5.+Assessments

Unit Plan Assessments

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 * Informal** - For my informal assessment for my students, I have decided to do a class discussion involving the use of parabolas and ellipses when constructing a bridge. Using this activity, I hope that give my students a better understanding of how to use these shapes in the real world. The students have already learned about parabolas and ellipses, they should know how to identify their equation and how to graph them. The students are to break-up into two teams. One group will be using a parabola formula, while the other is using an ellipse formula. As the students are working, I will be walking around the room, asking questions to different team members to make sure they are on task. After approximately half of the period, I will have them come back to their seats to discuss their findings. Will the parabola equation or the semiellipse equation work better? I will ask one person from each team to be the spokesperson. This person will be chosen at random, making sure everyone in the group is participating. As a class, we will vote on the best option for constructing this bridge. Here is what their handout will look like:======

Bridge Activity

- The local township has decided that a new bridge needs to be constructed over the Lehigh River in Bethlehem. This bridge will be used by cars and local trucks to help alleviate traffic. Your job is to construct a support for the bridge. The support needs to be at least 1500 feet and the center of the arch needs to be 500 feet. - Most of the trucks that will be using this bridge need approximately a 280 feet clearance to pass beneath the bridge. You must calculate the width of the channel to figure out if the trucker can fit under the bridge. - Come up with an equation of either the parabola or the semiellipse that is being used here. - How wide will the channel be? - What happens if the Lehigh floods, and waters rise ten feet? Will this affect your plan? - Provide a sketch of the parabola or semiellipse that is used for the bridge.

Parabola Quiz
 * Quiz** - After going through the parabola lesson plan, I will give a quiz on the concepts. Parabolas are the first shapes that I will be teaching in this unit, so I want to make sure the students understand what I have covered. This will be a short quiz, 5 questions. It should only take the students approximately 10 minutes to complete. It will be graded out of 5 points. Here is what the quiz will look like.

Section 1: Identify the y-intercept.

1. y = 3x^2 - 8x + 4

Section 2: Find the vertex in the quadratic function.

2. y = x^2 + 8x - 15

Section 3: Indicate whether the parabola is opening up or down.

3. y = -12x^2 + 3x + 6

Section 4: Draw the parabola on separate graph paper.

4. y = x^2 + 14x + 48

5. Label the vertex on question 7.


 * Test** - At the end of the unit, I will give the class a final test. I want to make sure they are able to identify the different shapes by their equations. I also hope they can identify some of these shapes in the real world. Here is what my test will look like:

Section 1: Identify each equation as a line, parabola, circle, ellipse, or hyperbola.

1. x^2 = 4 - 4y^2 2. x = (y - 5)^2 3. y = 2x - 4 4. 16x^2 - 25y^2 = 400 5. y = -3x - 8x + 4 6. 10x^2 = 40 - 10y^2

Section 2: Complete the following questions.

7. Find the vertex, the axis of symmetry, and direction of opening for a parabola with the following equation: y = 4x^2 - 8x =12.

8. Find the center and the radius of a circle whose equation is 3x^2+3y^2+12x - 6y - 33 = 0

9. The moon orbits the Earth in an elliptical path with the Earth at one focus. The major axis of the orbit is 774,000km and the minor axis is 773,000km. Using (0,0) as the center of the ellipse, write an equation for the orbit of the Moon.

10. Write an equation for a hyperbola with these characteristics: Vertices at (0, -1) and (6, -1); foci at (-1, -1) and (7, -1)

Section 3: Identify which shape you could use in each of the following real life situtations. 11. Find the position of a sunken ship. 12. An equation of a satellite dish. 13. The distance of a radio signal. 14. The orbit of Mars around the Sun. 15. The path of fireworks.

Section 4: Graph the following equations.

16. x = -2(y + 2)^2 + 3

17. -xy = -10

18. x^2 + y^2 + 6y - 7 = 0

19. 4x^2 + 9y^2 = 36

20. x^2 + (y-5)^2 = 9