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Extra Credit Assignment

Lesson plan

The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.

The extra credit assignment is to create a typed up lesson plan (you may do your lesson as a PowerPoint presentation as well but you still need to type up some rational – see the rubric for more information on this) . You may work with up to 1 other person on this. The topics you can choose from are:

1. Solving first compound inequalities

2. Solving absolute value equations

3. Solving absolute value inequalities

4. Solving literal equations

5. Rules for fractional exponents and negative exponents

6. Factoring [pic]

7. Factoring the sum/difference of two cubes, and the difference of two perfect squares

8. Completing the square

9. Solving and graphing quadratic inequalities

10. Simplifying complex fractions

11. Adding and subtracting rational expressions with unlike denominators

12. Multiplying and dividing rational expressions with unlike denominators

13. Solving “work” problems

14. Composition of functions

15. Finding the inverse of a function algebraically and graphically

16. Projectile motion problems – finding the maximum/minimum point of a quadratic function

17. Finding the roots of quadratic functions and higher degree functions using the graphing calculator

18. Simplifying radical expressions – including imaginary numbers and adding/subtracting radical expressions

19. Multiplying radical expressions – including radicals with imaginary numbers

20. Rationalizing radical expressions

21. Finding the magnitude of a complex number , graphing complex numbers, and simplifying powers of i

22. Describing the nature of the roots of a quadratic equation

23. Finding the sum and product of a quadratic equation and using the sum and product to find a missing term of a quadratic (given one root) and writing the equation of a quadratic equation given at least one root

24. Solving exponential equations

25. Graphing exponential equations

26. Converting between logarithmic form and exponential form

27. Using the laws of logarithms to expand a single logarithm

28. Using the laws of logarithms to express the sum or difference of multiple logarithms as one single logarithm

29. Using the laws of logarithm to solve logarithmic equations

30. Using the laws of logarithms to solve exponential equations

31. Permutations and combinations

32. Solving systems of equations algebraically

33. Solving systems of equations graphically

34. Writing the equation of a line given: a) two points b) a point and the slope of the line

The grading rubric is given on the next page.

Feel free to e-mail me at lopez1@bxscience.edu if you have any questions. The deadline for this project is Friday January 21, 2011 No exceptions will be made for late projects

Grading rubric for extra credit lesson plan

| |5 |4 |3 |2 |1 |0 |

|Aims and Objectives |At least two objectives are clearly |At least two objectives are clearly |Aim is given and accurately describes |Only one objective is stated but not |Only one objective given and no aim is |No aim or objective is given |

| |stated and the aim is in the form of a |stated and an aim is given but does not|objectives but only objective is given |clearly and an aim is given |given | |

| |question and it gives a clear and |accurately describe the lesson |but clearly stated. | | | |

| |accurate description of the lesson and | | | | | |

| |the aim corresponds with the objectives| | | | | |

| |given | | | | | |

|Development |Logical progression of the lesson by |Logical progression of the lesson but |The lesson is given as a procedure |The lesson is given as a procedure |The lesson is developed but no |No lesson given. |

| |building on previous knowledge. |the new material is not connected to |rather than a developed concept but at |rather than a developed concept and |references to previous material is | |

| |Questions are also clearly stated in |any previous material learned but at |least two model examples are given but |only one model example is given but no |given and only one model example is | |

| |the lesson to show the next logical |least two model examples are given. |no connection to previously learned |connection to previously learned |given with no explanation. | |

| |step. A good development should also | |material is made. |material is made. | | |

| |make references to previous learned | | | | | |

| |material and at least two model | | | | | |

| |examples given. | | | | | |

|Practice Problems with solutions |The first practice problem should be a |The first practice problem should be a |The first practice problem should be a |Practice problems are given but no |One or two practice problems given and |No problems given |

| |basic question that all students should|basic question that all students should|basic question that all students should|solutions are provided and the problems|answers are given but not solutions. | |

| |be able to do while the very last |be able to do while the very last |be able to do while the very last |are not progressive in difficultly | | |

| |practice problem should be a challenge |practice problem should be a challenge |practice problem should be a challenge |level but answers are given. | | |

| |for the advanced students. Solutions |for the advanced students. Solutions |for the advanced students. Only | | | |

| |are clearly shown and no step is |are given but not each step of the |answers to questions are given. | | | |

| |omitted and each step is explained in |solution is shown or explained. | | | | |

| |words. | | | | | |

|Summary |At least two questions asked for each |One question asked for each objective |One question asked for each objective |Only one question asked for all |One procedural question asked about an |No summary given. |

| |objective asked and each question asked|asked and each question asked is a |asked but there may be one or two |objectives but the question is not a |objective in the lesson. | |

| |is a “deep thinking” question (in other|“deep thinking” question (in other |procedural questions (such as “How do |procedural question. | | |

| |words, no procedural questions asked) |words, no procedural questions asked) |you find/do/…) | | | |

Average score:

The most points you can receive is 5. I will take the average score of all 4 categories and add that to a previous exam score.

An example of a good lesson plan (this would receive a score of 5 in all areas) is given on the next page:

Prior Knowledge:

• Combining like terms

• Pythagorean Theorem

Objectives: After the lesson, students will be able to:

• Find the sine, cosine, and tangent ratio’s of an angle in a right triangle

• Use sine, cosine, and tangent to find the missing side when an angle and a side is given

Aim: How can we find the sine, cosine, and tangent ratios of a right triangle and apply them to find missing sides?

Do Now: Solve for x

Development:

In a right triangle, we label the sides and vertices as follows:

At C, we have a right angle (90 degrees)

What is c called? The hypotenuse

From point A, what side is opposite of A? a

What about B, what side is opposite of B? b

Now, what about adjacent? Adjacent means next to.

What is adjacent to A? b and c

Now, while side c is next to a, in math we never say that the hypotenuse is adjacent to a leg, so only side b is adjacent to A.

We can say then for angle A: opposite = a, adjacent = b

For angle B: opposite = b, adjacent = a,

Since angle C is a right angle, we do not say anything is opposite or adjacent to it.

Now, how what ratio’s can we make using the three sides of the triangle? (a, b, and c)

We have: [pic]

For some ratio’s, we have special names: sine, cosine, and tangent

Definition:

[pic] !

mnemonic: SOH-CAH-TOA This holds for B and C also

Example: Find sinA, cosA, and tanA

We always measure trigonometric ratio’s with angles.

We can use the calculator to find certain trig ratio’s

Example – Find sin(50)

With these two tools, we can now tackle some problems

Example

Solve for x:

What do we know from the diagram? Angle, one side

What side do we know? Hypotenuse

Where is our given angle? At A

With reference to A, how is x related to A?

x is adjacent to A

So we know angle A and the hypotenuse of the triangle and we want to find the side that is adjacent to A.

What relationship do we know between hypotenuse and an adjacent side? Cosine

So we have: [pic]

Example – Solve for x

Practice: 646/1-4, 15-18

[pic]

Solutions

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

Follow up question: do you notice a relationship between the trigonometric ratio’s of S and R? some of them are equal to each other. For example: [pic]

Summary:

-How is this similar to Pythagorean theorem? T

- When looking for a missing side, when would we use trig ratio’s?

- What does the mnemonic SOH-CAH-TOA mean?

-----------------------

x

3

4

B

c

b

C

a

A

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