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News

October 2020

In this edition of the News you will find:

Red Square  Two Testimonies

Red Square  4 Free Picture Puzzles

Red Square  More MAH Activities

Red Square  Victorian Teachers

Red Square  Get to Know a Cameo
     ... Doug's Tablecloth
     ... Plate Triangles

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  • Two Testimonies

    Calculating Changes Pot Boiler

    Pot Boiler is the eNews from our Calculating Changes network.

    "Loved the MAH issue - beautifully and compellingly written."

    Charles Lovitt
    Mathematics education consultant and author

    See Link List below for a copy of this Pot Boiler issue as a PDF. Calculating Changes has contributed significantly to Maths At Home, which has now become Maths At Home At School as described in the newsletter.

    Working Mathematically with Viruses

    "It's great to see this being used as a teaching example - I wish I had known about the applications of maths when I was at school."

    Allen Cheng, MB BS, FRACP, MPH, MBiostat, PhD
    Professor of Infectious Diseases Epidemiology
    School of Public Health and Preventive Medicine, Monash University

    See Link List below to explore the activity. There is much to learn from the COVID crisis when your curriculum is focussed on learning to work like a mathematician.

  • 4 Free Picture Puzzles

    All 36 Picture Puzzles are based a teaching model of one screen, two learners, concrete materials and a challenge. Each challenge is presented as a slideshow with more pictures than words. As each slide is tackled the learner is led deeper into either an investigation or a concept building experience.

    The Free Tour has always offered two complete slideshows - Square Numbers and Sphinx Shapes - with full, detailed teaching notes.

    Recently we have added two more and embedded them as the main teaching craft model in their companion Maths At Home activity. You now have access to the Picture Puzzle and a lesson sequence already planned for you. The two new Picture Puzzles are:

    • Garden Beds
      - a practical hands-on understanding of all the main algebra sections of a text book.
    • Rows, Rectangles and Multiplication
      - students become efficient and effective users of long multiplication.

    See Link List below for Picture Puzzles. Take the Explore Free Tour link from the home page.

  • More MAH Activities

    New activities added in October are:

    • Rectangle Fractions Game (4 - 8): a game for two players and a partner to the activity Rectangle Fractions. It refreshes fraction concepts and develops addition and subtraction skills using a hands-on, straightforward game. Learners first play with a whole rectangle for which playing cards have been provided. They explore several rounds of the game, each of which only takes a few minutes to play. Then they chose their own whole rectangle size and make corresponding playing cards from the blanks supplied. As always keeping a journal is an important part of the activity. Once the game is learned it can be returned to many times, each time facing a new challenge by choosing a new whole rectangle. (This activity was sourced from Calculating Changes.)

    • Less Than Fractions (4 - 10): Number tiles (1 - 9) allow learners to experiment with fractions less than 1 in a hands-on, non-threatening, open-ended way. Early success is guaranteed because there are 36 possible answers and the obvious one is 1/2. The greater challenge is to add two fractions (each tile can be used only once) and still get an answer less than one. Again there are many ways to do this so every learner will find some success. However, a mathematician would ask: How many solutions are there? How do you know when you have found them all? and the opportunity to do this is offered. The activity involves comparing fractions to discover which one is less. That skill is explored further in three ways, one of which was invented by a Year 5 student. (This activity was sourced from eTasks.)

    See Link List below for the Maths At Home activity library. Scroll down or use Ctrl F to search a title.

  • Victorian Teachers

    We keep asking and some have responded. Has your email address been changed yet? If you want to keep receiving these messages you will need to let us know your new address. Just drop a line to doug@blackdouglas.com.au

  • Get to Know a Cameo

    Task 3, Doug's Tablecloth
    Based on a real experience, a piece of cloth of particular size has to be folded to fit into a drawer. Yes that's all that the problem involves, but it can be frustrating because the extra condition is that it must fit the known depth of the drawer exactly.

    The more or less automatic response for most people is to fold in half and half again and so on until it fits. Then they unfold and try again when it doesn't. Some do solve the problem using this trial and improve approach, but extra information about the number of folds and the number of thickness of folded material is given to assist thinking the problem through more deeply. It is designed to help learners to make use of a working backwards approach.

    When the solution is found, the What happens if ...? question is What measurement must the unknown side of the cloth have to be in order to fit the width as well as the depth of the drawer?. When that is done, the whole piece of cloth has been folded into equal parts, so the door is open to explore fractions of the whole found in the rows, columns and cells created by the creases.

    In the eTask Package this task is in the 'extra work' set because there is an extra card to print and laminate before cutting in two.

    Task 28, Plate Triangles
    Paper plates are laid out on the floor as an equilateral triangle. Counting plates in each row generates the Natural Numbers. Counting the total of plates from the beginning to the current row generates the Triangle Numbers. Once those two patterns are discovered the investigation goes further.
    • If I tell you any size triangle, can you tell me the number of plates in the longest row?
    • If I tell you any size triangle, can you tell me the total number number of plates in the whole triangle?
    The task can also be used to introduce, or reinforce, the use of spreadsheets.

    A second direction in the task introduces an arithmetic puzzle something like a magic square. Number discs are provided and are placed one to a plate in a Size 3 triangle. The challenge is to place them so the total is the same along all three sides. If you solve it for one set of 6 numbers, do it with another, and another and... Is there anything to discover about the sets of numbers that solve the puzzle?

    In the eTask Package this task is in the 'easy' set because paper plates and appropriate counters are easy to find in most schools.

Keep smiling,
Doug.
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. Working Mathematically with Viruses
    2. 3 New Cube Tube Videos
    3. Little Treehouse Book Collection
    4. Victorian Teachers
    5. Get to Know a Cameo
      ... Number Tiles, Garden Beds

Did You Know?

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