1a.+Arithmetic+-+Teachers

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Textbook Analysis Lesson Ideas

Textbook Analysis

 * **Fitzpatrick**Chapter 1
 * Excellent presentation of real number concepts (the best, most accurate Venn diagram).
 * Geometric approaches to generation of surds on the real number line.
 * **Grove**Chapter 1
 * Lots of revision for those who haven't mastered Stage 4 arithmetic.
 * Inaccurate and misleading Venn diagram of numbers. //(Can you spot at least 3 mathematical and pedagogical problems?)//
 * Inadequate coverage of rational, irrational and real number concepts for Extension 1 students. A naive approach which does not prepare students for tertiary mathematics.
 * **Jones & Couchman**3U Book 1, Chapter 1 & 2
 * Dry and mechanical, but covers the material.
 * Nice clear explanation of working out scientific notation.
 * Does not cover rational, irrational and real number concepts.
 * **Pender**3U Chapter 2
 * Proofs of irrationality of sqrt(2) provided. Exercises extend the idea to other numbers.
 * Fundamental concept of **closure** discussed - which really is something that Extension 1 students should be wondering about.
 * Discussion of number theory issues which would appeal to more advanced students.
 * Only textbook to examine equality of surdic expressions.

Lessons from "Improving Learning in Mathematics"
The Mostly Number series has several lesson plans directly relating to this topic:
 * N2 Evaluating statements about number operations
 * N11 Manipulating surds
 * N12 Using indices

Irrationality of Pi

 * This short sequence from Marcus du Sautoy's BBC series "The Code" explores the irrational nature of pi: @http://www.youtube.com/watch?v=fHxY41iDvzs. (The Code, Episode 1. Full pi sequence 24:30-34:30, animation 33:30-34:30)
 * @http://unihedron.com/projects/pi/A digital poster of Pi to 370,000 decimal places you can zoom in and out of

Exploring Surds

 * **Finding sqrt(2) on the number line**
 * **The Wheel of Theodorus**


 * **Exploring square root of 2 with A4 paper**. Students could measure the dimensions to find the ratio, fold the paper in half and explore the ratio of the resulting half page (now A5). A little algebraic modelling will explain why sqrt(2) is required. See the wikipedia page @http://en.wikipedia.org/wiki/ISO_216

Thinking about Number - the Strogatz articles
Steven Strogatz, professor of applied mathematics at Cornell University wrote an excellent 15-part series on mathematics for the New York Times in 2010. Beginning with a column on why numbers are helpful, he considers topics including negative numbers, calculus and group theory, finishing with the mysteries of infinity. The first four in the sequence are excellent background for quality engagement with the Arithmetic topic, with many references to important works in the mathematics literature some students may wish to follow. PDF versions of most of the articles are available on the website and could be given to students as supplementary reading.
 * From Fish to Infinity http://opinionator.blogs.nytimes.com/2010/01/31/from-fish-to-infinity/ features the wonderful "Fish, fish, fish" video.
 * Rock Groups @http://opinionator.blogs.nytimes.com/2010/02/07/rock-groups/
 * The Enemy of my Enemy http://opinionator.blogs.nytimes.com/2010/02/14/the-enemy-of-my-enemy/
 * Division and its Discontents @http://opinionator.blogs.nytimes.com/2010/02/21/division-and-its-discontents/

An index to the full set of articles is at []

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