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News

April 2022

In this edition of the News you will find:

Red Square  A School Without Tasks ...

Red Square  Learning from Homeschooling

Red Square  Calculating Changes

Red Square  Unit Plans

Red Square  Working With Mathematics Centre

Red Square  Get to Know a Cameo
     ... Same or Different
     ... Two Squares

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  • A School Without Tasks ...

    A school without tasks ... is like a school without books.

    Students select books to explore literature and develop language concepts and skills in context. < > Students select tasks to explore mathematics and develop mathematical concepts and skills in context.

     

    Teachers select one book as a whole class adventure to challenge and extend students. < > Teachers select one task as a whole class adventure to challenge and extend students.

    The context for school mathematics is learning to work like a mathematician.

    Welcome to

    • Joanna Klonaris (Tasmania)
    • Andrea Wilson and Helen Shepherd (Victoria)

    who in the past month have joined the many teachers who are building their own, or their school's, Task Library supported by the eTask Package.

    • Tasks are an invitation to a pair of students to practise working like a mathematician.
    • Tasks resource teachers to model working like a mathematician within a whole class investigation.
    • Tasks encourage the development of concepts and skills in a problem solving context.

  • Learning From Homeschooling

    Johanna Buijs has been homeschooling for 20 years.
    I require of my children attention to learning, but I don't feel the need to 'keep up'. I've been doing this long enough to realise that pushing a child faster than what they are understanding creates maths anxiety. We take a slow and steady approach now and I feel my younger children are benefitting from that and are definitely not falling behind in the process.
    In recent times Johanna has been using various activities from Maths At Home. At the end of March she contributed a wonderful compilation of her children's work to the Maths At Home version of the Garden Beds task.

    Hi Doug,
    Just popping into your inbox to say thanks for another great activity. The children and I had fun with Garden Beds today...
    The photo is one of several Johanna has included, along with details of conversations with and between her children and a description of her learning objectives, environment and teaching craft.

    If you teach anywhere from Year 2 to Year 8 you are encouraged to take a few minutes to visit this activity and seek out Johanna's contribution in the Gallery near the end. You will be surprised ... and perhaps inspired to consider, or reconsider, the place of this investigation in your curriculum. See Link List below.

    If you also spend time following the links in the activity you are guaranteed to discover something else about it that you hadn't thought of - even if you use it regularly.

  • Calculating Changes
    If you are a primary teacher have you made time to explore Calculating Changes?
    Calculating Changes has been engineering 'aha' moments in number for more than 25 years and continues to:
    • develop the pedagogy of Threaded Activities to...
    • engineer 'aha' moments in number K - 8 thereby...
    • enhancing children's number sense, concepts & skills so that...
    • they have a more powerful tool kit for working like a mathematician and...
    it is entirely built on contributions from classrooms.

    • Begin your exploration from the Calculating Changes in Brief link. (See Link List below.)
    • Make sure to follow the links within it that explain Threading, a unique pedagogy developed by Calculating Changes teachers.
    • The Home button at the top left of every page will take you to the main Calculating Changes index.

  • Unit Plans

    • There are many ways to structure the use of books from the book library into the language curriculum.
    • There are many ways to structure the use of tasks from the Task Library into the mathematics curriculum.

    Ten different ways are explained in detail in the link Integrating Tasks Into Unit Plans.
    See Link List below.

    • Some are plans for a lesson or two.
    • Some are plans for one, two or three weeks.
    • Some include alternative assessment practices.
    • All have been designed and developed by teachers in classrooms.
    • All are built on conscious, deliberate teaching craft choices.
    • All contribute to the development of student literacy - oral and written.

    There is something in this collection for every level of school - even Year 12. We first found the structure called Pass On Problem Solving in a Year 12 class where it was being used to train for exams using questions from past papers.

    Did you know?

    • Maths With Attitude eManuals provide 25 weeks of integrated, varied, flexible unit plans across all content strands and all year levels from Year 3 to Year 10.
    • Working Mathematically with Infants provides 20 weeks of detailed, flexible scope and sequence planning in number for each year level K - 2.

    See Link List below.

  • Working With Mathematics Centre

    We have been building Mathematics Centre for over 25 years. That's why there's so much stuff. But how do you find the stuff you need?

    • One way is to use the Search Box in the banner at the top of the Home Page.
      Try it from the home page in the Link List below.
      For example, type Triangle Numbers,
    • Another way is to print and/or save on your desk top the one page document titled Working With Mathematics Centre in the Link List below.
      It lists in categories the URLs of key pages.

  • Get to Know a Cameo

    Task 18, Same or Different
    This magnificent task is an unusual experiment which explores the concept of fairness from Year 4 on. At the other end of schooling it strikes at the heart of several content areas in Years 11 and 12. The experiment is simple to set up: a bag containing a certain number of blocks in two colours, two players and a game. The rules of the game are:
    • Players take turns to take a block from the bag.
    • In advance players have decided that one will always get a point if the blocks are the same colour; the other always gets the point when the colours are different.
    • Blocks are replaced and the game is repeated until the data indicates whether the chosen combination of colours is a fair or unfair game.
    The card makes it clear that there are only two fair games in all the possible combinations of two colours up to (6, 6). The challenge is to find them. The task gets richer when the fair games are discovered because they hint that this random experiment is governed by a special set of numbers.

    The cameo is a must read for Senior Secondary School teachers because Damian Howison has contributed commentary, lesson notes, slides and spreadsheets which detail how the task, in its whole class investigation life, extends into triangle number patterns, using combination theory to calculate probabilities, complementary probability, statistical inference from data and more in both his Year 11 and Year 12 classes. Further, the overriding objective of both lessons is continuing to learn to work like a mathematician.

    In the eTask Package this task is in the 'easy' set because it only needs 12 blocks, six in each of two colours, and an opaque bag.

    Task 57, Two Squares
    Calling on spatial perception and measurement skills, this task opens the door to the classic algebra rule a2 - b2 = (a - b)(a + b). The experiment is about placing one size square on top of another and calculating the uncovered space. The context of the experiment is the mathematician's question, Can I check this another way?. The discovery is that there is more than way to do the calculation - in fact there are several ways - and all are the result of subtracting the area of one square from the other; that is, the difference between the two squares. So the classic rule is only one way to evaluate the difference between two squares, which begs the question Why have mathematicians chosen that classic form?. Comparing the various calculation methods suggests an answer to that question too.

    There are two bonuses in the Cameo. First it records the approach of two teachers from St. Mary MacKillop College, Swan Hill, exploring the task in a workshop, who developed a numeric, rather than geometric, verification of the classic rule. Second is a link to a freely available Picture Puzzle which places the development of the classic rule in the context of a broader exploration of Square Numbers.

    In the eTask Package this task is in the 'easy' set because it only needs 3 durable squares of the given sizes, which can be easily cut from MDF or similar.

Keep smiling,
Doug.
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. Encouraged By Colleagues
    2. Crate Cubes
    3. Get to Know a Cameo
      ... Four Cube Houses, Tables For 25

Did You Know?

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