SAMPLE. Casualties vs magnitude. Magnitude of Earthquakes

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2 Earthquakes are caused by shifting tectonic plates, the mosaic-like sections of the earth s surface. Different interactions between adjacent plates are responsible for mountain ranges, valleys, volcanoes, and of course, earthquakes. Earthquakes are most commonly measured on the Richter Scale. Q1! Magnitude (Richter Scale) Q2 Number of Casualities The following bar graph shows the magnitude, measured by the Richter scale, of several historical earthquakes. Use the graph to answer the following questions 0 Magnitude of Earthquakes Earthquake Casualties vs magnitude Magnitude (Richter Scale) a) What was the magnitude of the Anchorage earthquake in 1964? a) In which country did the earthquake occur that had a magnitude of 6.9? b) Two earthquakes on the graph occurred in California. What is the mean magnitude of the earthquakes? A seismologist wants to see if there is any correlation between earthquake size and the number of casualties. He draws the following scatterplot using data from several historical earthquakes. Use the graph to answer the questions on the right. a) The 1908 earthquake in Messina, Italy was 7.2 in magnitude and had casualties. Circle the data point which represents the Messina earthquake. b) An earthquake in Tangshan, China in 1976 killed people. According to the graph, what was the magnitude of this earthquake? c) Approximately how many people were killed in the 9.1 magnitude earthquake in Sumatra in 2004? This exercise is continued on the next page...

3 ! d) The seismologist is still unsure if a correlation between the size of the earthquakes and the number of causalities is present. By analysing the graph, write down your observations in the correlation between the two pieces of data. Q3...This exercise is continued from the previous page. The graph below is another way of comparing earthquake intensities. Draw a straight line through the correct distance and magnitude below to identify the letters. Correctly identify all the letters to reveal which country was home to the world s largest earthquake. Distance (km) Note: The first letter has been completed for you as an example Magnitude The country home to the world s largest earthquake, scoring a massive 9.5 on the Richter scale, was:

4 Solar eclipses occur when the Moon is positioned between the Sun and the Earth, effectively blocking out the Sun. Eclipses can be measured by the duration of time the Sun is blocked and the extent the eclipse is seen in (also called the path width). Q1! Path Width (km) The data in the tables below shows the duration and path width of solar eclipses between 2002 and Using the following instructions, display this data in a scatter plot. Date Duration Path Width (seconds) (km) 10/06/ /12/ /11/ /04/ /10/ /03/ /09/ /02/ /08/ /01/ /07/ /01/ /07/ Duration and Path Width of Solar Eclipses Instructions Use the x axis for the duration. Use the y axis for the path width. Use different coloured pencils to draw in the data, so that the data is grouped by year that the eclipse occurred. Provide a key. Remember you will need a title for your graph and axis titles. Axis titles also need to show units. Key Duration (secs)

5 Number of recordings A complex interaction between the Earth, Moon and Sun and the forces they exert causes the rise and fall of sea levels known as tides. Tides are measured on a daily basis near the shore of most continents in order to predict future tides; these are important for various human activities such as fishing and boating. Q1 Q2! The sea heights at low and high tide in Port Moresby in Papua New Guinea on a given weekend were recorded and are listed below. Arrange the list in ascending order then calculate the mean, median, mode and range. 0.82m, 1.68m, 0.8m, 2.27m, 0.76m, 1.81m, 0.76m, 2.31m Mean Median Mode Range Using the graph below of the minimum sea heights recorded in Macquarie Island between January and February 2011, answer the following questions. Minimum sea heights in Jan-Feb 2011 in Macquarie Island a) What is the modal sea level height for the January to February period? b) In what range of sea heights is the median score in? c) If the total of all the sea heights recorded was 21.07, what was the mean height? (Use a calculator) Sea level (m)

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7 Firstly, thank you for your support of Mighty Minds and our resources. We endeavour to create highquality resources that are both educational and engaging, and results have shown that this approach works. To assist you in using this resource, we have compiled some brief tips and reminders below. About this resource This Mighty Minds Fundamentals Lesson focusses on one subtopic from the NAPLAN Tests and presents this skill through a theme from the Australian Curriculum (History, Science or Geography). This lesson is also targeted at a certain skill level, to ensure that your students are completing work that is suited to them. How to use this resource Our Fundamentals Lessons are split into two main sections, each of which contain different types of resources. The student workbook contains The main title page; and The blank student worksheets for students to complete. The teacher resources section contains This set of instructions; The Teacher s Guide, which offers information that may be needed to teach the lesson; The Item Description, which gives a brief overview of the lesson and its aims, as well as extension ideas; The student answer sheets, which show model responses on the student worksheets to ensure that answers to the questions are clear; The teacher s answer sheets, which provide a more detailed explanation of the model responses or answers; and Finally, the end of lesson marker. We suggest that you print the student workbook (the first set of pages) for the students. If students are completing this lesson for homework, you may also like to provide them with the student answer pages. Feedback and contacting us We love feedback. Our policy is that if you us with suggested changes to any lesson, we will complete those changes and send you the revised lesson free of charge. Just send your feedback to resources@mightyminds.com.au and we ll get back to you as soon as we can.

8 Data Type of Data Data can be described as Categorical or Qualitative: This is data that is described using names or labels. For example eye colour is a categorical variable, as the data would be described as blue or brown, etc. Numeric or Quantitative: This is data expressed as numbers which are measurable quantities. An example of quantitative data would be the heights of the students in a class. Quantitative data can then be described as: Tables Discrete: Discrete data is data which can only be described as a finite number of values. For example, if you were to measure the population of people in a town, this would be a discrete variable, because population can only be expressed using whole numbers. Continuous: Given the highest and lowest value of a set of data, continuous data can take on any value in between. This data is usually a measurement, for example, the volume of water in QLD dams. One Way Tables One way tables are those which display one variable. Data in one way tables is best displayed in a bar graph. Two Way Tables A two way table has two variables. In the example table, the two variables are country and medal type. Graphs Bar Graphs A bar graph displays categorical data. The bars can be 4 vertical or horizontal. One axis shows the categories of 2 data, whilst the other displays the frequency or scale of the data. 0 Country Pet types of Year 8 students Pet type Dog Cat Fish Bird Frequency Olympic Medal Tally 2012 Medal Type Gold Silver Bronze Total USA China Britain Number of students 8 6 Eye Colour of Year 8 Students Brown Blue Hazel Green Eye Colour This teaching guide is continued on the next page...

9 ...This teaching guide is continued from the previous page. Scatter plot A scatter plot consists of a horizontal (x) axis and a vertical (y) axis and displays a set of quantitative data. Each dot or point on the graph represents a data set. For example if a student gets 34 on a Maths test and 48 on an English test, the dot will represent (34,48). See the example on the right. Line graphs A line graph compares two variables and is most often used to display data which changes over time. The x axis (horizontal) displays the time, whereas the y axis shows the variable changing. The data is represented as dots, with a line connecting them. Note: line graphs do not have a line of best fit (a straight line which shows a data trend). Stem and Leaf plots A stem and leaf plot displays data in a table format. Data with one variable has two columns. The right column displays the digits from the data that are ones. The left column displays the tens. Stem and leaf plots can also display data with two variables, for example the weight of boys and girls in a class. As you can see in the graph on the right, the tens digit is displayed in the central column. The lowest weight for girls recorded was 45kg, with the tens digit, 4, in the central column, and the ones digit, 5, in the right column. Pie Graphs A pie graph consists of a circle which is divided into segments that represent data. Each segment meets at the central point of the circle. To draw a pie graph, data needs to be written as a percentage. For example if 6 students out of a total of 30 students surveyed prefer the season Spring, this is equivalent to 20% of students. Therefore, a total of 20% of the circle will represent Spring. English Test Score Number of Computers Sold Class 7B's Math & English Scores Math's Test Score Computers Sold at Mike's Tech Shop Year Weights (kg) of students Boys Girls 4 5, 9 9,7,6 5 1, 2, 2, 4, 5, 8, 8 8, 8, 6, 5, 3, 2, 6 2, 8 6, 2 7 Favourite Season Summer 40% Winter 35% Autumn Spring 10% 20% This teaching guide is continued on the next page...

10 ...This teaching guide is continued from the previous page. Measures of Central Tendency Mean The mean is the average score in a set of scores. It is calculated by dividing the sum of all scores by the number of scores. Median The median is the middle score when scores are arranged in order of increasing size. When there are an odd number of scores, the median is simply the middle score. When there are an even number of scores, the median is the average of the two middle scores. Mode The mode is the most common score. There can be more than one mode e.g. two modes are described as bimodal. Range The range is the difference between the highest score and the lowest score in a set of data. Example. What is the mean, median, mode and range of the following set of maths test results? 11, 13, 13, 14, 16, 16, 16, 16, 16, 17, 17, 18, 19, 19, 20. Mean: ( ) 15 = 16 Median: the middle score is the 8th score which is 16 Mode: the most common score is 16 Range: = 9 Mean = Sum of all scores Number of Scores Range = highest score lowest score

11 For the Teachers Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. Quake Questions, Total Eclipse and Tide Tracking Activity Description: This lesson contains three activities that are based on data skills, including graph and table interpretation and calculation of measures of central tendency. The first activity, Quake Questions, uses earthquake data presented in four different graph types: bar graph, scatter plot, line graph and pie chart. Students must interpret these accurately to answer the questions correctly. The second activity, Total Eclipse, provides students with data relating to solar eclipses that they must present in a scatterplot. In the last activity, Tide Tracking, students must calculate the mean, median, mode and range from raw data and a graph. Purpose of Activity: Students will revise and test their ability to interpret and create graphs, and calculate measures of central tendency. KLAs: Mathematics, Science CCEs: Recognising letters, words and other symbols (α1) Interpreting the meaning of tables or diagrams or maps or graphs (α6) Compiling lists/ statistics (α12) Recording/ noting data (α13) Graphing (π15) Calculating with or without calculators (Ф16) Substituting in formulae (Ф19) Applying a progression of steps to achieve the required answer (Ф37) Suggested Time Allocation: This lesson is designed to take approximately an hour to complete 20 minutes per activity. Teaching Notes: Allow students to complete each activity before discussing solutions as a class. Encourage all group discussion. Students will need a calculator to complete many of the questions in this activity. This Item Description is continued on the next page...

12 For the Teachers - continued This Item Description is continued from the previous page. Quake Questions, Total Eclipse and Tide Tracking Teaching Notes (cont d): Students should have basic knowledge of graphing before beginning this activity. As an extension students could collect their own data and organise it into different graphs. If students are struggling show them how to complete part of the activity so that that can more easily answer the remaining questions. Follow Up/ Class Discussion Questions: Discuss the ten largest earthquakes which have occurred. Where are they located? Is there a pattern? Why? How long does a solar eclipse last? how often do they occur? How does the tide change throughout the day?

13 NAP - ###### Earthquakes are caused by shifting tectonic plates, the mosaic-like sections of the earth s surface. Different interactions between adjacent plates are responsible for mountain ranges, valleys, volcanoes, and of course, earthquakes. Earthquakes are most commonly measured on the Richter Scale. Q1! Magnitude (Richter Scale) Q2 Number of Casualities The following bar graph shows the magnitude, measured by the Richter scale, of several historical earthquakes. Use the graph to answer the following questions 0 Magnitude of Earthquakes Earthquake a) What was the magnitude of the Anchorage earthquake in 1964? 9.2 a) In which country did the earthquake occur that had a magnitude of 6.9? Nepal b) Two earthquakes on the graph occurred in California. What is the mean magnitude of the earthquakes? San Fernando: 6.6 Alum Rock: 5.5 Mean = ( )/2 = 6.05 A seismologist wants to see if there is any correlation between earthquake size and the number of casualties. He draws the following scatterplot using data from several historical earthquakes. Use the graph to answer the questions on the right. Casualties vs magnitude Magnitude (Richter Scale) a) The 1908 earthquake in Messina, Italy was 7.2 in magnitude and had casualties. Circle the data point which represents the Messina earthquake. b) An earthquake in Tangshan, China in 1976 killed people. According to the graph, what was the magnitude of this earthquake? 9.8 c) Approximately how many people were killed in the 9.1 magnitude earthquake in Sumatra in 2004? This exercise is continued on the next page...

14 NAP - ######! d) The seismologist is still unsure if a correlation between the size of the earthquakes and the number of causalities is present. By analysing the graph, write down your observations in the correlation between the two pieces of data. The scatterplot graph shown does show a slight correlation between the number of casualties and the magnitude. It appears that as the magnitude of the earthquake increases, the number of casualties also increases. In most cases, the larger the magnitude of the earthquake, the more damage or danger around, therefore leading to more casualties. Q3...This exercise is continued from the previous page. The graph below is another way of comparing earthquake intensities. Draw a straight line through the correct distance and magnitude below to identify the letters. Correctly identify all the letters to reveal which country was home to the world s largest earthquake. Distance (km) Note: The first letter has been completed for you as an example Magnitude The country home to the world s largest earthquake, scoring a massive 9.5 on the Richter scale, was: C H I L E

15 Quake Catastrophe Question One: Students were required to interpret the bar graph provided that detailed the magnitude of earthquakes in different locations to answer the questions. Students were given the following graph: Questions and answers relating to the graph were as follows: a) Students were asked to find the magnitude of the anchorage earthquake in This would have been found by looking for its location on the horizontal (x) axis, then finding the magnitude of the corresponding bar by looking at the vertical (y) axis. The magnitude of the Anchorage earthquake is therefore approximately 9.2 on the Richter Scale. b) Students were asked which country had an earthquake magnitude of 6.9. By looking at the horizontal (x) axis, 6.9 is located, slightly lower than 7 on the scale. The only bar which has this height corresponds to the Sikkim 2011 Earthquake in Nepal. As the question asks for the country of the earthquake, the answer is Nepal. c) Students were asked to find the mean magnitude of the two earthquakes that occurred in California. First, students needed to find the magnitude of the two earthquakes in California by looking at the graph. The first occurred in San Fernando and had a magnitude of 6.6, whilst the second occurred in Alum Rock and had a magnitude of 5.5. the mean is calculated by adding together the two magnitudes then dividing them by two (the number of scores). ( )/2 = Therefore the mean magnitude is This answer guide is continued on the next page...

16 ...This answer guide is continued from the previous page. Question Two: Students were required to interpret the scatter plot of the magnitude of some major earthquakes and their corresponding casualty numbers to answer the questions provided. Students were given the following scatter plot: *note that the red circle correlates to the answer for question one. Answers were as follows: a) Students were asked to circle the point on the graph that represented the Messina Earthquake. The students were told that the earthquake had a magnitude of 7.2 and that there was casualties. This can be found on the horizontal (x) and vertical (y) axis, respectively. The point circled should correspond to that on the graph above. b) Students were asked to find the Magnitude of an earthquake that occurred in China that killed people. Students needed to locate the point on the graph which has casualties, by looking at the vertical (y) axis. They then needed to establish the magnitude of this point by looking at the horizontal (x) axis. The point representing the Tangshan, China earthquake corresponds to a magnitude of 9.8 on the Richter scale. c) Students were asked to find the number of casualties in the 9.1 magnitude earthquake in Sumatra in Students needed to locate a point on the scatter plot which has a magnitude of 9.1, then determine the number of casualties by looking at the points location on the vertical (y) axis. The point is just over halfway between and , and therefore represents about casualties. This answer guide is continued on the next page...

17 ...This answer guide is continued from the previous page. Question Three: To complete this activity students needed to use the table and graph to identify the country home to the world s largest earthquake. Students needed to be aware that a ruler was necessary to complete this activity accurately. Firstly, students should have looked at the distance and magnitude of an earthquake in the table. Once identified, students were required to line these two numbers up and draw a straight through them. If done correctly, the line would also pass through a letter on the end line. This letter then corresponded to a specific number in the final word. The graph and table students were given is shown below, along with the model response. Students should have found that the country with the world s largest earthquake was Chile. The following diagram shows how students should have found this answer:

18 NAP - ###### Solar eclipses occur when the Moon is positioned between the Sun and the Earth, effectively blocking out the Sun. Eclipses can be measured by the duration of time the Sun is blocked and the extent the eclipse is seen in (also called the path width). Q1! Date Duration Path Width (seconds) (km) 10/06/ /12/ /11/ /04/ /10/ /03/ /09/ /02/ /08/ /01/ /07/ /01/ /07/ Path Width (km) The data in the tables below shows the duration and path width of solar eclipses between 2002 and Using the following instructions, display this data in a scatter plot Duration and Path Width of Solar Eclipses Instructions Use the x axis for the duration. Use the y axis for the path width. Use different coloured pencils to draw in the data, so that the data is grouped by year that the eclipse occurred. Provide a key. Remember you will need a title for your graph and axis titles. Axis titles also need to show units. Key Duration (secs)

19 Total Eclipse Question One: This question asked students to draw a scatter plot based on the information provided in the graph. To achieve this, students were required to place a marker on the intersection of the path width and duration. Further explanation of this is provided below. Students were also asked to draw each year s data in a different colour and provide a key. The model answer is provided in colour on the students page, but in the answer below it has also been numbered in case access to colour printing or computers is limited Date Duration (seconds) Path Width (km) 11/07/

20 NAP - ###### Number of recordings A complex interaction between the Earth, Moon and Sun and the forces they exert causes the rise and fall of sea levels known as tides. Tides are measured on a daily basis near the shore of most continents in order to predict future tides; these are important for various human activities such as fishing and boating. Q1 In order: 0.76m, 0.76m, 0.8m, 0.82m, 1.68m, 1.81m, 2.27m, 2.31m Mean = ( ) / 8 = 1.4m Median: (8 + 1) / 2 = 4.5 so median is average of 4 th and 5 th scores, ( ) / 2 = 1.25m Mode is 0.76, since it is the only score that is repeated Range = = 1.49 Q2! The sea heights at low and high tide in Port Moresby in Papua New Guinea on a given weekend were recorded and are listed below. Arrange the list in ascending order then calculate the mean, median, mode and range. 0.82m, 1.68m, 0.8m, 2.27m, 0.76m, 1.81m, 0.76m, 2.31m Mean Median Mode Range 1.4m 1.25m Using the graph below of the minimum sea heights recorded in Macquarie Island between January and February 2011, answer the following questions. Minimum sea heights in Jan-Feb 2011 in Macquarie Island Sea level (m) a) What is the modal sea level height for the January to February period? m b) In what range of sea heights is the median score in? Total scores = = 49 Median is 25 th score, in the m range. c) If the total of all the sea heights recorded was 21.07, what was the mean height? (Use a calculator) Mean = /49 = 0.43m

21 Tide Tracking Question One: Students were given a set of data of sea heights at low and high tide in Port Moresby. From this data, they needed to calculate the mean, median, mode and range. First, students need to put the scores in ascending order to assist in calculating the median and mode. The ascending order is: 0.76m, 0.76m, 0.8m, 0.82m, 1.68m, 1.81m, 2.27m, 2.31m Mean: sum of all scores number of scores ( ) / 8 = 1.4m Mode is 0.76, since it is the only score that is repeated. Median: middle score (8 + 1) / 2 = 4.5 so median is average of 4th and 5th scores, ( ) / 2 = 1.25m Range: highest score lowest score = 1.49 Question Two: Students were given a bar graph which displays the minimum sea heights recorded in Macquarie Island. The data is displayed in ranges, e.g m. Students needed to use the graph to answer the following questions. Questions and answers were as follows: a) Students were asked to find the modal sea level height for the January to February period. The mode is the most common score, or in this case, the most common range. This was simply the range which had a corresponding bar with the highest magnitude. Therefore the modal range was m. b) Students were asked to find the range of sea heights which contained the median score. The median score is the middle score. Students first needed to find the total amount of scores by adding together the number of scores represented by each bar. This is calculated by = 49. The median score is therefore (49+1)/2 = 25 th score. The first range, has the 1 st score, the range has the 2 nd to 9 th score (as there are 8 scores represented by the bar) and the range has the 10 th to 20 th score. The range has the 21 st to 37 th score, so the 25 th score must belong to this range. c) Students were asked to find the mean sea height given that the total height was The mean is calculated by dividing the total of the scores by the number of scores. As the total of scores in and previously it was found that there was 49 scores in total, the mean was 21.07/49 = 0.43m.

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