WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name _ Irene M Runco_____ Date 5.4.15_ Length of Lesson _15 days_ Content Area Honors Algebra 2
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STAGE I – DESIRED RESULTSLESSON TOPIC: CHAPTER 10
Exponential and Logarithmic Relations / BIG IDEAS:
Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
UNDERSTANDING GOALS (CONCEPTS):
· Graphing exponential functions How are these graphs different from those used in chapter 9?
· Solve exponentials equations and inequalities Is there a standard method to solve an exponential equation? How does this differ from everything else learned so far this year ?
· Evaluate and solve logarithmic equations and inequalities What do you do if the bases are not the same ? Can you solve these ?
· Simplify expressions using properties of logarithmsWHat about negative numbers ? Can they have logs?
· Solving logarithmic equations and inequalities involving common logs
· Evaluating and solving equations dealing with natural logs What is e ? How did it come about ? How and why do we use it ?
· Use logarithms to solve problems dealing with exponential growth and decay. What is the defining part of the equation that leads to decay or growth ? What does this do graphically ? / ESSENTIAL QUESTIONS:
· What are the advantages/disadvantages of the various methods to represent exponential functions (table, graph, equation) and how do we choose the most appropriate representation?
· How do exponential equations and their graphs and/or tables help us interpret events that occur in the world around us?
· How do you explain the benefits of multiple methods of representing polynomial functions (tables, graphs, equations, and contextual situations)?
VOCABULARY
· Logarithm
· Common log· Natural log
· Exponential growth
· Exponential decay
· Logarithmic equation
§ inequality
§ function
· Rate of decay
· Rate of growth
· e /
STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES):
Students will be able to:· Graphing exponential functions
· Solve exponentials equations and inequalities
· Evaluate and solve logarithmic equations and inequalities
· Simplify expressions using properties of logarithms
· Solving logarithmic equations and inequalities involving common logs
· Evaluating and solving equations dealing with natural logs
· Use logarithms to solve problems dealing with exponential growth and decay.
STAGE II – COMMON CORE STANDARDS ADDRESSED
CC.9-12.CED.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
CC.9-12.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
CC.9-12.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
CC.9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★
CC.9-12.F.IF.7 · Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
· CCSS.Math.Content.HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
· CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
· CCSS.Math.Content.HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
· CCSS.Math.Content.HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
· CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
CC.9-12.F.IF.8 · Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
· CCSS.Math.Content.HSF-IF.C.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
· CCSS.Math.Content.HSF-IF.C.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
CC.9-12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
CC.9-12.F.BF.4 · Find inverse functions.
· CCSS.Math.Content.HSF-BF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
· CCSS.Math.Content.HSF-BF.B.4b (+) Verify by composition that one function is the inverse of another.
· CCSS.Math.Content.HSF-BF.B.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
· CCSS.Math.Content.HSF-BF.B.4d (+) Produce an invertible function from a non-invertible function by restricting the domain.
CC.9-12.A.REI.11 · Find inverse functions.
· CCSS.Math.Content.HSF-BF.B.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
· CCSS.Math.Content.HSF-BF.B.4b (+) Verify by composition that one function is the inverse of another.
· CCSS.Math.Content.HSF-BF.B.4c (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.
· CCSS.Math.Content.HSF-BF.B.4d (+) Produce an invertible function from a non-invertible function by restricting the domain.
CC.9-12.F.LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
STAGE III – ASSESSMENT EVIDENCE
PERFORMANCE TASK:
Students will participate in
1. class discussions,
2. guided notes & practice,
3. computer work,
4. whiteboard activities / OTHER EVIDENCE:
· Daily warm up or exit polls ,
· homework,
· Keystone Diagnostic Tool,
· Study Island and Glencoe.unit tests,
· quizzes,
· formative assessments.
· Student work in portfolio
STAGE IV: LEARNING PLAN
INSTRUCTIONAL PROCEDURES:
(Active Engagement, Explicit Instruction, Metacognition, Modeling, Scaffolding)
ACTIVE ENGAGEMENT USED:
· Cooperative learning
· Think pair share
· Notetaking
· Higher level thinking
DESCRIBE USAGE
Students will work from basic procedures to solve equations
Solving world problems
Solving real world applications
Proving properties of algeb
SCAFFOLDING USED
:
· Chunking
· Building on Prior knowledge
· Providing Visual Support
MINI LESSONS:
· Sketching the graph of an exponential function
· Writing an exponential function given two points
· Changing logarithmic form and exponential form
· Solving a logarithmic equation and inequality
· Using properties of logarithms
· Changing bases with common logs
· Using natural logs and e
· Using exponential decay and growth in real life situations / MATERIALS AND RESOURCES:
Unit 10 Chapter : Exponential Equations and Inequalities
( Glencoe Text )
Warm ups & Exit polls(daily)
Homework (daily)
Guided practice and Enrichment from Glencoe Grab & Go workbooks
Glencoe teacher works…chalkboard is
Good for Promethean Board use. Use end of powerpoint for extra examples and practice.
Use 5 minute check as exit slip. / INTERVENTIONS:
Study Island
A+ Math
Math Lab
Khan Academy Videos
Keystone Diagnostic Tool
National Library of Virtual Manipulatives is an excellent site for use with promethean boards for this unit.
On line activities are very good in this chapter for finding a pattern and making predictions based on your observations.
Truly struggling students will be referred to guidance/SAP (RTI)
• Small group/ flexible grouping will occur if necessary.
• Students will be encouraged to stay for or find help with a math teacher during free time, after school, or lunch. / ASSIGNMENTS:
Note: all assignment are from the same page, but different questions are assigned based on grouping by teacher.
· Weekly blogs
· Word problem practice from 2008 copy of Algebra 2 (on line form Glencoe.com)
· Enrichment from 2008 Glencoe ( advanced)
· Khan Academy videos
§ 10-1 pp 527-530
§ 10-2 pp 535-538
§ 10-3 pp 544-546
§ 10-4 pp 549-551
§ 10-5 pp 557-559
§ 10-6 pp563-565
Note: Reading with Mathematics pages from Grab & Go are especially good for standard classes.
Monday 156 B / Tuesday 157 A / Wednesday 158 B / Thursday 159 A / Friday 160 B
Writing exponential expressions and equations / Logarithms and logarithmic functions / Small group practice on sections 1 & 2 / Properties of logs / Word problem review of logs
p. 528 #33-55 odd / p. 535 # 4 – 17 / p. 536 # 33-66 odd / p.544 #13- 32 / Worksheet
Math Lab – Tuesday, Thursdays
Wednesday- ??????