Vocabulary
Describe usage: Warm up to include spiraling review of prior knowledge to include upcoming lesson. All notes are guided notes to build vocabulary, interspersed with group activities. Graphic organizers utilized when appropriate to compare/contrast vocabulary.
Other techniques used:
MINI LESSON:
Based on daily assessments (formative and summative), additional modeling, instruction, homework, review, interventions, group work, computer or teacher guided practice will be done. / MATERIALS AND RESOURCES:
Chapter 3 (Precalculus text and supplementals)
Warm ups (daily)
Homework (daily)
worksheets/ activities
Unit Test
Additional materials as needed (rulers, compass, grid paper, etc)
CONTENT AREA READING:
Guided Notes / INTERVENTIONS:
Struggling students will be referred to RTII
Small group/flexible grouping will occur.
Various computer programs. / ASSIGNMENTS:
•Complete Chapter 4 Note Sheets
Text Problems
Pg. 367: 1-14
Pg. 367: 15-61 eoo
Pg. 367: 71-81 odd
Pg. 377: 1-16
Pg. 377: 17-30
Pg. 378: 25-53 odd
Pg. 387: 1-21 odd
Pg. 388: 23-55 odd
Pg. 389: 57-67 odd
Pg. 399: 1-21 odd
Pg. 400: 43-67 odd
Pg. 401: 75-80