ALGEBRA

 

 

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ALGEBRA II

 
 

 

DATE:________

MYP CRITERIA:

B

D

 

TOTAL:                                              %

 

 

Name:________________________________________

 

 

TEACHER:___________________________

Instructions

BLUE OR BLACK INK ONLY

1.     Make sure you read through the assessment.

2.     Read the instructions for each question carefully.

3.     Be sure to answer all required questions.

4.     CHECK your answers before handing in your paper.

5.     Calculators are not allowed.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GRASPS Use of GRASPS in the Unit
Goal

1.  Provide a statement of the task

2.  Establish a goal, problem, challenge, or obstacle in the task

You will design a parabolic bridge connecting the mainland of Abu Dhabi with Lulu island. You will need to find the quadratic pattern, model and simplify the data. You will design a final bridge model based on your calculations and findings including your quadratic functions and a concluding essay. You should consider the impact on the environment and the immediate community in relation to the scientific and technologically advanced materials that will be used in putting up the bridge.
Role

1.  Define the role of the student in the task

2.  State the job of the students in the task.

You are an engineer that has been employed to design a parabolic bridge by Abu Dhabi municipality.
Audience

1.  Identify the target audience within the context of the scenario

2.  Example audiences might include a client or committee

Board members of the municipality of Abu Dhabi.
Situation

1.  Set the context of the scenario

2.  Explain the situation

You need to design and make a model of a new bridge that will not deter from the natural environment as well as provide the community with potential solutions for transportation.
Product

1.  Clarify what the students will create and they will create it

Your final product will be a model of a parabolic bridge. An additional report including graphs and calculations to explain his/her findings.  This report must include their conclusion that would state their findings on the use and safety of the bridge as how it will benefit the community without having a negative impact on the surrounding environment.

 

 

Standards and Criteria

1.  Provide students with a clear picture of success

2.  Identify specific standards for success

3.  Issue rubrics to the students

CCSS.MATH.CONTENT.HSA.REI.B.4

Solve quadratic equations in one variable.

CCSS.MATH.CONTENT.HSA.REI.B.4.B

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit Topic:

 THINKING WITH MATHEMATICAL MODELS: LINEAR

AND INVERSE VARIATION

Performance Task Description:

  • You are a Civil Engineer and have been assigned to do a feasibility study of a proposedsuspension bridge (figure 2) to connect Al Lulu Island to the Abu Dhabi Mainland.
  • Use the following parameters and information to start your project.

 

The bridge will link Abu Dhabi Mainland to Al Lulu Island.

  • Describe the project and state the advantages.
  • Investigate the required materials you need to construct the bridge taking into consideration the environmental impact.
  • In figure 1, the distance between the two shores is 900 m.
  • The Abu Dhabi Municipality have chosen the design shown on figure 2
  • Use the quadratic formula to find:
    • Establish the correct quadratic equation that is congruent with the distance between the island and the mainland.

Given data: Under the bridge at 200m from the bridge’s edge the height is120m.

Use the following formula y=a(x-r)(x-s)  to find the quadratic equation in factored form, then turn it to standard form.

  • Determine the midpoint.
  • Determine the maximum height of the bridge and according to your judgement does this height make sense to you? Explain your reasoning.
  • What is the discriminant of the formula of your bridge?

Make a conclusion statement.

How to write a feasibility study

  1. Describe the project.
  2. Outline the potential solutions resulting from the project.
  3. List the criteria for evaluating these solutions.
  4. State which solution is most feasible for the project.
  5. Make a conclusion statement.

 

Figure 2 Proposed bridge

Achievement Level Descriptor Task Specific descriptor
0 The student does not reach a standard described by any of the descriptors below. You do not reach a standard described by any of the descriptors below.
1-2 CRITERION B;

The student is able to:

i.            apply, with teacher support, mathematical problem-solving techniques to discover simple patterns

ii.            state predictions consistent with patterns.

 

CRITERION D:

The student is able to:

i.            identify some of the elements of the authentic real-life situation

ii.            apply mathematical strategies to find a solution to the authentic real-life situation, with limited success.

Your work shows that you are

Ø  unable to apply the mathematical problem-solving technique in quadratic equations even with teacher support

Ø  using quadratic equation limitedly in predicting the pattern to be used to find the distance between the island and the mainland

Ø  unable to relate the given quadratic equation to identify the elements present in the island and mainland

Ø  unsuccessful in the use of the quadratic equation to find the solution in building the bridge

 

 

3-4 CRITERION B:

The student is able to:

i.            apply mathematical problem-solving techniques to discover simple patterns

ii.            suggest general rules consistent with findings.

 

CRITERION D:

The student is able to:

i.            identify the relevant elements of the authentic real-life situation

ii.            select, with some success, adequate mathematical strategies to model the authentic real-life situation

iii.            apply mathematical strategies to reach a solution to the authentic real-life situation

iv.            discuss whether the solution makes sense in the context of the authentic real-life situation.

Your work shows that you

Ø  applied quadratic equations to discover a simple pattern to solve the problem

Ø  suggested a general rule in solving similar problems involving quadratic equations

Ø  somehow able to identify the link between quadratic equations andthe elements present in the island and mainland.

Ø  are somewhat successful in selecting the height of the bridge using quadratic equation.

Ø  used a scale but the measurements were inaccurate

Ø  shortly discussed the layout of the bridge and how quadratic equation was used to determine its measurements

5-6 CRITERION B:

The student is able to:

i.            select and apply mathematical problem-solving techniques to discover complex patterns

ii.            describe patterns as general rules consistent with findings

iii.            verify the validity of these general rules.

 

CRITERION D

The student is able to:

i.            identify the relevant elements of the authentic real-life situation

ii.            select adequate mathematical strategies to model the authentic real-life situation

iii.            apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation

iv.            explain the degree of accuracy of the solution

v.            explain whether the solution makes sense in the context of the authentic real-life situation

 

Your work shows that you

Ø  selected and applied a reasonable position for the bridged discovering a complex pattern about bridge making and your justification was qualitative.

Ø  described patterns and used a correct scale and your drawing or design on paper is congruent with real measurements

Ø  verified the validity of the established quadratic equation that is related to the distance between the island and the mainland

Ø  identified the maximum height of the bridge using the quadratic equation and you have explained if the height of the bridge is practical or not practical explicitly

Ø  selected and determined the midpoint where the height is maximum.

Ø  applied the discriminant of the formula of your bridge and reached a solution

Ø  arranged your information and was able to explain the degree of accuracy of your solution

Ø  explained the solution with sense in the context of the model in relation to the location of the actual bridge

 

 

 

7-8 CRITERION B

The student is able to:

i.            select and apply mathematical problem-solving techniques to discover complex patterns

ii.            describe patterns as general rules consistent with correct findings

iii.            prove, or verify and justify, these general rules.

 

CRITERION D

The student is able to:

i.            identify the relevant elements of the authentic real-life situation

ii.            select appropriate mathematical strategies to model the authentic real-life situation

iii.            apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation

iv.            justify the degree of accuracy of the solution

v.            justify whether the solution makes sense in the context of the authentic real-life situation.

You have:

Ø  selected and applied an accurate position for the bridged after discovering a complex pattern about bridge making, and write your justification.

Ø  described patterns and used a correct scale and your drawing or design on paper is congruent with real and accurate measurements

Ø  proven, verified and justified the validity of the established quadratic equation related to the distance between the island and the mainland

Ø  correctly identified the maximum height of the bridge using the quadratic equation and you have explained if the height of the bridge is practical or not practical explicitly

Ø  correctly selected and determined the midpoint where the maximum height will be situated using the quadratic equation

Ø  precisely applied the discriminant of the formula of your bridge and reached a correct solution

Ø  arranged your information and was able to justify the degree of accuracy of your solution

Ø  justified the solution using quadratic equation that makes sense in the context of the model in relation to the location of the actual bridge

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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