Introduction to proportional reasoning

The following exercises don't require to know any complicated formulas or equations. Instead, they are supposed to be solved (but it's not the end target) with your free thinking. Make drawings!

1. Better the sea or the mountain? (ratio problem).
Download: PDF (176 KB)

2. The jewels in a crown (ratio problem).
Download: PDF(176 KB)

3. What is Proportional Thinking? (An exercise to make you think! No Maths required)
Download: PDF(281 KB) - with kind permission of the authors, Dirk de Bock, Wim Van Dooren and Lieven Verschaffel, Catholic University of Leverkusen, Belgium.

Pre-algebra

Fraction models (an internal link to some exercises on fractions)

STUDY AND RESEARCH IN MATHEMATICS

601. The first thing to be attended to in reading any algebraic
treatise is the gaining a perfect understanding of the different
processes there exhibited, and of their connection with one an-
other. This cannot be attained by the mere reading of the book,
however great the attention which may be given. It is impos-
sible in a mathematical work to fill up every process in the man-
ner in which it must be filled up in the mind of the student before
he can be said to have completely mastered it. Many results
must be given of which the details are suppressed, such are the
additions, multiplications, extractions of square roots, etc., with
which the investigations abound. These must not be taken on
trust by the student, but must be worked out by his own pen,
which must never be out of his own hand while engaged in any
mathematical process. DE MORGAN, A.