Math with Coach Underwood
|Wednesday February 4th – Friday 20th |
| |UNIT 4 • EXPONENTIAL AND LOGARITHMIC FUNCTIONS |
|Standard(s)/ |Lesson 1: Exponential Functions |
|Element(s) |Lesson 2: Introducing Logarithmic Functions |
| |Lesson 3: Solving Exponential Equations using Logarithms |
| | |
| |Common Core Georgia Performance Standards |
| |Lesson 1: MCC9–12.A.SSE.3c ★ MCC9–12.F.IF.7e ★MCC9–12.F.IF.8b★ |
| |Lesson 2: MCC9–12.F.IF.7e ★MCC9–12.F.IF.8b ★MCC9–12.F.BF.5 (+)★ |
| |Lesson 3: MCC9–12.A.SSE.3c★MCC9–12.F.IF.8b★ MCC9–12.F.BF.5 (+)★MCC9–12.F.LE.4★ |
| | |
| |Standards for Mathematical Practice |
| |All 8 Standards will be used in this lesson |
|Essential Question(s) |Essential Questions |
| | |
| |Lesson 1 |
| |1. How can you rewrite an exponential function using the properties of exponents? |
| |2. What information can an exponential function provide when it is rewritten? |
| |3. How can you determine whether the growth rate of an exponential function is positive or negative? |
| |4. How can you graph an exponential function? |
| |5. What are some key features of an exponential function that can be determined from its graph? |
| |6. How can problems involving interest rates be solved using exponential functions? |
| | |
| |Lesson 2 |
| |1. What is a logarithm? |
| |2. How can a logarithm be written in exponential form and vice versa? |
| |3. What is the difference between a common logarithm and a natural logarithm? |
| |4. How does the graph of a logarithmic function change when the base changes? |
| |5. How can logarithms that are not common be calculated on a calculator? |
| |6. How are the properties of logarithms similar to those for exponents? |
| | |
| |Lesson 3 |
| |1. Why is a logarithmic equation appropriate for modeling the magnitude of an earthquake based on the Richter scale? |
| |2. If a natural logarithmic equation and a common logarithm equation each represent exponential decay, which equation model (natural or |
| |common) would represent a faster rate of decay? |
| |3. For problems involving growth and decay, why is a graph sometimes a more useful tool in determining the growth/decay after many years? |
| |4. How does the growth of an investment earning continuously compounded interest compare to that of an investment earning interest that is|
| |compounded quarterly? |
|Activator |Mini-Lesson:(Skill)- EXPONENTIALAND LOGARITHMIC FUNCTIONS |
| |Adaptation of Content Links to Background Links to Past Learning |
| |Strategies incorporated |
| | |
| |Each day for each lesson we will watch a youtube video that ties in the lesson concept with the practice and do two to five problems. |
|Work Session |Whole Class Small Groups Partners Independent |
| | |
|Teaching Strategies |2/4/15- Lesson 4.1.1: Rewriting Exponential Functions PPPT with guided notes and practice problems examples |
| |2/5/15- Lesson 4.1.2: Properties of Exponential Functions PPPT with guided notes and practice problems examples |
| |2/6/15- Unit 4 Lesson 1 Post Assessment |
| | |
| |2/9/15- Lesson 4.2.1: Defining Logarithms PPPT with guided notes and practice problems examples |
| |2/10/15- Lesson 4.2.2: Graphs of Logarithmic Functions PPPT with guided notes and practice problems examples |
| |2/11/15- Lesson 4.2.3: Properties of Logarithms PPPT with guided notes and practice problems examples |
| |2/12/15- Unit 4 Lesson 2 Post Assessment |
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| |2/13/15- Hands on Lesson Project |
| | |
| |2/16/15- Lesson 4.3.1: Common Logarithms PPPT with guided notes and practice problems examples |
| |2/17/15- Lesson 4.3.2: Natural Logarithms PPPT with guided notes and practice problems examples |
| |2/18/15- Unit 4 Lesson 3 Post Assessment |
| | |
| |2/19/15- Unit 4 Assessment Review |
| |2/20/15- Unit 4 Assessment |
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| | |
|Key Vocabulary |Lesson 1-asymptote- an equation that represents sets of points that are not allowed by the conditions in a parent function or model; a |
| |line that a function gets closer and closer to, but never crosses or touches base- the quantity that is being raised to a power in an |
| |exponential expression; in ax, a is the base compound interest- interest earned on both the initial amount and on previously earned |
| |interest continuously compounded interest- compound interest that is being added to the balance at every instant delta (Δ) a Greek letter |
| |commonly used to represent the change in a value domain the set of all input values (x-values) that satisfy the given function without |
| |restriction e an irrational number with an approximate value of 2.71828 end behavior the behavior of the graph as x approaches positive or|
| |negative infinity exponent the quantity that shows the number of times the |
| |base is being multiplied by itself in an exponential expression; also known as the power. In ax, x is the |
| |power/exponent. exponential decay an exponential equation with a base, b, that is between 0 and 1 (0 < b < 1); can be represented by the |
| |formula f(t) = a(1 – r)t, where a is the initial value, (1 – r) is the decay factor, t is time, and f(t) is the final value exponential |
| |expression an expression that contains a base raised to a power/exponent exponential function a function in the form f(x) = a(bx) + c, |
| |where a, b, and c are constants and b is greater than 0 but not equal to 1exponential growth an exponential function with a base, b, |
| |greater than 1 (b > 1); can be represented by the formula f(t) = a(1 + r)t, where a is the initial value, (1 + r) is the growth factor, t |
| |is time, and f(t) is the final value natural exponential function an exponential function with a base of e percent rate of change the |
| |percentage by which a function increases or decreases within a certain interval power the quantity that shows the number of times the base|
| |is being multiplied by itself in an exponential expression; also known as the exponent. In ax, x is the power/exponent. range the set of |
| |all outputs of a function; the set of y-values that are valid for the function rate of change a ratio that describes how much one quantity|
| |changes with respect to the change in another quantity; also known as the slope of a line y-intercept the point at which the graph crosses|
| |the y-axis; written as (0, y) |
| | |
| |Lesson 2- |
| |argument the result of raising the base of a logarithm to the power of the logarithm, so that b is the argument of |
| |the logarithm loga b = c asymptote an equation that represents sets of points that are not allowed by the conditions in a parent function |
| |or model; a line that a function gets closer and closer to, but never crosses or touches change of base formula a formula that can be used|
| |to rewrite a logarithm so that it has a base of 10: for logb x, where b is not equal to 10, logb x is equal to logx/logb common logarithm |
| |a base-10 logarithm which is usually written without the number 10, such as log x = log10 x compound interest formula a formula used to |
| |calculate the balance on a loan or investment for which interest earned on the principal over time is added to the principal and also |
| |earns interest: A= P(1+(r/n))^nt, where A is the ending amount, P is the principal or initial amount, r is the annual interest rate |
| |expressed as a decimal, n is the number of times per year the interest is compounded, and t is the time in years inverse operation the |
| |operation that reverses the effect of another |
| |operation logarithm a quantity that represents the power to which a base b must be raised in order to equal a quantity x; written logb x |
| |logarithmic equation an equation involving logarithms. Given an exponential |
| |equation of the form x = by, the logarithmic equation is y = logb x, where y is the exponent, b is the base, and x is |
| |the argument. logarithmic function the inverse of an exponential function; for the exponential function g(x) = 5x, the inverse logarithmic|
| |function is x = log5 g(x) natural logarithm a logarithm whose base is the irrational number e; usually written in the form “ln,” which |
| |means “loge” |
| | |
| |Lesson 3- |
| |continuously compounded interest compound interest that is being added to the balance |
| |at every instant continuously compounded interest formula a formula used to calculate the balance on a loan or |
| |investment for which compound interest is being added to the balance at every instant: A = Pert, where |
| |A is the ending amount, P is the principal or initial amount, e is a constant, r is the annual interest rate |
| |expressed as a decimal, and t is the time in years e an irrational number with an approximate value of |
| |2.71828 half-life the time it takes for a substance that is decaying exponentially to decrease to 50% of its original amount |
| | |
| |Active Inspire, Elmo, Calculators, Clickers, Mechanical Pencils, Dry Erase Boards |
| | |
| |Hands On Meaningful Link to Objective Promotes Engagement |
| |-Provide handouts and guided notes for our students who have IEPs |
| | |
|Technology Integration |Modeling Guided Practice Independent Practice Comprehensible input |
| | |
|Differentiation |Reading Writing Speaking Listening |
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|Scaffolding |Circle Map, Bubble Map, Flow Map, Brace Map, Tree Map, Double Bubble Map, Multi-Flow Map, Bridge Map |
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|Groupings | |
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|Thinking Maps | |
|Co-Teaching |(Choose one and identify each teacher’s roles and responsibilities within the lesson.) |
| |6th period- Ms. Ely and I will practice… |
| |Team Teaching 2/4/15-2/20/15 |
|Summarizer |Thinking Maps Implementation & Writing To Win Journal Entries # |
|Assessment/ |Observing student work of classwork and daily assignments |
|Evaluation |Homework: Student Resource Unit 4 |
| |Problems from each lesson for homework on the second day of instruction |
| |Post Assessment- Unit 4 Lesson 1: 2/6/15 |
| |Post Assessment- Unit 4 Lesson 2: 2/12/15 |
| |Post Assessment- Unit 4 Lesson 3: 2/18/15 |
| |Unit 3 Post Assessment—2/20/15 |
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