Algebra 2 Unit 2 Logarithms
BY THE END OF THIS UNIT:
CORE CONTENT
Cluster Title: FunctionsStandard : F – IF. 7e. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline and amplitude.
Concepts and Skills to Master
· Identify, compare and analyze, the key features (domain, range, intercepts, transformations) of exponential and logarithmic functions.
· Given real-world data, identify behaviors that tend to be explained using logarithmic and exponential functions.
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Domain and Range
· Transformations
· Finding intercepts using graphing calculators
· Adjust calculator windows to appropriately model data
Academic Vocabulary
Base, logarithm, exponential function, change of base formula
Suggested Instructional Strategies
· Put quantitative concepts in context – examples
Earthquakes, including magnitude scales and the Gutenberg – Richter relation; Floods and flooding; Grain sizes; Radioactive decay and carbon dating; Populations growth; Changes in atmospheric CO2; Appreciation/ Depreciation: Medicine
· Teach definition of logarithm and change of base formula in order to allow students to complete tables and graph logarithmic functions. / Resources
· Textbook Correlation: Section 7 – 2, 7 – 3 and 7 – 4 problems 3 and 4
Sample Formative Assessment Tasks
Skill-based task
Complete the table of values for both and
x / f(x)
1
2
4
16
/ Problem Task: Hurricane Activity
CORE CONTENT
Cluster Title: FunctionsStandard: F – IF.8.
a. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function
b. Use the properties of exponents to interpret expression for exponential functions. For example, identify percent rate of change in functions such as , , , and classify them as representing exponential growth or decay.
Concepts and Skills to Master
· Use formulas or equations of functions to calculate outcomes of exponential growth or decay and apply them to real – life situations such as compound interest, radioactivity, and population growth.
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Writing percents as decimals
· Unit conversion – i.e. months to years
· Proper keystrokes for complex calculations using calculator
Academic Vocabulary
Logarithm, exponential function, compounded interest, half – life, appreciation, depreciation
Suggested Instructional Strategies
· M & M activity
· Make sure students use tables in addition to graph and identify trends
· Relate simple interest formula (I = prt) to compound interest formulas / Resources
· Textbook Correlation: 7 – 2
· TI – Activity: “Deposit and Forget It” (requires TINspire graphing calculator)
· M & M Lab Activity (TI - Carbon dating)
· Discovery Education
“Working with Functions of Exponential Growth”
Sample Formative Assessment Tasks
Skill-based task
Jane deposits $ 200 into her account that is compounded quarterly with 3% interest. If she does not deposit any additional funds, how much money will Jane have in 5 years? / Problem Task:
a) Use the Challenge problems found on page 449 # 42 – 44 and problems 36 and 37 on page 448.
b) Given , explain how replacing c with (-c) affects the function.
CORE CONTENT
Standard F – LE.4. For exponential models, express as a logarithm the solutions to where a, c and d are numbers and the base b is 2, 10 or e ; evaluate the logarithm using technology.
Concepts and Skills to Master
· Understand the properties of logarithms
· Expand and condense logarithmic expressions
· Solve logarithmic equations using technology and algebraically for Honors students
SUPPORTS FOR TEACHERS
Critical Background Knowledge· Rules of exponents
· Solving linear and quadratic equations
· Use of calculator to graph functions and approximate solutions
· Change of base formula
Academic Vocabulary
Base, logarithmic equation, exponential functions
Suggested Instructional Strategies
· Use Excel and applets in addition to graphing calculators to incorporate technology
· For Standard Algebra 2, show students how to solve algebraically, but focus on technology to solve problems.
· For Honors Algebra 2 emphasize solving algebraically, logarithmic and exponential inequalities - see Concept Byte / Resources
· Textbook Correlation: 7-3; 7-4; 7-5
· Concept Byte: - 7- 6 … HONORS
· Ti – Activity “Evaluating Logarithms”
Sample Formative Assessment Tasks
Skill-based task:
Solve:
1. Solve
2. Solve
3.
4. / Problem Task
In the formula , P is the atmospheric pressure in millimeters of mercury at elevation h meters above sea level. If equals 760 mm, at what elevation is the pressure 42 mm?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes.