Mathematics proficiencies

Understanding / Fluency / Problem-Solving / Reasoning

Year 10

Statistics and probability: Baffling box plots

Summary of task

From a given set of information about two footballers, students were asked to determine which footballer was more worthy of a reward. Students had to provide justification for their decision.

Proficiencies

At this year level understanding includes applying the four operations to algebraic fractions, finding unknowns in formulas after substitution, making the connection between equations of relations and their graphs, comparing simple and compound interest in financial contexts and determining probabilities of two- and three-step experiments.

At this year level fluency includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using calculations to investigate the shape of data sets.

At this year level problem-solving includes calculating the surface area and volume of a diverse range of prisms to solve practical problems, finding unknown lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find solutions to simultaneous equations and inequalities and investigating independence of events.

At this year level reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media statements and interpreting and comparing data sets.

1 Fluency
Represents a larger interquartile range and smaller range for Loyd than for Franklin following appropriate choice of lower quartiles and minimum values 2 Understanding
Chooses and represents appropriate upper quartile for Loyd and appropriate maximum value (‘best season’) for Franklin that is higher than maximum value for Loyd 3 Understanding
Represents upper quartile for Franklin and represents median for Loyd and for Franklin 4 Reasoning
Explains location of medians, and upper quartile for Franklin, and chosen locations of upper quartile for Loyd, maximum values, lower quartiles and minimum values through annotations on the boxplots

  • Annotations

  • 1
    Fluency
    Represents a larger interquartile range and smaller range for Loyd than for Franklin following appropriate choice of lower quartiles and minimum values
  • 2
    Understanding
    Chooses and represents appropriate upper quartile for Loyd and appropriate maximum value (‘best season’) for Franklin that is higher than maximum value for Loyd
  • 3
    Understanding
    Represents upper quartile for Franklin and represents median for Loyd and for Franklin
  • 4
    Reasoning
    Explains location of medians, and upper quartile for Franklin, and chosen locations of upper quartile for Loyd, maximum values, lower quartiles and minimum values through annotations on the boxplots
1 Reasoning
Compares the two boxplots and justifies the choice of more consistent player by referring to the difference in range 2 Reasoning
Compares the two boxplots and justifies the choice of inductee by referring to the difference in median and the difference in maximum value

  • Annotations

  • 1
    Reasoning
    Compares the two boxplots and justifies the choice of more consistent player by referring to the difference in range
  • 2
    Reasoning
    Compares the two boxplots and justifies the choice of inductee by referring to the difference in median and the difference in maximum value