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Activity: Forensic formulas

AOs | Indicators | Learning outcomes | Snapshot | Learning experience
Cross curricular | Assessment | Spotlight | Links

Purpose

Students will relate tables, equations and graphs to find relationships in a forensic context.

Achievement objectives

  • NA6-5 Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns.
  • NA6-7 Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns.
  • NA6-8 Relate rate of change to the gradient of a graph.

Indicators

  • Solves problems which can be modelled by linear equations and inequations, quadratic and simple exponential equations, and interprets solutions in context.
  • Uses algebra and graphing for solving linear equations and inequations.
  • Makes connections between representations such as number patterns, spatial patterns, tables, equations and graphs.
  • Understands that change of one variable with respect to another can be represented in various forms such as a table, an equation, or in words.

Specific learning outcomes

Describing forensic data using tables, formulas and graphs.

Diagnostic snapshot(s)

Forensic scientists use formulas like those below to find the height of people from their tibia bone.

MALE FEMALE
H = 81.788 + 2.4t H = 72.64 + 2.5t

Guiding questions:

  • What other information can you get from the formulas in this table?
  • Can you draw a graph of these formulas?
  • What do the formula mean? (gradient? y-intercept?)
  • Why are there two different formulas?
  • How would you go about testing these formulas?

Planned learning experiences

  • Activity: Measuring bones to predict height (worksheet)
  • Students collect own data and test whether the above formulas are true (extensions – children vs adults/amount of data required).
  • Students collect data on radius/humerus bones and generate a formula of their own to predict height.
  • Students compare their formula to the following:
MALE FEMALE

H = 73.66 + 3.0h

H = 80.518 + 3.7r

H = 65.024 + 3.1h

H = 73.406 + 3.9r

  • Recap of drawing linear graphs from formula.
  • Linking gradient of graph to the ‘m’ in y = mx + c to its meaning in this context (use of academic language).
  • Discussion about correlation / scatter plots, leading to linear relationships.

Possible adaptations to the activity

This task is linked to finding models of ‘real-life’ data.

Conjectures about body measurements could also be made from a picture of Vitruvian man, and the link between proportions such as width of the shoulders is a quarter of a person’s height to data and equations such as h = 4 and w = 14h.

The activity could be extended into a look at the body measurements and Vitruvian man from a statistics focus. See  CensusAtSchool: Masterpiece 2; CensusAtSchool: Masterpiece 3.

Cross curricular links

  • Science – Physics AO / AS
  • Art – Use of canons for sculpture

Planned assessment

This teaching and learning activity could lead towards assessment in the following achievement standards:

  • 1.3 Investigate relationships between tables, equations or graphs.

If a statistics focus was taken then the following achievement standard could also be considered:

  • 1.11 Investigate bivariate numerical data using the statistical enquiry cycle.

Spotlight on

Pedagogy

  • Enhancing the relevance of new learning:
    • Encouraging students to explain their thinking.
    • Structuring mathematical discussion and argument.
  • Making connections to prior learning and experience:
    • Checking prior knowledge using a variety of diagnostic strategies.
    • Providing real-life problems in which the context is relevant to students.
  • E-learning:
    • Using technology to explore concepts.

Key competencies

  • Thinking:
    • Students hypothesis, investigate, analyse and evaluate.
    • Students deal with uncertainty and variation, they seek patterns and generalisations.
  •  Using language, symbols, and text link:
    • Students use the language of algebra to communicate and reason.
    • Students use symbols and diagrams to solve problems.

Values

  • Students will be encouraged to value innovation, inquiry, and curiosity, by thinking critically, creatively, and reflectively.

Māori/Pasifika

  • Ka Hikitia
  • Pasifika Education Plan
  • Caution: In some cultures forensic information could be seen as inappropriate, so the context could be adapted to a focus from the Vitruvian Man angle.
  • Exploration of dimensions of sculpture in these cultures would also be a good starting point.

Planning for content and language learning

  • ESOL Online
  • Provide multiple opportunities for authentic language use with a focus on students using academic language:
    • Is the language focus on key language?
    • Do I make sure the students have many opportunities to notice and use new language?

Links

Download a Word version of this activity:

Activity_Forensic formula (Word, 120 KB)

Last updated July 30, 2015



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