Geometric Representation

Transcription

1 Geometric Representation MTH Scored Activity 1 Student Identification Name: Address: Telephone: Date submitted: Part 1 Explicit Evaluation of Subject-Specific Knowledge: /10 Total Part 2 Evaluation of Competencies: /40 /50 Date corrected: Evaluator s signature:

2 MTH GEOMETRIC REPRESENTATION This scored activity was produced by the Société de formation à distance des commissions scolaires du Québec (SOFAD). Production team (French version) Project Coordinators: Authors: Content Revisors: Linguistic Revisors: Docimological Revisor: Illustrations: Graphic Design: Proofreading: Isabelle Tanguay (SOFAD) Nancy Mayrand (SOFAD) Robert Longpré (SOFAD) Marie-Pierre Beaudoin Jean-Claude Hamel Gilles Gascon Isabelle Hachez Steeve Lemay Alain Bombardier Jonathan Lafond Michelle Côté Marie-Pierre Gazaille Julie Gravel Serge Mercier Serge Mercier Johanne St-Martin First Printing: May 2013 Production team (English version) Project Coordinator: Translator: Typesetting: Proofreading: Nancy Mayrand Claudia de Fulviis Daniel Rémy Johanne St-Martin Sources Page 3 Barry Barnes / Shutterstock This work was funded by Quebec s Ministère de l Éducation et de l Enseignement supérieur through contributions from the Canada-Quebec Agreement for Minority-Language Education and Second- Language Instruction. Sofad gratefully acknowledges this assistance. SOFAD All rights for translation and adaptation, in whole or in part, reserved for all countries. Any reproduction by mechanical or electronic means, including microreproduction, is forbidden without the written permission of a duly authorized SOFAD representative. Despite the preceding statement, SOFAD authorizes all adult education centres that use the corresponding learning guide to reproduce this scored activity. August SOFAD

3 SCORED ACTIVITY 1 Introduction Scored Activity 1 covers Learning Situation 1 in the Geometric Representation guide. It is divided into two parts. Part 1 Explicit Evaluation of Subject-Specific Knowledge This section contains a series of unrelated questions. Each question targets one or more specific concepts. Part 2 Evaluation of Competencies You will be presented with situations similar to the ones you encountered in each of the learning situations. You will be asked to complete a series of tasks involving the concepts you have learned, but in a new context. Most education centres require you to have an average of 60% or more on the socred activities in order to take the final examination. Instructions Complete the Student Identification section. Carefully read each question before answering. The use of a calculator is permitted. Write your answers in the space provided. Show all the steps of your work and calculations. Locate the weighting for each question. Once you have completed this scored activity, promptly submit it to your instructor or tutor. As a precaution, we recommend that you retain a copy for your own records. SOFAD 3

4 MTH GEOMETRIC REPRESENTATION Memory Aid Conversion of measurements Imperial system The basic unit of length in this system is the yard (yd), which is subdivided into feet (ft) and inches (in). Some equivalences between commonly used imperial units of measurement are given below. Length Area Volume 1 yd = 3 ft 1 ft = 12 in 1 yd 2 = 9 ft 2 1 ft 2 = 144 in 2 1 yd 3 = 27 ft 3 1 ft 3 = 1728 in 3 Converting measurements from one system to the other Some equivalences between imperial units and international units of measurement are given below. Length Area Volume 1 yd 0.91 m 1 ft 3 dm 1 in 2.5 cm 1 yd m 2 1 ft dm 2 1 in cm 2 1 yd m 3 1 ft dm 3 1 in cm 3 4 SOFAD

5 SCORED ACTIVITY 1 Part 1: Explicit Evaluation of Subject-Specific Knowledge 1 A square mosaic with sides measuring 60 cm each, consists of two types of ceramic tiles: rectangles and squares. Let x be the width of the rectangular tiles in centimetres. a) Determine the area of a rectangular tile and the area of a square tile. 60 cm 60 cm Answer: b) Assuming that x = 2, determine whether the two results you obtained in a) are correct. Answer: SOFAD 3 points 5

6 MTH GEOMETRIC REPRESENTATION 2 In most countries, the term football refers to the sport that we call soccer. American football is a completely different sport. Below are diagrams of the regulation size fields for these two sports. Note that the diagrams are not necessarily to scale. American football field Soccer field 105 m 120 yd m 160 ft What is the percentage ratio of the areas of the two fields? 2 points Answer: 3 A truck transports chips in bulk which will then be packaged in small boxes in the shape of rectangular prisms. The truck is 30x m long, y m deep and 10x m high. The chip boxes are x dm long, 2 dm deep and 6 dm high. How many boxes of chips can be prepared if the truck and the boxes are filled to capacity? 2 points Answer: 6 SOFAD

7 SCORED ACTIVITY 1 4 The two letters shown below are 3 cm high and 2 cm wide. All the strokes are of the same width x, expressed in centimetres. The horizontal stroke in the centre of the letter E is of the same length as the horizontal stroke in the letter H. Determine the reduced algebraic expressions that represent the area of each letter and find the common factors. 2 cm 3 cm x Answer: 3 points Total for Part 1 /10 SOFAD 7

8 MTH GEOMETRIC REPRESENTATION Part 2: Evaluation of Competencies This second part evaluates the development of your competencies in mathematics. It contains one evaluation situation divided into two tasks. The following criteria (cr.) will be used to evaluate the competencies targeted in this course: Competency 1: Uses strategies to solve situational problems Cr. 1.1 Indication (oral or written) that the situational problem has been understood Cr. 1.2 Application of strategies and appropriate mathematical knowledge Cr. 1.3 Development of an appropriate solution Cr. 1.4 Appropriate validation of the steps in the solution Competency 2: Uses mathematical reasoning Cr. 2.1 Formulation of a conjecture suited to the situation Cr. 2.2 Correct use of appropriate mathematical concepts and processes Cr. 2.3 Proper implementation of mathematical reasoning suited to the situation Cr. 2.4 Proper organization of the steps in an appropriate procedure Cr. 2.5 Correct justification of the steps in an appropriate procedure Competency 3: Communicates by using mathematical language Cr. 3.1 Correct interpretation of a mathematical message Cr. 3.2 Production of a message in keeping with the terminology, rules and conventions of mathematics, and suited to the context 8 SOFAD

9 SCORED ACTIVITY 1 Evaluation Situation Renovating the Agora The Agora is a business centre and a place where people come together to eat, socialize, work and relax. At present, it is divided into two sections: the Lobby and the Hall. In order to comply with the new fire prevention standards, management has decided to expand the Agora and add a new section, which will be called the Annex. At the same time as this work is being done, the Agora will be repainted, and the flooring, furniture, door and windows will be replaced. As it now stands, the Agora consists of two sections in the shape of rectangular prisms, the taller of which has a glass ceiling. The Annex will be in the shape of a cube and will be as wide as the Lobby. Figure A.1 Lobby Annex Hall (x 10) m 1.5 m (x 4 m) (2x + 3) m You are on the committee tasked with calculating the indoor surface area to be painted in all three sections of the Agora. With the help of a firefighter, you must also determine the maximum number of people that can be accommodated in the new Agora to ensure compliance with the fire prevention standards once the Annex has been built. The committee wants to paint the walls two different colours and the ceilings white. The large back wall will be painted yellow and all the other walls will be painted grey. The windows on the two identical sides of the Hall will be preserved and no windows will be added to the Lobby, since it has a glass ceiling. To help you with your work, the architect in charge of building the Annex has given you a list of measurements to be taken into account. There will be no walls between the three sections. The Annex will be x metres wide. The height of the Lobby will be twice that of the Annex. The Hall is three times the length of the Annex from which one metre will be subtracted. The Annex, the Lobby and the Hall will be of the same depth. The Annex and the Hall will be of the same height. The dimensions of the door of the Lobby are (x 3) m by (x 1) m. There will be a window on each outer wall of the Annex. These three windows will be identical. SOFAD 9

10 MTH GEOMETRIC REPRESENTATION Task 1 Your committee will calculate the surface areas to be painted in each section of the Agora. As the centre s management will buy the paint, you will submit a report in the form of a table listing the following information for each section of the Agora: The surface area of the walls to be painted grey. The surface area of the walls to be painted yellow. The surface area of the ceilings. Your table must also provide the total surface area that will be painted in each colour for all three sections of the Agora. Lobby 1.5 m Annex Hall (x 10) m (x 4 m) (2x + 3) m 10 SOFAD

11 SCORED ACTIVITY 1 Score for each criterion Cr Cr Cr /25 points SOFAD 11

12 MTH GEOMETRIC REPRESENTATION The firefighter explains that a simple way to calculate the maximum number of people who may assemble in the Agora (maximum occupancy) is to divide the room volume by the space occupied by one person. According to the standards, this space is x m 3 per person. However, the same firefighter is concerned that the Agora s maximum occupancy calculated using this method will be wrong because the height of the middle section of the complex, the Lobby, is not to standard. You meet with management to inform them of the firefighter s concern. Task 2 In order to provide your boss with realistic data regarding the Agora s maximum occupancy and to have your project approved by the fire department, you will: Formulate and validate a conjecture regarding the Agora s maximum occupancy. Formulate a conjecture in response to the firefighter s concern that the height of the Lobby is not to standard. Propose a possible solution for calculating the Agora s actual maximum occupancy. Estimate: Verification: 12 SOFAD

13 SCORED ACTIVITY 1 Conclusion about the Agora s maximum occupancy (without taking the firefighter s concern into account): Proposal for a conjecture to be made with respect to the firefighter s concern: Validation: Possible solution: Score for each criterion Cr Cr Total for Part 2 /40 /15 points SOFAD 13

14 MTH GEOMETRIC REPRESENTATION Student s questions 14 SOFAD

15 SCORED ACTIVITY 1 Tutor s comments SOFAD 15

16 August 2016