DATA COLLECTION MTH-3052-2 Scored Activity 1 Student Identification Name: Address: Email: Telephone: Date submitted: PART 1 Explicit Evaluation of Subject-Specific Knowledge: /20 Total PART 2 Evaluation of Competencies: /80 /100 Date corrected: Evaluator s signature:
MTH-3052-2 DATA COLLECTION 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: Robert Longpré (SOFAD) Nancy Mayrand (SOFAD) Jean-Claude Hamel Isabelle Hachez Steeve Lemay Caroline Martin Isabelle Hachez Michelle Côté Marie-Pierre Gazaille Julie Gravel Serge Mercier Serge Mercier Marie-Pierre Gazaille Production Team (English Version) Project Coordinators: Translator: Content Revisor: Typesetting: Proofreading: Jean-Simon Labrecque (SOFAD) Valerie Vucko (i-edit) Rhonda Sherwood Alex Roslin Graeme McDonald Alex Roslin Sources Page 3 Page 9 Page 13 Barry Barnes / Shutterstock Prapann / Shutterstock Cb162 / Creative Common This work is financed by the Ministère de l Éducation, du Loisir et du Sport du Québec. Part of this financing comes from the Canada-Québec bilateral agreement related to minority language education and second languages instruction. SOFAD All rights for translation and adaptation, in whole or in part, reserved for all countries. Despite the following statement, SOFAD authorizes all adult education centres that use the corresponding learning guide to reproduce this scored activity. Any reproduction by mechanical or electronic means, including microreproduction, is forbidden without the written permission of a duly authorized SOFAD representative. 2 SOFAD
SCORED ACTIVITY 1 Introduction Scored Activity 1 covers Learning Situations 1 and 2 in the Data Collection learning 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 a situation 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 scored 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 of 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
MTH-3052-2 DATA COLLECTION PART 1: Explicit Evaluation of Subject-Specific Knowledge 1 Here is data on the number of groups and students in each academic level in a secondary school. There is a total of 35 groups and 1074 students. Each group consists of about 30 students divided almost equally between boys and girls. Distribution of students according to academic level Level Number of groups Total number of students Cycle One, Year One 8 235 Cycle One, Year Two 8 243 Cycle Two, Year One 8 262 Cycle Two, Year Two 6 176 Cycle Two, Year Three 5 158 The school has to conduct two sample surveys. For each survey, determine a possible composition of the sample by using the most appropriate sampling method. For each survey, specify the sampling method chosen and why it was chosen. a) To organize the Valentine s Day dance, the student council wants to survey a sample of 90 students. The sample should take into consideration the students academic level and include an equal number of girls and boys. Sampling method used and justification: b) The school administration wants to know what types of meals the students would like the cafeteria to serve. The principal wants to ask students from a certain number of groups to answer a detailed questionnaire. The sample would include approximately 150 students; their grade level and gender are not important. To minimize disruption to the groups, teachers want these 150 students to answer the survey at the same time. Sampling method used and justification: 4 points 4 SOFAD
SCORED ACTIVITY 1 2 A police officer uses a radar gun to measure the speed (km/h) of passing cars on a highway. Here is the data obtained for the last 50 cars whose speed he captured with the radar gun. 105 103 110 100 95 105 118 121 103 98 107 112 109 95 110 102 105 132 125 106 103 110 108 112 104 106 96 102 94 109 112 108 114 109 102 100 95 101 110 113 103 108 110 100 106 110 108 115 130 107 Represent this data collection and the relative frequencies obtained with a distribution table and an appropriate graph. 4 points SOFAD 5
MTH-3052-2 DATA COLLECTION 3 Jade is a competitive cross-country skier and competes in several races across Québec each year. One of the races is a 160-km marathon that takes place over two days. The following list shows the distances in kilometres of the races Jade has competed in this year. 12 5 14 5 10 5 7 16 5 25 12 16 160 Which of the three measures of central tendency studied in the first two learning situations do you think is the most representative of the distances Jade has competed in? Determine these three measures, and use your results to explain your point of view. Explanation: 4 points 4 A hockey team has its ups and downs during the first 15 games Distribution of 15 games of the season. In one game, it didn t score any goals, but in three other games it scored 6 goals. The table on the right shows the distribution of these 15 games according to the number of goals scored. The coach says the mean goals scored per game is the most representative of the three measures of central tendency. according to number of goals scored Number of goals scored Number of games 0 1 1 1 2 4 3 2 4 2 5 2 6 3 Do you think the coach is right? Determine the three measures of central tendency, and use these results to explain your point of view. 4 points Explanation: 6 SOFAD
SCORED ACTIVITY 1 5 Annual compulsory instruction time in elementary and secondary schools varies greatly from one country to another. The table below provides the data for selected UNESCO countries. What conclusion can you make about the dispersion of the data regarding annual compulsory instruction time at the secondary level compared to the elementary level? To answer this question, do a comparative analysis of the two distributions. This analysis should be based on a box-and-whisker plot created for each distribution and on two observations you can draw from these graphs. Annual compulsory instruction time Elementary Secondary Elementary Secondary Country Time (h) Time (h) Country Time (h) Time (h) Hungary 724 885 Czech Republic 706 862 Sweden 741 741 England 899 929 Turkey 864 864 Denmark 813 900 Finland 683 829 Austria 811 959 Luxembourg 924 908 Greece 812 796 Norway 773 836 Spain 875 1050 Ireland 915 929 Belgium 930 1020 Korea 703 859 France 847 1065 Japan 800 877 Australia 984 997 Iceland 889 969 Italy 924 1023 Germany 793 887 Netherlands 940 1000 Portugal 888 934 Source: UNESCO Observations: 4 points Total for Part 1 /20 SOFAD 7
MTH-3052-2 DATA COLLECTION PART 2: Evaluation of Competencies This section evaluates the development of your competencies in mathematics. It contains two evaluation situations. Each one is divided into two tasks. The following criteria will be used to evaluate the competencies targeted in this section: Competency 1: Uses strategies to solve situational problems Cr. 1.1 Indication of an appropriate understanding of the situational problem Cr. 1.2 Mobilization of the appropriate mathematical knowledge and strategies 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 appropriate to the situation Cr. 2.2 Correct application of concepts and processes suited to the situation Cr. 2.3 Proper implementation of mathematical reasoning suited to the situation Cr. 2.4 Proper organization of the steps in an approach suited to the situation Cr. 2.5 Correct justification of the steps in an approach suited to the situation Competency 3: Communicates by using mathematical language Cr. 3.1 Correct interpretation of a mathematical message Cr. 3.2 Production of a message appropriate to the communication context and in keeping with the terminology, rules and conventions of mathematics 8 SOFAD
SCORED ACTIVITY 1 Evaluation Situation 1 Our Beautiful White Winters! Everyone seems to be talking about global warming and how it is leading to climate change and causing the glaciers to melt at an accelerated rate. It is an issue we can no longer ignore. The effects can be seen all year long, from more heat wave days during the summer to increased rainfall during the winter. Our seasons seem to be increasingly out of whack. It's common to hear people say: It seems to me that when I was younger, there was a lot more snow in the winter! To illustrate this phenomenon, the airport in Québec City has provided data on the annual snowfall for the years 1951-1969 and 1992-2011. The data is presented using different types of representation: Graph 1 Annual snowfall in Québec City from 1951-1969 Min: 219.3 Q 1 : 241.2 Q 2 : 297.8 Q 3 : 325.8 Max: 497.1 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 SNOWFALL (cm) Figure 1 Graph 2 NUMBER OF YEARS WITH THIS AMOUNT OF SNOWFALL 7 6 ANNUAL SNOWFALL IN QUÉBEC CITY FROM 1951 TO 1969 Annual snowfall (cm) during the years 1951-1969 229.4 234.4 241.2 5 264.6 287.8 312.1 4 3 409.8 497.1 263.3 2 226.0 477.0 303.3 1 200 250 300 350 400 450 500 SNOWFALL (cm) 429.0 314.0 325.8 288.5??? SOFAD 9
MTH-3052-2 DATA COLLECTION It makes you wonder if one day our beautiful white winters will only be a distant memory... Let s find out. Use the information provided on the previous page to complete the following two tasks: Task 1 The meteorological technician at the Québec City airport was only able to find 16 of the 19 data points (see Figure 1) that were used at the time to create Graph 1. However, he remembers having read that the mean of the 9 highest data points was 376.844 cm. He asks you to help him complete his report. More specifically, he wants you to find the 3 missing data points and to justify the approach you used to find each value. Score for each criterion Cr. 1.2 5 4 3 2 1 Cr. 1.3 5 4 3 2 1 Cr. 2.2 5 4 3 2 1 Cr. 2.5 5 4 3 2 1 /20 points The 3 missing data points: 10 SOFAD
SCORED ACTIVITY 1 Task 2 Earlier in the situation we mentioned the following observation: It seems to me that when I was younger, there was a lot more snow in the winter! Do you agree with this statement? Explain your answer using the appropriate measures of central tendency. Explanation: Score for each criterion Cr. 1.1 10 8 6 4 2 Cr. 2.1 5 4 3 2 1 Cr. 2.2 5 4 3 2 1 /20 points SOFAD 11
MTH-3052-2 DATA COLLECTION Evaluation Situation 2 A Skate Park in Town Your town s municipal council is debating the possibility of building a skate park in a new residential neighbourhood that has many families. However, the project is highly controversial, and some residents are vehemently opposed to the idea. They say there has been a lack of consultation, and they are worried the park will change the nature of their neighbourhood. Others, on the other hand, think the project is a fantastic idea. The community youth director defends the project based on the following argument: It s a great opportunity for teens to practice a sport they love! he says. The local newspaper recently conducted an in-house survey on the issue: Skate Park STRONG MAJORITY SUPPORT PROJECT The proposed plan to build a skate park in the Hirondelles neighbourhood continues to be a hot topic. To find out what residents think, our reporters conducted a survey last Saturday. According to the responses gathered, a strong majority of neighbourhood residents seem to be in favour of the project. Mayor Lalonde refused to comment on the survey results. We ll have to look into it more closely, he said. Although the survey was not scientific, it does shed more light on the situation. Surprisingly, ot ruling it out the mayor did not say a 60% 55% 50% 45% 40% 35% 30% 25% OPINION OF THOSE SURVEYED ON THE PROPOSED SKATE PARK For Against Methodology: Five streets in the neighbourhood were randomly chosen. We interviewed 10 people walking on each of these streets. The mayor is sceptical and wants more clarity on the issue. He therefore asks a city employee to conduct a second sample survey, but this time by phone with neighbourhood residents ages 15 and older. He also wants all age groups to be adequately represented in the sample. Those called were chosen at random. 12 SOFAD
SCORED ACTIVITY 1 Here is some recent data on the distribution of the population in this neighbourhood by age group: Table 1 Distribution of neighbourhood residents according to age Ages Frequency 15 to 24 years old 425 25 to 34 years old 411 35 to 44 years old 362 45 to 54 years old 396 55 to 64 years old 225 65 to 74 years old 132 The following table presents the results of the phone survey; the answers have been grouped by age group. The sample included 125 people. Table 2 Answers obtained on the proposed skate park in the neighbourhood Ages (y) Answers obtained [15, 25[ F F F F A F F F X F F F A F F X F F F A A F F F X F F [25, 35[ A F F X F X A A A X F F F A F F A X A A X F F F A F A [35, 45[ F A A A A X X F F A F F A X F A A F A X A X F [45, 55[ A A F X A X X A A X F F X A F A A X X A A A X A A [55, 65[ X A F X X A X X X F A X A A [65, 75[ F X X X A X A X X (Legend: F = for the project; A = against the project; and X = does not know) You have just been hired as the town s community coordinator. The mayor wants to better understand the political issues surrounding this debate and to present the town council with a detailed analysis. With these goals in mind, the mayor assigns you two tasks: SOFAD 13
MTH-3052-2 DATA COLLECTION Task 1 To help with the analysis of the results of the phone survey, you must present a portrait of the responses of citizens who are for and against the project based on their age. More specifically, the mayor asks you to do the following: Organize the FOR and AGAINST responses collected during the telephone survey using the appropriate tables and graphs. Determine the measures of central tendency. Analyze the results obtained based on your representations and measures of central tendency. Analysis: Score for each criterion Cr. 1.2 5 4 3 2 1 Cr. 2.3 5 4 3 2 1 Cr. 3.2 10 8 6 4 2 /20 points 14 SOFAD
SCORED ACTIVITY 1 Task 2 To help the mayor make his decision, he asks you to compare the results of the newspaper s in-house survey with those of the telephone survey. In your analysis, you must do the following: Validate whether the sample was representative in both surveys. Identify two possible sources of bias for each survey. Compare the results of the two surveys using the appropriate graph. Score for each criterion Cr. 1.4 5 4 3 2 1 Cr. 2.2 5 4 3 2 1 Cr. 2.4 10 8 6 4 5 /20 points Total for Part 2 /80 SOFAD 15
Student s questions Tutor s comments 5802-07 February 2015