GEOM ET R IC
R E P R E S E N TAT I O N S A N D T R A N S F O R M AT I O N S
M TH-21 0 2 -3
Sco red Act iv it y 1
Date sent: ................................................................... Student's identification
Name: ..............................................................................................
Address: .........................................................................................
.........................................................................................
Tel. No.: ...........................................................................................
Email: ..............................................................................................
Mark: ............................ /100
September 2012
1930-07
MT H -2 1 0 2 -3 – GEOMETRIC REPRES EN TATIONS AND T RANSFORMATIONS
This scored activity was produced by the Société de formation à distance des commissions scolaires du
Québec.
Project Coordinator:
Ronald Côté (SOFAD)
Project Coordinator (initial version):
Jean-Simon Labrecque (SOFAD)
Author:
Jean-Claude Hamel
Illustration:
Marc Tellier
Content Revision:
Steeve Lemay
Judith Sévigny
Translation:
Claudia de Fulviis
Proofreading:
Claudia de Fulviis
Desktop Publishing:
Daniel Rémy (I. D. Graphique inc.)
Graphical Layout:
Alain Lemay
© Société de formation à distance des commissions scolaires du Québec
All rights for translation and adaptation, in whole or in part, reserved for all countries. Any reproduction by mechanical
or electronic means, including micro-reproduction, is forbidden without the written permission of a duly authorized
representative of the Société de formation à distance des commissions scolaires du Québec (SOFAD).
2
© SO FA D
SCORE D ACT IVI T Y 1
Most education centres require that you obtain
an average of 60% or more in order to write the official
examination.
Scored Activity 1 deals with learning situations 1 and 2 of the guide entitled Geometric Representations
and Transformations. Once you have completed this activity, send it to your tutor together with any
related documents.
© S O FAD
3
MT H -2 1 0 2 -3 – GEOMETRIC REPRES EN TATIONS AND T RANSFORMATIONS
Instructions
• Fill in the "Student's Identification" section.
• Carefully read each question before answering it.
• Write your answers in the appropriate spaces and give complete solutions, as applicable.
• The weighting for each question is indicated to the left of each number, in parentheses.
• You may use a calculator.
4
© SO FA D
SCORE D ACT IVI T Y 1
Scored Activity 1
Memory Aid
Measurement conversions
You can use the following equivalencies to convert measurements from one system of measurement to the
other:
Measures of capacity
Measures of mass
1 fl oz ≈ 30 mL
1 oz ≈ 30 g
1 c ≈ 250 mL
1 lb ≈ 0.454 kg
1 gal ≈ 4.5 L
Measures of length
Measures of area
Measures of volume
1 in = 2.54 cm
1 in2 ≈ 6.5 cm2
1 in3 ≈ 16.4 cm3
1 ft ≈ 30.5 cm
1 ft2 ≈ 9.3 dm2
1 ft3 ≈ 28.3 dm3
1 yd ≈ 0.91 m
1 mi ≈ 1.6 km
Temperature
To convert degrees Fahrenheit to degrees Celsius:
T(°C) = 59 × (T(°F) − 32)
To convert degrees Celsius to degrees Fahrenheit:
T(°F) = 95 × T(°C) + 32
Marks
(4)
1. Gabrielle is 5 ft 11 1/2 in tall. It is not surprising that she is a very good volley-ball player,
as in this sport being tall is a great asset, especially when a player is in front, near the net,
which by regulation is 2.24 m high.
a) By how many centimetres is the net's height greater than Gabrielle's height?
b) When Gabrielle raises her arms, her fingertips reach a height of about 57 cm above her
head. With her arms raised, by how much do her fingertips exceed the height of the
net? Give your answer in both inches and centimetres.
© S O FAD
5
MT H -2 1 0 2 -3 – GEOMETRIC REPRES EN TATIONS AND T RANSFORMATIONS
(4)
2. The shot put is an Olympic event dating back to 1896 for men and 1948 for women. This
50-year difference may explain why the weight of the men's shot and that of the women's
shot were initially determined using different units of measure. The men's shot weighs 12
lb and the women's shot weighs 4 kg.
a) Compare these two weights. The men's shot is how many times heavier than the
women's?
The javelin throw is another Olympic event. The regulation javelin weights are in SI
units. The men's javelin weighs 800 g and the women's javelin weighs 600 g.
b) Express these two weights in pounds and ounces using whole numbers.
(4)
3. In a punch recipe, 30 fluid ounces of soda must be added to 3 1/2 cups of unsweetened
juice.
a) Can a 2-litre pitcher hold this much liquid? Justify your answer.
b) By using the same amount of juice, that is, 3 1/2 cups, how many fluid ounces of soda
should be added to the recipe in order to get exactly 2 litres of punch?
6
© SO FA D
SCORE D ACT IVI T Y 1
(4)
4. This winter, Julian went to Florida with his children. When they left Montréal by plane, the
outside temperature was -10°C. When they arrived in Orlando, Florida the temperature was
90°F.
a) By how many degrees Celsius is Orlando's temperature higher than Montréal's?
b) Express this temperature difference in degrees Fahrenheit.
(2)
5. How much does a gallon of gasoline weigh in pounds given that a litre of gasoline weighs
about 740 g?
(4)
6. Ariane drove to New York in her new car. When she started out, the 60-litre gas tank was
full. In the United States, she stopped once to buy 14 gallons of gasoline. One American
gallon is equal to
5
6
of an imperial gallon. When she got to New York, she noticed that the
gas tank was half empty.
According to the dealer, her car has a fuel consumption rate of 9.2 l/100 km on the highway.
Ariane wonders if this is true. To check the dealer's claim, she needs to know what distance
she covered on this trip, but she did not make a note of the number of kilometres indicated
on the odometer before she started out. However, according to the maps she consulted, she
travelled 255 km in Canada and 360 miles in the United States.
Estimate her actual fuel consumption rate during this trip. Compare it to the car dealer's
rate.
© S O FAD
7
MT H -2 1 0 2 -3 – GEOMETRIC REPRES EN TATIONS AND T RANSFORMATIONS
(4)
7. Locate the following rational numbers on the number line below:
0
(2)
1
2
3
3
4
, 1 23 , 2 12 , 2 56 and 3 83 .
4
8. Determine the quantities indicated by the following measuring instruments.
a) A measure of length in inches
b) A measure of capacity in cups
(4)
9. Express the following measurements in inches using a mixed number. Round off your
answer to the nearest sixteenth.
a) The height of a candleholder
b)
The width of a paper tissue box
26 cm
22.1 cm
8
© SO FA D
SCORE D ACT IVI T Y 1
(4)
10. Illustrated below are two boxes filled with loose tea. The capacity of the first box is 360
mL and it contains 100 g of tea leaves. For the second box, we know only its dimensions in
inches.
1
32
TEA
TEA
100 g
4
3
54
Calculate the volume of the second box, then use this result to estimate how many grams of
tea it can hold.
(4)
11. A square tile with each side measuring 16 14 in must be cut so that it can be used to cover
a rectangular surface measuring 12 85 in by 10 43 in. To do this, the two bands marked X in
the diagram below will be cut away from the tile.
1
12
5
8
16 4 in
in
3
10 4 in
Calculate the area of each band to be cut off. Give your answer in square inches using a
mixed number, then in square centimetres rounded off to the nearest unit.
© S O FAD
9
MT H -2 1 0 2 -3 – GEOMETRIC REPRES EN TATIONS AND T RANSFORMATIONS
Review of the Operational Competencies
What is an operational competency? An operational competency does not relate to any subject in
particular, but can be used in all the subjects. For example, the competency Adopts effective work
methods is developed to different degrees in all subjects. While such a competency is not the focus of any
course in particular, it is closely related to the subject-specific competencies (in Mathematics, Science,
English, History, etc.) which encompass it to different degrees even if you are not necessarily aware of
this. There are several operational competencies. This course deals with two of them: Communicates and
Thinks logically.
Communicates
With regard to the two learning situations (1 and 2) you have just completed, which are the focus of this scored
activity, ­indicate your ability to interpret and transmit the following information.
Mode of
communication
Symbolic
language
Information
Yes In part No
q
q
q
q
q
q
- Using a mathematical formula to calculate a value
q
q
q
- Conversion between inches and centimetres
q
q
q
- Conversion between feet and centimetres
q
q
q
- Conversion between yards and metres
q
q
q
- Conversion between miles and kilometres
q
q
q
- Conversion between cups and millilitres
q
q
q
- Conversion between teaspoons and millilitres
q
q
q
- Conversion between tablepoons and millilitres
q
q
q
- Conversion between gallons and litres
q
q
q
- Conversion between fluid ounces and millilitres
q
q
q
- Conversion between pounds and grams
q
q
q
- Conversion between ounces and grams
q
q
q
- Mass of one millilitre of water in grams
q
q
q
- Distinction between capacity and volume
q
q
q
- Meaning of proportional reasoning
q
q
q
- Conversion between square inches (in²) and square centimetres (cm²)
q
q
q
- Conversion between cubic inches (in³) and cubic centimetres (cm³)
q
q
q
- Identifying the symbols that represent units of measure in the
Imperial System: a) length: in, ft, yd, mi d) capacity: fl oz, gal, pt
b) area: in², ft², yd²
e) weight: oz, lb, t
c) volume: in³, ft³, yd³
f) temperature: °F
- Identifying the symbols that represent units of measure in the SI
System
Vocabulary
10
a) length: cm, dm, m, km
d) capacity: mL, L
b) area: cm², m², ha
e) mass: g, kg, t
c) volume: cm³, m³, km²
f) temperature: °C
© SO FA D
SCORE D ACT IVI T Y 1
Calculations
- Adding decimal numbers
q
q
q
- Subtracting decimal numbers
q
q
q
- Multiplying decimal numbers
q
q
q
- Dividing decimal numbers
q
q
q
- Converting fractions to decimal numbers, and vice versa
q
q
q
- Rounding off a number to the nearest place value
q
q
q
- Converting °F to °C, and vice versa, using a mathematical formula
q
q
q
q
q
q
- Adding fractions
q
q
q
- Subtracting fractions
q
q
q
- Multiplying fractions
q
q
q
- Dividing fractions
q
q
q
- Adding mixed numbers
q
q
q
- Subtracting mixed numbers
q
q
q
- Finding the area of a square and of a rectangle
q
q
q
- Finding the volume of a cube and of a rectangular space
q
q
q
q
q
q
q
q
q
q
q
q
- Converting a quantity from one system of measurement to the other
using the conversion factor
- Finding equivalent fractions
Practical
activity
- Ability to convert measurements in a kitchen recipe from Imperial
units to SI units, and vice versa
- Ability to use Imperial measures of length, area and volume in
building a flower box
Thinks logically
Indicate your ability to perform the following operations.
Operations
Yes In part No
- Applying proportional reasoning
q
q
q
- Applying the distributive property of multiplication over addition
q
q
q
- Checking the //réalisme of calculations
q
q
q
- Selecting the appropriate information before performing a calculation
q
q
q
- Estimating the //la grandeur d’un résultat par l’arrondi avant sa confirmation
q
q
q
- Solving problems methodically
q
q
q
- Anticipating the value of a result
q
q
q
© S O FAD
11
Student's questions
Tutor's comments