Tasks | Early Adolescence | Change of Scale & Origin

Tasks - Years 10, 11 & 12

Change of Scale & Origin   by Thelma Perso, Senior Curriculum Officer Mathematics

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Chance & Data	Understand Chance Collect and Organise Data Summarise and Represent Data Interpret Data
Working Mathematically	Mathematical Strategies Apply and Verify
Expected Outcomes:	Students learn the effect of changing the scale and origin on the mean and standard deviation.
Context:	Year 9,10, Foundations of Mathematics, Discrete Mathematics.
Learning Activities/ Experience:	Enter the following data as x : 5, 3, 6, 9. 8. 12.2 Find the   x ________   x ________ (std. dev.) Change the Origin Now add 3 to each of the scores. Return to the home screen, then 3  +  L1  STO  L2  ENTER What is the new mean?   y ________ new std. dev. ?  y= ________ What do you notice? Change the Scale Now multiply each of the original values by 10. Return to the home screen, then 10  +  L1  STO  L2  ENTER What is the new mean?   y ________ new std. dev. ?  y= ________ What do you notice? As a result of what you have discovered predict the mean and standard deviation if- a) 8 is subtracted from each score   x ______ x ______ b) each score is multiplied by 4   x ______ x ______ Use your calculator to see if you are correct. Can you generalise your findings? What do you think might happen if you change the scale and the origin? Predict the new mean and standard deviation if you add 7 to each score and, at the same time, divide each score by 10. New mean? __________ New standard deviation? __________ Use your calculator to check whether you are correct.
Resources:	TI 82 , 83 Graphics Calculators.