Name Semester 2 Major Assessment Task: Basketball Parabola Investigation Subject Challenge Maths Year Level 9 Due Date Conditions Students will get 2 hours of class time and will be given at least a week after this to finish this task at home. Curriculum links Year 9 Patterns and algebra Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (VCMNA306) Linear and non-linear relationships Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (VCMNA311) Year 10 Linear and non-linear relationships Explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital technology as appropriate (VCMNA339) Solve simple quadratic equations using a range of strategies (VCMNA341) Solve equations using systematic guess-check-and-refine with digital technology (VCMNA342) Year 10A Patterns and algebra Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (VCMNA357) Linear and non-linear relationships Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (VCMNA359) Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (VCMNA361) Use function notation to describe the relationship between dependent and independent variables in modelling contexts (VCMNA363) Purpose Students will increase their confidence in mathematical modelling real life scenarios. Students will become more familiar with the key features of parabolas, specifically: turning points, axis of symmetry Students will develop their mathematics communication skills. Marking Rubric Extended Abstract Compares and contrasts actual path of ball from parabola path (dotted and solid line) Explains which key features of parabolas in plan should stay constant and which will change Describes decisions behind method Excludes inappropriate data with reasons Relational Includes coordinates/equa tions of key features of parabolas Multistructural Identifies key features of parabolas Plans method that emphasises independent and dependant variables Calculates average of x and y coordinate of vertex Unistructural Sketches approximate shape of parabolas Writes out a method Prestructural Indicative behaviors Insufficient evidence Drawing parabolas Insufficient evidence Planning Collects 3 vertex data points for each independent variable increment Insufficient evidence Data collection Capabilities Assessment Task Subject Marks: _______ / 20 Comment: Uses appropriate data collected, with justification Explains how the constants in turning point form of a parabola effect the shape of a parabola Demonstrates understanding of the meaning of the solutions that make a quadratic =0 Finds turning point equation for all 5 independent variable increments States turning point of parabolas Synthesises results and method to discuss factors that affect results Explains recommendation to basketball team using evidence Uses evidence to make a conclusion Identifies factors that affect the shape of parabolas Insufficient Insufficient evidence evidence Understanding Use of of quadratic mathematical features reasoning Communication Problem solving Basketball parabola investigation Year 9 Challenge Mathematics calculated from the above rubric, one mark per criteria Basketball Parabola Investigation Introduction: In our Parabolas unit we are looking at how gravity affects the path of a moving object. Your task is to design an experiment to investigate ONE of these factors (release distance from hoop, release angle, release force, release height) and how it affects the vertical and horizontal distance from the shooter’s hands to the vertex of the parabola. This is to help coach the basketball team on how to more consistently get their shots in. Aim: to investigate how (circle one independent variable: release distance from hoop, release angle, release force, release height) affects the coordinates of the vertex of a basketball shot (when aiming to get it in), and therefore how this independent variable affects the turning point equation of the quadratic. Getting knowledge ready: what do we already know about parabolas? Roughly sketch some parabolas below and indicate their key features. Hypothesis: as (independent variable) increases, the coordinates of the vertex of the parabola that the basketball traces out will (describe changes in x and y coordinate of vertex)… Draw some sketches of parabolas (at least 3) to represent how you predict the independent variable will affect the shape of the parabola path. Method: Work in groups of 4 (one shooter, one cameraperson, one ball gatherer, one ruler holder) Choose your independent variable, and what 5 increments of it you will use (which distances, which heights, which angles, etc) Try to make sure that all other variables are kept constant for a fair experiment (only change the independent/experimental variable). Decide what these variables will be and how you will ensure they stay constant. Mark out where you will be shooting from with masking tape Mark out where the cameraperson Film shooting 3 shots (in) for each change in independent variable, keep the camera steady Watch video to obtain approximate turning point for each shot Write out your method step by step, with your independent variable in mind: Equipment: 1 basketball 1 meter ruler 1 video camera (phone is fine) A makeshift tripod to hold the camera still A basketball hoop Masking tape Optional: chair (careful), protractor, trundle wheel On top of the required equipment our group will also need: Draw a diagram of your setup, including a sketched, hypothesised parabolic path with the key features of a parabola: Draw a diagram of a hypothesised parabolic path overlaid onto a Cartesian plane with an appropriate origin (recommended origin = shooters feet) and hoop coordinate. Results (keep going until you get 3 shots in for each variable): Indepen dent variable (distanc e, angle, force, height) Trial 1: vertex Coord (x,y) In/out/ BB? Trial 2: vertex Coord (x,y) In/out/ BB? Trial 3: vertex Coord (x,y) In/out/ BB? Trial 4: vertex Coord (x,y) In/out/ BB? Indepen dent variable (distanc e, angle, force, height) Trial 5: vertex Coord (x,y) In/out/ BB? Trial 6: vertex Coord (x,y) In/out/ BB? Trial 7: vertex Coord (x,y) In/out/ BB? Trial 8: vertex Coord (x,y) In/out/ BB? Indepen dent variable (distanc e, angle, force, height) Trial 9: vertex Coord (x,y) In/out/ BB? Trial 10: vertex Coord (x,y) In/out/ BB? Trial 11: vertex Coord (x,y) In/out/ BB? Trial 12: vertex Coord (x,y) In/out/ BB? Indepen dent variable (distanc e, angle, force, height) Trial 13: vertex Coord (x,y) In/out/ BB? Trial 14: vertex Coord (x,y) In/out/ BB? Trial 15: vertex Coord (x,y) In/out/ BB? Trial 16: vertex Coord (x,y) In/out/ BB? Did you have to omit any data collected? (think about a fair experiment) If so, leave it in the table/s above but put a line through it or colour code it. Give reasons for omission in data analysis. What criteria did you use to keep or “discard” data? Analysis: Independent variable Average Average Range Range vertex x vertex y vertex x vertex y coordinate coordinate coordinate coordinate (in) (in) (in) (in) Independent variable Average Average Range Range vertex x vertex y vertex x vertex y coordinate coordinate coordinate coordinate (BB) (BB) (BB) (BB) Independent variable Average Average Range Range vertex x vertex y vertex x vertex y coordinate coordinate coordinate coordinate (out) (out) (out) (out) Discuss the average and range of the vertex coordinates as the independent variable changes (what is the trend?) Were you able to keep all other variables constant or did you have to change them to be able to get the ball into the hoop? What other factors could have affected your results? What mistakes did you make if any, how would you change it next time? What assumptions have been made? Graph your 5 parabolas that have the maximum at the average vertex coordinates recorded for your “in” shots (all on the same grid is fine). For each of the above parabolas record the following information: These Desmos links may be useful: “Basketball Shot Quadratic”: https://www.desmos.com/calculator/zeqvbnno9m “Parabola equation from 3 points”: https://www.desmos.com/calculator/elssfphm2p Parabola Release height (yint) 1 Vertex (h,k) Axis of symmetry x=c Equation for turning point form y=a(x-h)2-k 2 3 4 5 Investigate (could use sliders on Desmos links above or otherwise) how each of the constants (a, h, k) affect turning point form. Explain your findings. Choose one of the parabolas from the table above, expand the bracket (using your knowledge about binomial expansion, show working). Apply the quadratic formula to solve for x when the quadratic = 0 (may need to do some research). What is the significance of the result/s? Conclusion (summarise results, ensure you have agreed or disagreed with your hypothesis and “answered” your aim): What advice would you give to the basketball team to ensure they get more shots in?