[Note: GERMAN versions of the Week 1 tasks are available HERE. I welcome suggestions on how to improve the translations!]
In this week's tasks we express fractions as parts of a line segment. We make use of the notion of equal intercepts which provides a way of partitioning a line segment into any desired number of equal parts. (The notion is fundamental to understanding geometric similarity and enlargement, though that is not the focus of these tasks.) There was a time when students would have met a theorem on equal intercepts, as in this geometry text book first published in 1937.
from Latimer and Smith (1956 edition), A Course in School Geometry. Harrap & Co, London.
Monday: The purpose of this task is simply to introduce the notion of equal intercepts. It is fairly obvious that the equally-spaced parallel green lines cut the given radius into 3 equal parts, so AB = 6cm.
Tuesday: We are told AB = 6cm. So we can compare AB to AC by finding the length of AC which is ⅝ of 9cm = 5⅝cm. So AB is longer.
We can also take a more direct approach by just comparing the fractions ⅔ and ⅝. Some students might do this formally by expressing both fractions as 24ths, but there is also scope for making sense of the fractions in a less formal way. For example, some students might notice that ⅔ is 5/7½, and so is greater than ⅝. Or they might compare the two fractions to ½: one is ½/3 or ⅙ more than ½; the other is only ⅛ more than ½.
Wednesday: This task involves quarters and eighths so students are likely to draw on some knowledge, formal or informal, of equivalent fractions.
Starting at point
A, the green parallel lines cut the red line segment a quarter of the
way along, 2 quarters along and 3 quarters along. Point D is midway
between the latter two points, which can be described as 2½ quarters of the way along, or halfway plus an ⅛ of the way along, or ⅝ of the way along.
Starting at point
A, the green parallel lines cut the red line segment a quarter of the
way along, 2 quarters along and 3 quarters along. Point D is midway
between the latter two points, which can be described as 2½ quarters of the way along, or halfway plus an ⅛ of the way along, or ⅝ of the way along.Thursday: Here we are back to finding specific lengths rather than comparing fractions per se.
Friday: Here we compare different fractions of the radius of 9 units (or 9cm).
