Te Kete Ipurangi
Communities
Schools

### Te Kete Ipurangi user options:

Activities:

Activities:

Maths activities:

Stats activities:

# Activity: Forensic formulas

## 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 + 3.0hH = 80.518 + 3.7r H = 65.024 + 3.1hH = 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).

### Possible adaptations to the activity

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.

• 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:

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

## 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 -  The ESOL Principles
• 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?