Geometric Representation

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Student Identification

M T H - 3 0 5 3 - 2

S c o r e d A c t i v i t y 1

Part 1 – Explicit Evaluation of Subject-Specific Knowledge: /10

Part 2 – Evaluation of Competencies: /40

Date corrected:

Evaluator’s signature:

ToTal

/50

MTH-3053-2 – GEOMETRIC REPRESENTATION

2 3© SOFAD © SOFAD

This scored activity was produced by the Société de formation à distance des commissions

scolaires du Québec (SOFAD).

Production team (French version)

Project Coordinators: Isabelle Tanguay (SOFAD)

Nancy Mayrand (SOFAD)

Robert Longpré (SOFAD)

Authors: Marie-Pierre Beaudoin

Jean-Claude Hamel

Content Revisors: Gilles Gascon

Isabelle Hachez

Steeve Lemay

Alain Bombardier

Jonathan Lafond

Linguistic Revisors: Michelle Côté

Marie-Pierre Gazaille

Docimological Revisor: Julie Gravel

Illustrations: Serge Mercier

Graphic Design: Serge Mercier

Proofreading: Johanne St-Martin

First Printing: May 2013

Production team (English version)

Project Coordinator: Nancy Mayrand

Translator: Claudia de Fulviis

Typesetting: Daniel Rémy

Proofreading: 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 2016

SCORED ACTIVITY 1

2 3© SOFAD © SOFAD

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.

MTH-3053-2 – GEOMETRIC REPRESENTATION

4 © SOFAD

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 yd2 = 9 ft2

1 ft2 = 144 in2

1 yd3 = 27 ft3

1 ft3 = 1728 in3

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 yd2 ≈ 0.84 m2

1 ft2 ≈ 9.3 dm2

1 in2 ≈ 6.5 cm2

1 yd3 ≈ 0.765 m3

1 ft3 ≈ 28.3 dm3

1 in3 ≈ 16.4 cm3

5© SOFAD

SCORED ACTIVITY 1

Part 1: Explicit Evaluation of Subject-Specific Knowledge

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.

Answer:

b) Assuming that x = 2, determine whether the two results you obtained in a) are correct.

Answer:

1

60 cm

60 cm

3 points

MTH-3053-2 – GEOMETRIC REPRESENTATION

6 © SOFAD

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.

50 40 30 20 1040302010

5040302010 40 30 20 10

120 yd

160 ft

68 m

105 m

American football �eld Soccer �eld

What is the percentage ratio of the areas of the two fields?

Answer:

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?

Answer:

2

2 points

3

2 points

7© SOFAD

SCORED ACTIVITY 1

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.

Answer:

Total for Part 1 /10

4

3 cm

2 cm

x

3 points

MTH-3053-2 – GEOMETRIC REPRESENTATION

8 © SOFAD

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

9© SOFAD

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

Annex

Lobby

Hall1.5 m

(x – 4 m) (2x + 3) m

(x – 10) 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.

MTH-3053-2 – GEOMETRIC REPRESENTATION

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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.

Annex

Lobby

Hall1.5 m

(x – 4 m) (2x + 3) m

(x – 10) m

11© SOFAD

SCORED ACTIVITY 1

/25 points

Score for each criTerion

Cr. 1.1 10 8 6 4 2

Cr. 2.2 10 8 6 4 2

Cr. 3.2 5 4 3 2 1

MTH-3053-2 – GEOMETRIC REPRESENTATION

12 © SOFAD

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 m3 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:

13© SOFAD

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:

Total for Part 2 /40 /15 points

Score for each criTerion

Cr. 2.1 10 8 6 4 2

Cr. 2.2 5 4 3 2 1

MTH-3053-2 – GEOMETRIC REPRESENTATION

14 © SOFAD

Student’s questions

15© SOFAD

SCORED ACTIVITY 1

Tutor’s comments

5803-07 August 2016