Coach Reichenbach's Blog

Lesson for Thursday, December 1

Math 3  Review of solving exponential and logarithmic equations.  Book page 161 problems 1-36  Quiz will be on Friday, and test will be next Thursday, December 8

We are continuing with logs and exponential functions.  We are looking at the properties of logs, inverse, product, quotient, power, and change of base.  Problems consist of expanding, condensing, solving exponential equations and log equations.

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

 Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Calculus: Students will correct Quiz that was taken on Wednesday over related rates, test on Friday.  Continue with related rate problems.  Students were given multiple problems on another worksheets. Also problems out of the book page 251 1-10 all, 13,14,19,21-25 all, 28-34 all  

Standards:

 M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 Essential Question

 How do you identify and solve related rate problems?

 Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

Lesson for Wednesday, November 30

Math 3  the students will be given two worksheets to solve logarithmic equations.   They will continue to use the 5 properties of logs to solve them.  Quiz on Monday, test next Thursday, Dec 8

 We are continuing with logs and exponential functions.  We are looking at the properties of logs, inverse, product, quotient, power, and change of base.  Problems consist of expanding, condensing, solving exponential equations and log equations.

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

 Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Calculus:  Quiz on Wednesday over related rates, test on Friday.  Continue with related rate problems.  Students were given multiple problems on another worksheets. Also problems out of the book page 251 1-10 all, 13,14,19,21-25 all, 28-34 all  Quiz on Wednesday over related rates, test on Friday.

Standards:

 M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 Essential Question

 How do you identify and solve related rate problems?

 Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

 

Lesson for Tuesday, November 29

Math 3  Worksheet 12.1 and problems out of the workbook on page 181 13-27 all,  Quiz on Monday, December 5 and Test on Thursday, December 8.  We are continuing with logs and exponential functions.  We are looking at the properties of logs, inverse, product, quotient, power, and change of base.  Problems consist of expanding, condensing, solving exponential equations and log equations.

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

 Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Calculus:  Continue with related rate problems.  Students were given multiple problems on another worksheets. Also problems out of the book page 251 1-10 all, 13,14,19,21-25 all, 28-34 all  Quiz on Wednesday over related rates, test on Friday.

Standards:

 M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 Essential Question

 How do you identify and solve related rate problems?

 Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

 

Lesson for Monday, November 28

Math 3  Continue with properties of logarithms  homework is from the book page 157 problems 1-26 and page 158 problems 1-21. 

Properties consist of the power rule, quotient rule, product rule, change of base and converting from exponential to log and log to exponential

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

 Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Element: MM3A3.c.

Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Calculus:  Continue with related rate problems.  Students were given multiple problems on two worksheets.

Standards:

 M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 Essential Question

 How do you identify and solve related rate problems?

 Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

 

 

Lesson for Friday, November 18

Happy Holidays and have a great Thanksgiving

Math 3   We will start with properties of logarithms and assignment is out of the workbook pages 172-176.

Calculus:  Continue with related rate problems. 

Lesson for Thursday, November 17

Math 3 Test over graphs of logarithms and exponential functions, their transformations, changing logs to exponential and exponential to logs.

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Calculus:  Continue with related rates.  Students were given another worksheet with related rate problems.  Retest on finding derivatives on thursday.

Related Rate Problemsi

 

Standards:

 

M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 

Essential Question

 

How do you identify and solve related rate problems?

 

Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 

Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

 

1.  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 

1. Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

Lesson for Thursday, November 16

Math 3  Review for test on Thursday.  NO additional assignment:

Standards for Math 3 Logarithmic functions and exponential functions

 MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Calculus:  Continue with related rates.  Students were given another worksheet with related rate problems.  Retest on finding derivatives on thursday.

Related Rate Problemsi

 

Standards:

 

M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 

Essential Question

 

How do you identify and solve related rate problems?

 

Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 

Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

 

1.  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 

1. Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

 

Lesson for Tuesday, November 15

Math 3,Continue with transformations of logarithmic graphs and exponential graphs.  Work is out of the book pages 153 and 154 all problems test on Thursday.   Also students will be given a worksheet with multiple choice questions.

Review for the test on Thursday.  topics include;  graphing and tranformations of exponential and logarithmic function, simplifying exponential expressions, solving word problems involving growth and decay.  Students will be given a review worksheet to complete.

Standards for Math 3 Logarithmic functions and exponential functions

MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Element: MM3A3.c.

Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Element: MM3A3.d.

Calculus:  Continue with worksheet on Related Rate problems.

Related Rate Problemsi

 Standards:

 M.CALC.1.9 Optimization Problems
The learner will be able to apply derivative; solve optimization and related rate of changes problems.

 Essential Question

 How do you identify and solve related rate problems?

 Steps to follow:

1     Understand the problem

1.  Identify the variables and rate of change you want and rate of change of what you know.
2.  .  Develop a mathematical model of the problem
   1.  Draw a picture
   2. Label all parts (known, unknown, constant and variables)
   3. Write an equation
      1.  This equation could be a formula or one you had to derive
3.  Differentiate both sides
4. Substitute values at this time
5. Interpret the solution

 Examples:

1.  You have a hot air balloon it is rising vertically and is being tracked by a range finder that is 500 feet from the point of liftoff.  When the range finder is at an angle of π/4 the angle is increasing at the rate of 0.14 radians per minute.  How fast  is the balloon rising at that moment?

 2.  A police cruiser, approaching a right angled intersection from the north is chasing a speeding car that has turned the corner and is now moving straight east.  When the cruiser is 0.6 miles north of the intersection and the car is 0.8 miles to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph.  If the cruise is moving at 60 mph at the instant of measurement, what is the speed of the other car?

 3. Water runs into a conical tank at the rate of 9 cubic feet  per minute.  The tank stands point down and has a height of 10 feet and a base radius of 5 feet.  How fast is the water level rising when the water is 6 feet deep?

 

 

 

 

Lesson for Monday, November 14

Math 3

Task logarithmic and exponential functions derived from a word problem.  Test will be on Thursday over all material covered so far on logs and exponential functions.

Calculus:  We will start using derivatives to solve real life problems.  The first type will be to solve related rate problems.  the students will be given a work sheet on Monday.  I will hand back the test that was given on Friday.

Lesson for Friday, November 11

Happy Veteran's Day

Math 3 Continue with logarithmic functions and writing exponential functions as log functions and log functions as exponential functions, graphing log functions, homework is to finish the problems assigned on Thursday out of the book page 147 problems 1-26 all and page 148 problems 1-24 all.   

Standards for Math 3 Logarithmic functions and exponential functions 

MM3A2

Students will explore logarithmic functions as inverses of exponential functions.

Element: MM3A2.a.

Define and understand the properties of n^th roots.

Element: MM3A2.b.

Extend properties of exponents to include rational exponents.

Element: MM3A2.c.

Define logarithmic functions as inverses of exponential functions.

Element: MM3A2.d.

Understand and use properties of logarithms by extending laws of exponents.

Element: MM3A2.e.

Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Element: MM3A2.f.

Graph functions as transformations of f(x) = a^x, f(x) = loga(x), f(x) = e^x, f(x) = ln x.

Element: MM3A2.g.

Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

 Element: MM3A3.b.

Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using appropriate technology.

Element: MM3A3.c.

Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Element: MM3A3.d.

Calculus:  Test on  Friday, November 11.  Topics include the derivative of the inverse of a function, inverse trig functions, exponential functions,log functions, using the chain rule, product rule, quotient rule, and power rule.  The student should also be able to write the tangent line at a point and use implicit differentiation to accomplish the above.

Standards for Week of November 8

Calculus:

M.CALC.1.6 Derivatives: Inverse Function
The learner will be able to differentiate the inverse of a function, including inverse trigonometric functions. 

M.CALC.1.7 Differentiation: Find/Apply
The learner will be able to determine the successive derivatives of a function and apply them to problems, such as speed, velocity and acceleration.

M.CALC.1.4 Differentiation: Use/Rules
The learner will be able to use the rules of differentiation (power rule, product rule, chain rule, and quotient rule) with algebraic and transcendental functions. 

M.CALC.1.3 Differentiation: Apply
The learner will be able to apply the derivative to determine the slope of a curve at a point, the equation of the tangent line to a curve at a point and the equation of the normal line to a curve at point.

M.CALC.1.5 Differentiation: Chain Rule
The learner will be able to apply the chain rule to composite functions, and implicitly defined functions.