administration & marking guide · mathematics 504 cst mid-year examination january 2011...
TRANSCRIPT
Mathematics 504 CST
Mid-Year Examination
January 2011
Administration & Marking Guide
563-504
Administration Guide
Design Team: EMSB
Introduction
This examination is consistent with the principles regarding the evaluation of learning outlined by the Ministère de l'Éducation, du Loisir et du Sport. The tasks in this examination focus concepts and processes covered in the third year of the Secondary Cycle Two Mathematics program: Cultural, Scientific and Technical option (CST5). This guide provides information about the administering the evaluation situations as well as information with respect to scoring the work on the tasks that make up this evaluation situation.
1. Presentation of the examination
1.1 Description of the materials
The following documents are provided as part of this evaluation situation:
One (1) Administration and Marking Guide which contains a description of the administration conditions as well as the marking key for the student tasks.
One (1) Student Booklet for the situations focusing on Competencies 2 (Uses Mathematical Reasoning).
1.2 Description of the evaluation situations and connections to the Québec Education
Program (QEP) Number of items 16, distributed as follows
• 6 multiple choice • 4 short-constructed answers • 6 extended application answers
Description of the 6 extended answers focusing on competency 2
For each situation, the table below gives a brief description of the task to be carried out, the competency it targets and the concepts and processes involved in the marking guide.
Title of the situation Concepts and processes
Question 11
A colourful display!
Solving a system of inequalities: algebraically or graphically
Question 12
An investment in stocks
Optimizing a situation, taking into account different constraints
Choosing one or more optimal solutions
Analyzing and interpreting the solution(s), depending on the context
Question 13
The Municipal Campground
Optimizing a situation, taking into account different constraints
Solving a system of inequalities: algebraically or graphically
Choosing one or more optimal solutions
Analyzing and interpreting the solution(s), depending on the context
Question 14
A visit to the museum
Representting a graph
Euler circuit
Question 15
Snow removal
Network of minimum value
Question 16
Multitasking at the airport
Critical path
2. Timetable for administering the examination and time allotted for the
evaluation situations This evaluation situation should be administered in one 3 hour time block on or after January 14th 2011.
3. Possible adjustments
Students are to do the tasks in this evaluation situation individually. No teacher assistance is permitted in Cycle Two. Teachers should consult the professionals who support the students with an Individualized Educational Plan (IEP) on a case to case basis in order to determine the appropriate adjustments for each student.
4. Procedure for administering the evaluation situation
4.1 Initial preparation
Ask the students to draw up a memory aid. Students may use a memory aid that they have prepared for another evaluation situation if it is the original hand-written copy.
Review the evaluation criteria with the students and explain the indicators for each criterion. For this purpose, you may copy the evaluation grids (Appendix A) onto transparencies.
Remind them that any required calculations or explanations will be taken into account in grading their work.
4.2 General procedure
Materials for each student • Student Booklet • Calculator (with or without a graphic display) • Geometry set (ruler, compass, protractor, etc.) • Memory aid
5. Administering the evaluation situation:
On the day of the evaluation situation, ask students to go through their booklet to become familiar with its content. Also, make sure they know where in their booklet they must write their answers, calculations, or explanations.
Ask them to read page the instructions and the evaluation criteria that will be used to evaluate their level of competency development in the different task. Located at the bottom of the pages in the student booklet are evaluation grids which indicate the criteria to be applied in each situation. In the marking guide, you will find more information about the specific requirements of the tasks as well as interpretation tools to determine the student's performance level (1, 2, 3, 4, and 5) for each evaluation criterion involved.
Describe the basic rules: − Students may use a calculator, but must clearly indicate the sequence of
operations involved without, however, rewriting all the detailed calculations performed with the calculator.
– Student may use resources such as a dictionary or a memory aid that they will
have prepared on their own. The memory aid consists of one letter-sized sheet of paper (8½ x 11). Both sides of the sheet may be used. Any mechanical reproduction of this memory aid is forbidden.
– The booklet should be completed within the time frame indicated on the cover
page of the document. When time is up, collect the examination booklets.
6. Marking Key
PART A: Multiple-Choice Questions Questions 1 to 6 4 marks or 0 marks
D C
A A
C B
PART B: Short-Constructed Answer Questions
Questions 7 to 10 4 marks each
The coordinates of vertex P of this polygon of constraints are (16, 16).
The company must sell 300 chairs and 70 tables to maximize its revenue.
The minimum amount of time that Sandy needs to drive the guests to their hotel and return to the airport is 60 minutes.
Graph representing this situation
1 4
2 5
3 6
7
8
9
10
PART C: Extended Application Questions Questions 11 to 16 10 marks each (marked on 100% each according to rubric)
A COLOURFUL DISPLAY! EXAMPLE OF APPROPRIATE REASONING
GRAPHING SYSTEM OF INEQUALITIES AND POINTS
2x – 3y 6 3x +2y 12
x 0 3
y -2 0
Try point (0, 0):
60
600
6y3x2
FALSE!
Shade the sector that does not contain the
point (0, 0).
x 0 4
y 6 0
Try point (0, 0):
120
1200
12y2x3
FALSE!
Shade the sector that does not contain the
point (0, 0).
CONCLUSION
Only, Anna is right because the point indicated by her is situated in the region where the two semi-planes are super-imposed; all of the fireworks will be visible in this region.
11
AN INVESTMENT IN STOCKS
EXAMPLE OF APPROPRIATE REASONING
MINIMUM AMOUNT OF MONEY INVESTED TO BUY SHARES ON MONDAY
VERTEX AMOUNT OF MONEY: 40x + 8y
A(20,20) $960
B(10,60) $ 880 Minimum
C(80,80) $3 840
D(70,30) $3 040
NUMBER OF SHARES BOUGHT ON TUESDAY
Number of software company shares bought: 3 10 = 30
Number of mining company shares bought: 60 – 20 = 40
AMOUNT OF MONEY INVESTED TO BUY SHARES ON TUESDAY
$50 30 + $7 40 = $1780
AMOUNT OF MONEY INVESTED TO BUY SHARES ON MONDAY AND TUESDAY
$880 + $1780 = $2660
CONCLUSION
Joanne invested $2660 to buy shared for this client on Monday and Tuesday.
12
THE MUNICIPAL CAMPGROUND EXAMPLE OF APPROPRIATE REASONING
MAXIMUM POSSIBLE DAILY REVENUE FOR THE SUMMER OF 2009
VERTEX REVENUE: 25x + 35y
P(30,0) $750
Q(30,40) $2 150
R(50,50) $3 000 Maximum
S(100,0) $2 500
MODIFIED POLYGON OF CONSTRAINTS
Inequality representing the additional constraint: y ≤ 40
The coordinates of the new vertex are: (60, 40)
MAXIMUM POSSIBLE REVENUE FOR THE SUMMER OF 2010
VERTEX REVENUE: 25x + 35y
P(30,0) $750
Q(30,10) $2 150
(60,40) $2 900 Maximum
S(100,0) $2 500
DECREASE IN THE MAXIMUM POSSIBLE REVENUE
$3000 - $2900 = $100
CONCLUSION
The owner’s maximum possible daily revenue will decrease by $100 after agreeing to the residents’ demands.
13
A VISIT TO THE MUSEUM EXAMPLE OF APPROPRIATE REASONING
NEW CORRIDOR TO BE BUILT
In this graph, students must add an edge to obtain a circuit that travels over each edge only
once. This circuit exists if the degrees of all the vertices are even numbers.
VERTEX DEGREE
A 2
B 4
C 3 odd-numbered
D 2
E 3 odd-numbered
Students must an edge connecting vertices C and E to make the degree of each vertex an
even number. Therefore, the new corridor will be built between rooms C and E.
NEW GRAPH
MINIMIUM DISTANCE SOPHIE MUST TRAVEK DURING HER NEXT VISIT TO THE MUSEUM
CIRCUIT VALUE
A,B,C,E,A 69 Minimum
A,E,C,D,E,A 99
A,E,C E,A 76
A,B,C,E,A 71
CONCLUSION
During her visit to the museum, Sophie must travel a minimum distance of 69 m.
14
SNOW REMOVAL
EXAMPLE OF APPROPRIATE REASONING
TOTAL SNOW REMOVAL COSTS LAST YEAR Total length of roads needing snow removal: 12 + 10 + 12 + 15 + 5 + 11 + 8 + 8 = 81 km Total snow removal costs: 81 km $1000/km = $81 000
TOTAL LENGTHS OF ROADS NEEDING SNOW REMOVAL THIS YEAR We are looking for a tree of maximum value consisting of 5 edges connecting the 6 vertices of the graph representing the average number of users.
TOTAL SNOW REMOVAL COSTS THIS YEAR
Total length of roads needing snow removal: 11 + 15 + 8 + 5 + 12 = 51 km
Total snow removal costs: 51 km $1300/km = $66 300
DECREASE IN TOTAL SNOW REMOVAL COSTS $81 000 - $66 300 = $14 700 CONCLUSION
Compared with last year, total snow removal costs will decrease by $14 700 this year.
15
MULTITASKING AT THE AIRPORT
EXAMPLE OF APPROPRIATE REASONING
MINIMUM AMOUNT OF TIME NEEDED TO GET THE PLANE READY ON A NORMAL DAY
Luggage Inside plane Fuel
A. Unload luggage (15) B. Deplane passengers (10) D. Fill the fuel tank (20)
E. Load luggage (20) C. Clean the plane (15)
F. Board passengers (15)
G. Warm up the engine (5)
PATH VALUE
A,E,G 40
B, C, F, G 45 Minimum time (critical path)
D, G 25
MINIMUM AMOUNT OF TIME NEEDED TO GET THE PLANE READY TODAY
Luggage Inside plane Fuel
C. Unload luggage (15) D. Deplane passengers (10) E. Fill the fuel tank (20)
E. Load luggage (35) C. Clean the plane (15)
F. Board passengers (15)
G. Warm up the engine (5)
PATH VALUE
A,E,G 55 Minimum time (critical path)
B, C, F, G 45
D, G 25
INCREASE IN AMOUNT OF TIME TO GET PLANE READY
55 minutes – 45 minutes = 10 minutes CONCLUSION The crew took 10 minutes more to get the plane ready.
16
Appendix
Evalu
ati
on
Cri
teri
a
Descriptive Chart for Evaluating Competency Appendix A Uses Mathematical Reasoning
Observable Indicators of Student Behaviour
Level 5 Level 4 Level 3 Level 2 Level 1
Cr3
Proper application
of mathematical
reasoning suited to
the situation
Takes every aspect of the situation into account.
Uses efficient strategies in applying his/her mathematical reasoning.
Uses mathematical concepts and processes that enable him/her to meet the requirements of the situation efficiently.
Takes the main aspects of the situation into account.
Uses effective strategies in applying his/her mathematical reasoning.
Uses mathematical concepts and processes appropriate for the situation.
Takes some aspects of the situation into account.
Uses a few effective strategies for certain steps in applying his/her mathematical reasoning.
Uses some mathematical concepts and processes appropriate for the situation.
Takes few aspects of the situation into account.
Uses few appropriate strategies in applying his/her mathematical reasoning.
Uses very few mathematical concepts and processes appropriate for the situation.
Takes no aspect of the situation into account.
Uses inappropriate strategies in applying his/her mathematical reasoning.
Uses mathematical concepts and processes that are inappropriate for the situation.
Cr2
Correct use of
concepts and
processes
appropriate to the
situation
Applies the chosen mathematical concepts and processes appropriately.
Applies the chosen mathematical concepts and processes appropriately, but makes minor errors (e.g. miscalculations, inaccuracies, omissions).
Applies the chosen mathematical concepts and processes, but makes some conceptual or procedural errors.
Applies the chosen mathematical concepts and processes, but makes several conceptual or procedural errors.
Applies mathematical concepts and processes inappropriately, making many conceptual or procedural errors.
Cr4
Proper organization
of the steps in an
appropriate
procedure
Presents a complete and organized procedure that explicitly outlines what was done or how it was done.
Presents a complete and organized procedure that explicitly outlines what was done or how it was done, even though some of the steps are implicit.
Presents a procedure that is not very explicit about what was done or how it was done, because the work is unclear or not very organized.
Presents a procedure consisting of isolated elements, showing little or no work that explicitly outlines what was done or how it was done.
Presents a procedure that is completely unrelated to the situation or does not show any procedure.
Cr5
Correct justification
of the steps in an
appropriate
procedure
When required to justify or support his/her statements, conclusions or results, uses solid mathematical arguments.
Rigorously observes the rules and conventions of mathematical language.
When required to justify or support his/her statements, conclusions or results, uses appropriate mathematical arguments.
Observes the rules and conventions of mathematical language, despite some minor errors or omissions.
When required to justify or support his/her statements, conclusions or results, uses some appropriate mathematical arguments or uses rudimentary mathematical arguments.
Makes some errors or is sometimes inaccurate in using the rules and conventions of mathematical language.
When required to justify or support his/her statements, conclusions or results, uses only slightly appropriate mathematical arguments.
Makes several errors related to the rules and conventions of mathematical language.
When required to justify or support his/her statements, conclusions or results, uses erroneous or inappropriate mathematical arguments
Shows little or no concern for the rules and conventions of mathematical language.
Cr1
Formulation of a
conjecture
appropriate to the
situation
Formulates an astute conjecture based on a rigorous analysis of the situation or on examples that consider every aspect of a situation.
Formulates an appropriate conjecture based on a fitting analysis of the situation or on examples that consider most of the important aspects of the situation.
Formulates a partially appropriate conjecture based on an analysis of the situation or on examples that consider some aspects of the situation.
Formulates a conjecture that is not very appropriate, based on an analysis that considers few aspects of the situation, or on examples chosen purely by chance.
Formulates a conjecture that is unrelated to the situation.