Reference Material

Others in the network have found useful information and support in these sources.
If you discover useful material not listed here, please email the information to:
doug@blackdouglas.com.au

• Maths300 is mounting the most interesting 300 maths lessons which can be found to stimulate discussion about what makes a better maths lesson. Many of the lessons are supported by specially written software.

  All lessons on the site aim to develop the process of Working Mathematically. The following lessons from that site directly relate to the Calculating Changes objective of enhancing children's number sense. In fact, some of the ideas in these lessons were contributed by Calculating Changes schools.

  In addition, Poly Plug is an excellent concrete material for exploring many of these lessons and other investigations. You can find those ideas through Poly Plug & Tasks which is also listed on the Members' Activities page.

  Lesson 9: First Principles Percent Lesson 10: Bob's Buttons Lesson 15: Calculator Walk Lesson 26: Highest Number Lesson 32: Walk The Plank Lesson 33: Estimating Fractions Lesson 34: What's My Rule? Lesson 35: Nine & Over Lesson 43: Area of a Circle Lesson 45: Circumference of a Circle Lesson 49: Making 1000 Lesson 52: Multo Lesson 62: 4 & 20 Blackbirds Lesson 66: Dominoes Lesson 69: Football Ladder Lesson 70: Pick A Box Lesson 71: Eureka Lesson 72: Fraction Magic Square Lesson 76: Protons & Anti-Protons Lesson 77: Rectangle Fractions Lesson 78: Row Points Lesson 84: Number Charts Lesson 87: Make A Million Lesson 89: Red & Black Card Game Lesson 93: Playing With Patterns Lesson 94: Trial, Record & Improve Lesson 95: Domino Trails Lesson 96: Take Away Of The Day Lesson 97: Tackling Times Tables Lesson 98: Magic Squares Lesson 99: What's It Worth? Lesson 101: Odds & Evens Lesson 103: Palindromes Lesson 104: Factorgrams

  Lesson 105: Goldbach's Conjecture Lesson 114: Find My Pattern Lesson 122: How Many People Can Stand? Lesson 126: Make A Moke Lesson 128: Cars in a Garage Lesson 141: Jumping Joey Lesson 142: Maths In Motion Lesson 144: Rod Mats Lesson 145: Estimating Averages Lesson 146: Division Boxes Lesson 150: Fermi Problems Lesson 156: Chart Strategies Lesson 158: Goods & Bads Lesson 161: Dice Footy Lesson 162: Multiplication in a Table Format Lesson 167: Twelve Days of Christmas Lesson 168: Truth Tiles 2 Lesson 169: Human Computer Lesson 173: Factors Lesson 174: Cookie Count Lesson 175: Dice Cricket Lesson 176: Counting Machines Lesson 178: Tables For 25 Lesson 181: Natalie's LCM Task (LCM = lowest common multiple) Lesson 182: Fractions to Decimals (on a rope!) Lesson 183: Snakes & Ladders Lesson 186: Addo Lesson 187: Times 99 Lesson 189: Four Piles Problem Lesson 191: Fractions & Fraction Charts Lesson 192: Number Partitions (Ramanujan's Problem) Lesson 193: Dice Basketball

• NRICH is one of the world's top mathematics education sites. NRICH leaders Lynne McClure and Liz Woodham were introduced to Poly Plug at a conference workshop. As a result they developed and trialed the Poly Plug activities below.
  Each activity includes teachers' notes, a Flash interactive that can be run on your electronic whiteboard directly from the site and various print materials.
  • All Change
    Three levels of interactive challenge. For Calculating Changes Members this activity NRICHes Fill The Board.
  • Spot Thirteen
    A variation of Task 9, Row Points, which is probably best used as an introduction to the task.
  • Poly Plug Pattern
    Extends a pattern beyond one board. Vicky's Problem from the Calculating Changes Free Tour could be an introduction to this activity. Also, CCh Members could build a pattern unit using these ideas and Pattern Boards, Rory's Pattern Game and Uncover Counting
  • Poly Plug Rectangles
    This is a variation and extension of Task 114, Where Is The Rectangle?, which offers several levels of challenge in the Teachers' Notes and video from classrooms. The activity is also related to Poly Plug Battleships and Copy Cats in the CCh Free Tour.

The research of the Calculator Aware Number (CAN) Project is a cornerstone of Calculating Changes. It is documented in several ways on this site. The other research listed here provides additional support. In particular this information may be valuable in educating your school community about the objectives of Calculating Changes. For example, with appropriate reference, excerpts could find a place in a sequence of school newsletters.

• Young Children and the Teaching of Algorithms: What Does Research Show?
  Doug Clarke
  Associate Professor
  Mathematics Education
  Australian Catholic University (St Patrick's Campus)

• Groves, Susie & Cheeseman, Jill Young Children Using Calculators, Deakin University
  Contact
  Deakin University Library, Burwood, VIC, 3125
  Phone: +61 3 9244 6200
  Email: Library Information

• Groves, S. et al Calculators in Primary Mathematics: The Newsletters, Deakin University
  Contact
  Deakin University Library, Burwood, VIC, 3125
  Phone: +61 3 9244 6200
  Email: Library Information

All Paul Swan books can be accessed from his site.