GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS MTH Scored Activity 1. Date sent:... Student's identification. Name:...

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1 GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS MTH Scored Activity 1 Date sent:... Student's identification Name:... Address: Tel. No.: Mark:... /100 September

2 MTH GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS This scored activity was produced by the Société de formation à distance des commissions scolaires du Québec. Project Coordinator: Project Coordinator (initial version): Author: Illustration: Content Revision: Translation: Proofreading: Desktop Publishing: Graphical Layout: Ronald Côté (SOFAD) Jean-Simon Labrecue (SOFAD) Jean-Claude Hamel Marc Tellier Steeve Lemay Judith Sévigny Claudia de Fulviis Claudia de Fulviis Daniel Rémy (I. D. Graphiue inc.) 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 SOFAD

3 SCORED ACTIVITY 1 Most education centres reuire 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. SOFAD 3

4 MTH GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS Instructions Fill in the "Student's Identification" section. Carefully read each uestion before answering it. Write your answers in the appropriate spaces and give complete solutions, as applicable. The weighting for each uestion is indicated to the left of each number, in parentheses. You may use a calculator. 4 SOFAD

5 SCORED ACTIVITY 1 Measurement conversions Scored Activity 1 Memory Aid You can use the following euivalencies to convert measurements from one system of measurement to the other: Measures of capacity 1 fl oz 30 ml 1 c 250 ml 1 gal 4.5 L Measures of mass 1 oz 30 g 1 lb kg Measures of length Measures of area Measures of volume 1 in = 2.54 cm 1 ft 30.5 cm 1 yd 0.91 m 1 mi 1.6 km 1 in cm 2 1 ft dm 2 1 in cm 3 1 ft dm 3 Temperature To convert degrees Fahrenheit to degrees Celsius: T ( C) = 5 9 (T ( F) 32) To convert degrees Celsius to degrees Fahrenheit: T ( F) = 9 5 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. SOFAD 5

6 MTH GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS (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 liuid? 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 SOFAD

7 SCORED ACTIVITY 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 eual to 5 of an imperial gallon. When she got to New York, she noticed that the 6 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. SOFAD 7

8 MTH GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS (4) 7. Locate the following rational numbers on the number line below: 3 4, 1 2 3, 2 1 2, and (2) 8. Determine the uantities 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 SOFAD

9 SCORED ACTIVITY 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. TEA 100 g TEA Calculate the volume of the second box, then use this result to estimate how many grams of tea it can hold. (4) 11. A suare tile with each side measuring 16 1 in must be cut so that it can be used to cover 4 a rectangular surface measuring 12 5 in by 10 3 in. To do this, the two bands marked X in 8 4 the diagram below will be cut away from the tile in in in Calculate the area of each band to be cut off. Give your answer in suare inches using a mixed number, then in suare centimetres rounded off to the nearest unit. SOFAD 9

10 MTH GEOMETRIC REPRESENTATIONS AND TRANSFORMATIONS 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 Vocabulary Information Yes In part No - 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 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 - Using a mathematical formula to calculate a value - Conversion between inches and centimetres - Conversion between feet and centimetres - Conversion between yards and metres - Conversion between miles and kilometres - Conversion between cups and millilitres - Conversion between teaspoons and millilitres - Conversion between tablepoons and millilitres - Conversion between gallons and litres - Conversion between fluid ounces and millilitres - Conversion between pounds and grams - Conversion between ounces and grams - Mass of one millilitre of water in grams - Distinction between capacity and volume - Meaning of proportional reasoning - Conversion between suare inches (in²) and suare centimetres (cm²) - Conversion between cubic inches (in³) and cubic centimetres (cm³) 10 SOFAD

11 SCORED ACTIVITY 1 Calculations - Adding decimal numbers - Subtracting decimal numbers - Multiplying decimal numbers - Dividing decimal numbers - Converting fractions to decimal numbers, and vice versa - Rounding off a number to the nearest place value - Converting F to C, and vice versa, using a mathematical formula - Converting a uantity from one system of measurement to the other using the conversion factor - Finding euivalent fractions - Adding fractions - Subtracting fractions - Multiplying fractions - Dividing fractions - Adding mixed numbers - Subtracting mixed numbers - Finding the area of a suare and of a rectangle - Finding the volume of a cube and of a rectangular space 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 - Applying the distributive property of multiplication over addition - Checking the //réalisme of calculations - Selecting the appropriate information before performing a calculation - Estimating the //la grandeur d un résultat par l arrondi avant sa confirmation - Solving problems methodically - Anticipating the value of a result SOFAD 11

12 Student's uestions Tutor's comments