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.

Transcription

1 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. Binary operations from a table finding the identity element and the inverse of an element using a table 2. Combining like terms and solving multi-step equations 3. The properties of real numbers (associative, commutative, and distributive) and subsets of real numbers (natural numbers, whole numbers, rational numbers, etc ) 4. Subsets of a set, complement of a set, and unions and intersections of sets 5. Factoring a GCF from a polynomial 2. Factoring a quadratic in the form x + bx+ c 2 7. Factoring a quadratic in the form ax + bx+ c where a 1. Factoring the difference of two squares 9. Factoring a quadratic completely. Writing the equation of a line given: a) two points b) the slope and a point 11. Writing the equation of a line that is parallel or perpendicular to another line and passes through a specific point 12. Solving systems of equations algebraically 13. Solving systems of equations using the substitution method 14. Solving systems of equations using the elimination method 15. Graphing the equation of a line using the slope intercept method 1. Graph a system of linear inequalities 17. Solving consecutive integer problems 1. Area and circumference of a circle 19. Venn diagram word problems 20. Solving literal equations 21. Solving distance problems objects traveling in osite directions 22. Solving distance problems objects traveling in the same direction 23. Solving distance problems objects that have a different travelling rate 24. Proportions solving percent problems using proportions 25. Solving ratio problems 2. Functions evaluating functions, testing to see whether or not a relation is a function and writing the rule of a function given a graph or a table of values 27. Multiply and dividing rational expressions 2. Finding the rate of change and slope and explaining the different types of slope 29. Solving compound inequalities 30. Negative and zero exponents 31. Dividing a polynomial by a monomial 32. Multiplying polynomials with polynomials (Including trinomials to trinomials) 33. Set builder notation and interval notation Vertex form of a parabola and shifting the graph y= x using vertex form The grading rubric is given on the next page. If you have any questions, feel free to me at lopez1@bxscience.edu The deadline for this project is Friday January 21, 2011 No exceptions will be made for late projects

2 Grading rubric for extra credit lesson plan Aims and Objectives At least two objectives are clearly stated and the aim is in the form of a question and it gives a clear and accurate description of the lesson and the aim corresponds with the objectives given Development Logical progression of the lesson by building on previous knowledge. Questions are also clearly stated in the lesson to show the next logical step. A good development should also make references to previous learned material and at least two model examples given. Practice Problems with solutions The first practice basic question that all students should be able to do while the very last practice At least two objectives are clearly stated and an aim is given but does not accurately describe the lesson Logical progression of the lesson but the new material is not connected to any previous material learned but at least two model examples are given. The first practice basic question that all students should be able to do while the very last practice Aim is given and accurately describes objectives but only objective is given but clearly stated. The lesson is given as a procedure rather than a developed concept but at least two model examples are given but no connection to previously learned material is made. The first practice basic question that all students should be able to do while the very last practice Only one objective is stated but not clearly and an aim is given The lesson is given as a procedure rather than a developed concept and only one model example is given but no connection to previously learned material is made. Practice problems are given but no solutions are provided and the problems are not progressive in difficultly level but answers are given. Only one objective given and no aim is given The lesson is developed but no references to previous material is given and only one model example is given with no explanation. One or two practice problems given and answers are given but not solutions. No aim or objective is given No lesson given. No problems given

3 challenge for the advanced students. Solutions are clearly shown and no step is omitted and each step is explained in words. Summary At least two questions asked for each objective asked and each question asked is a deep thinking question (in other words, no procedural questions asked) challenge for the advanced students. Solutions are given but not each step of the solution is shown or explained. One question asked for each objective asked and each question asked is a deep thinking question (in other words, no procedural questions asked) challenge for the advanced students. Only answers to questions are given. One question asked for each objective asked but there may be one or two procedural questions (such as How do you find/do/ ) Only one question asked for all objectives but the question is not a procedural question. One procedural question asked about an objective in the lesson. 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. No summary given.

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

5 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 x 4 3 Development: In a right triangle, we label the sides and vertices as follows: c a At C, we have a right angle (90 degrees) A b C What is c called? The hypotenuse From point A, what side is osite of A? a What about B, what side is osite of B? b Now, what about adjacent? Adjacent means next to. What is adjacent to A? b and c B 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: osite = a, adjacent = b For angle B: osite = b, adjacent = a, Since angle C is a right angle, we do not say anything is osite 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: a a b, b b c, c c a, c, a, b For some ratio s, we have special names: sine, cosine, and tangent Definition:

6 osite side of A sin A= hypotenuse adjacent side of A cos A= hypotenuse osite side of A tan A= adjacent side of A! 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: adjacent cos A= hypotenuse x cos55= 1 Example Solve for x

7 Practice: 4/1-4, 15-1 Solutions sin R = = hyp adj cos R = = hyp tan R = = adj sin S = = hyp adj cos S = = hyp tan S = = adj 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: cos S = sin R 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?