Galbraith Stillmans Modelling Framework Purpose Discuss modelling process

Galbraith & Stillman’s Modelling Framework

Purpose • Discuss modelling process & numeracy knowledge • Give you an idea about how your students might go about solving this problem • Give you ideas for how you could adapt this question for your students

Understanding the Problem • Messy Real World Situation (A) Real World Problem Statement (B) • Define key terminology: In this context. . Circulation = copies sold NOT copies produced

Devising a plan • Real World Problem Statement (B) Maths Model (C) • Information we needed to research: – Circulation figures of the Townsville Bulletin – A relationship between newspaper produced and the number of trees required to produce it – Composition of the paper: new and recycled?

Carrying Out the Plan Problem Statement (B) Maths model (C) Maths Solution (D) • Circulation figures from the Townsville Bulletin • Composition of paper: totally new!

Carrying Out the Plan • A relationship: 12 full-grown trees produce 1 tonne of virgin newsprint OR (as a rate) 12 trees PER tonne of virgin newsprint OR (as a ratio) 12 trees : 1 tonne of virgin newsprint • Newsprint described in terms of mass…

Key Assumptions • the weight of the ink on the paper was negligible • the inserts (such as catalogues) were included as a part of the newspaper itself • the inserts were made of the same material as the newspaper • The mass of newspapers does not vary much from weekday to weekday or weekend to weekend average a good representation

Contextual and Strategic Knowledge which impacted our Maths Model • The weekend bulletin is generally much heavier than the weekday bulletins • Separate averages should be taken for the weekend bulletin and weekday bulletins

The Maths Model (C) • Please refer to the big green box in the right hand corner of your handout for our mathematical model • Quite straightforward basically scaling up the average mass we found

The Maths Solution (D)/ Real World meaning of (E) • A range: 17, 613 trees – 18, 586 trees • The Townsville bulletin requires between 17, 613 and 18, 586 full-grown trees to produce the complete circulation in a year. • Extend in report section (G): how long does a it take for a tree to be classed as fully grown? How often and how many trees need to be planted to keep up with the demand of the TB?

Evaluation/Report (F) • Our method was logical • The number of trees was not ridiculously high a million trees would have been unrealistic • 0. 73 x 75 = 54. 75% of a tree is fibre • Comparison between other papers