Mathematical Studies SL IA 1 Choosing a Topic

Mathematical Studies SL IA 1. Choosing a Topic & Planning Michelle Shaw March 2017

General “The project is an individual piece of work involving the collection of information or the generation of measurements, and the analysis and evaluation of the information or measurements. ” ("Mathematical Studies SL Teacher Support Material. " Mathematical Studies SL Teacher Support Material. N. p. , n. d. Web. 19 Mar. 2017. ) • Grading: üPaper 1: 40% üPaper 2: 40% üProject: 20%

Overview 1. Choose a topic (A: 3) 2. Formulate a plan 3. Information/ measurements (B: 3) 4. Mathematical processes (C: 5) 5. Intrepretation and discussion of results (D: 3) 6. Validity (E: 1) 7. Structure and communication (F: 3) 8. Notation and terminology (G: 2) Full Criteria are in the “Internal Assessment” folder on Manage. Bac

1. Choosing a topic • Identifying an appropriate topic • Developing a topic into a more specific question • Devising a task that is well focused, well defined and appropriate • Expressing the task clearly

1. Choosing a topic • Consider their hobbies or other areas of interest. • Consider real-life applications of mathematics. • Look at the list of titles that have been submitted previously. • Look at descriptions of successful projects that have been submitted previously.

List of previously submitted titles Aesthetics • • Calculating beauty: the golden ratio Colour preferences Daylight in a classroom: architectural design Is my mirror showing an accurate image? Origami applications to mathematics Shadows and height M. C. Escher: symmetry and infinity of art

List of previously submitted titles Business and finance • • • A comparative study of shares, real estate, bonds and banks Analysis of stock market changes Buying a car: payment options Economic development and levels of income Mortgage loans Running a restaurant and dance club Investigating mobile phone traffic Analysis of basic U. S. stocks over the period 1980 -1999 Investing in a hotel in Costa Rica Organising a wedding

List of previously submitted titles Food and drink • • • A comparison between calorie intake and gender Dine in or dine out? High school lunches Jelly bean study Take the cola challenge The cookie problem: taste is all-important The operation of a tuck shop Investigating eating trends of today’s youth Costs of products bought online compared to local grocery stores

List of previously submitted titles Health and fitness • • Breakfast and school grades Breast and cervical cancer: ethnic comparison BMI (body mass index) Infant mortality Investigating reaction times A comparison between lung capacity, age, weight and body fat Aids awareness in Maseru Blood pressure

List of previously submitted titles Nature and natural resources • Analysis of the cost and utility of gas versus electricity in an average domestic situation • Calculating time of sunrise and sunset • Earthquakes • The quality of local water • A statistical investigation of leaves • The affect that different temperatures have on the level of growth of bacteria in water from a garden pool • Sunspot cycles • Animal population

List of previously submitted titles • People Characteristics of federal prisoners Gender based discrimination Perception of time The psychology of memory Voter turnout Correlation study of TV versus sleep times • Power to weight ratio • A study of the effect of colour on human emotions • • Which type of movies do males/females prefer? • Does gender influence choice of favourite animal? • Relation between unemployment and criminality in Sweden from 1988 -1999 • Relations between international and bilingual students: jobs, pocket money and spending behaviour

List of previously submitted titles School-based titles • • • Girls’ sport and grades Left-handed students Performance of local students compared with foreign students Searching for the ideal sound Sport and nationality

List of previously submitted titles Sport • Baseball bat speed compared with body weight • Effective short corners in hockey • Factors affecting athletic performance • Height, weight and swimming performance • How far do tennis balls roll? • Resistance of fishing line • Stoppage times in National Football League (NFL) games • Will female swimmers ever overtake male swimmers? • Comparing heights from sports data • Rollerblading and the maths behind it • The effect of sport on grade point average (GPA) • Olympic Games in Sydney 2000: track and field times

List of previously submitted titles Travel and transport • • Cost efficiency of vehicles Driving skills Petrol prices Seat belt use Traffic movement in an urban area Transport safety in town centres Running late and driving habits Traffic study of Schipol International Airport • The effect of blood alcohol content law on the number of traffic collisions in Sacramento • Public transportation costs and car usage: a personal comparison

List of previously submitted titles Miscellaneous • Average puppy weights in the first few weeks • Counting weeds • International phone call pricing • Memory • Practice makes perfect • Predicting cooling times • Sine waves in pitch frequencies • Spanning trees • Topography and distance • Video games and response times • The Ferris wheel • The geometry involved in billiards • Investigation into different brands of batteries • Statistical comparison of the number of words in a sentence in different languages • How many peas are there in a 500 g box of peas? • Correlation between women’s participation in higher education and politics from 1955 --2000

Description of successful project 1: • • • What is the minimum amount of aluminium foil needed to wrap a bar of chocolate in the shape of a Toblerone? (triangular prism) Measure the Toblerone bar and calculate the fixed volume assuming the triangles to be equilateral. Find equations for area of triangle, volume, length and surface area. Method 1—Trial and error (this addresses criterion B). Method 2—Graphing. Method 3—Calculus. Complete the study with conclusion and evaluation and discuss how the assignment could perhaps be improved. Also comment on how the three methods compare and which is the most accurate.

Description of successful project 2: Relationship between shoe sizes and height (This topic was chosen because the candidate found it interesting how the CSI determine height from shoe sizes) • Select men and women of various ages. • Measure their heights. • Record their shoe sizes. • Perform simple mathematics (such as mean, mode, standard deviation). • Draw bar charts. • Use the simple mathematics to divide the groups into categories (less than the mean age and greater than the mean age, for example). • Perform further mathematical processes such as chi-squared test and correlation coefficient as appropriate. • Give a detailed discussion of the results. • Talk about the validity of the results and the processes used

Description of successful project 3: • • What are the mathematical patterns for car premiums? Collect information from websites. Dependent variables— amount of premium. Controlled variables—age of driver and accident-free years. Constant—type of car. Quotes were given for different ages and accident-free years. Graphs were plotted—age vs premium, accident free years vs premium, and accident-free years vs age. Model the above graphs with functions (perhaps obtained using the regression features of the GDC) if this is possible. Give a thorough discussion of the results, as well as some comments on the validity.

Description of successful project 3: • • • • The relationship between an elite male tennis player’s height and the percentage of first serves he gets in. Obtain the dimensions of tennis court. Use Pythagoras’ theorem and trigonometry to determine the angle of depression for the tennis ball served from three different heights and just passing over the net. Use the angle of depression to calculate how far from the net each serve will land. Create hypotheses about first serves and whethere is a correlation between height and percentage of first serves in. Research the statistics on the percentage of first serves at a Grand Slam Tournament. Create a table comparing heights with percentage of first serves in. Calculate means. Plot data on scatter graph. Determine type of correlation. Find r. Place data in contingency table. Use chi-squared test for independence (as appropriate). Present results and have discussion on conclusions. Comment on the validity of the results and how the experiment could be improved.

Homework due 27 th March 2017 Fill out the planning form (on Manage. Bac) and upload to the dropbox by 23: 55