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News

September 2021

In this edition of the News you will find:

Red Square  Maths At Home Update

Red Square  Rhonda's Quilt

Red Square  Those B___y Times Tables

Red Square  Get to Know a Cameo
     ... Intersections
     ... Money Money Money

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  • Maths At Home Update

    Three new activities during September so there are now 72 activities in the learners' library, and among them, something for everyone. They are designed to support you in providing home learning during school closure. Many learners will be able to work independently directly from the web page. Adult involvement is assumed for the very young, or those who find learning difficult. When we return to eye contact learning the Maths At Home the content, teaching craft and structure of the activity notes will be easily adapted to the whole class setting or homework projects.

    • Princess Catharina's Gold Rings (4-10)
      ... Princess Catharina has twelve gold rings. She keeps them in a three drawer trinket box with a top drawer, a middle drawer and a bottom drawer. Each ring is made with a different number of grams of gold. The Princess loves maths, so she makes a puzzle for the servant who has to look after the rings. The rules of the puzzle explain which drawer each ring goes in. The servant loves it, because it turns out there is more than one way to use the rules. Life is never boring with this Princess.

    • Cube Nets (2-10)
      ... A mathematician loves it when there is more than one answer to a problem and that is exactly the case in this activity. Teachers love it too, because it means there are more ways for a learner to be successful. The starting point is a definition of a net in mathematics and identifying collections of six squares that do and don't make the net of a cube. Then, having made their first cube from a net provided, learners are introduced to a mathematical playground on the web called PolyPad. It's freely available and provides tools to aid the search for all the cube nets. Learners can efficiently make nets on screen and use the built in tools to find out if the nets become virtual cubes. Throughout the activity learners are working like a mathematician and being encouraged to imagine, predict and test.

    • Ainsley and the Planting Problem (3-9)
      ... This problem is perfect for learning to work like a mathematician. It contains very little 'text book' mathematics - single digit mental arithmetic mostly - but it also contains opportunity after opportunity to display and develop higher order thinking skills, which are the most important part of a mathematician's work. The problem is embedded in a story shell about planting a garden so that each of three children can look after one plant for each year of their age. It encourages drawing a diagram, making a model, looking for the limits in a problem, breaking a problem into parts and trying every possible case. We first learned of the problem through one child's Year 3 remote learning maths class and the activity includes some of that child's reasoning. The problem grows from there to provide plenty of challenge for a broad range of learners.

    See Link List below for Maths At Home, then take the Learners link for the activity library and use your browser's search function, or scroll down. Remember, if you register you will know about new activities the moment they are published.

  • Rhonda's Quilt

    Rhonda is a quilter. This photo is one quarter of a whole quilt she made with identical panels. She was very excited when she realised that the exposed corners of the black rectangles 'make a curve'.

    Here's questions we thought of. Choose what suits you. If you think of others please send them to:
    doug@blackdouglas.com.au

    • Find something in the classroom that you can use to construct the black pattern (or at least its outer edge).
    • Use graph paper to draw the rectangles and decide co-ordinates for the exposed corners.
    • If these corners do lie on a curve, then for each one you should be able to do the same calculation on the x co-ordinate to find its corresponding y co-ordinate. What is that calculation?
    • Predict the co-ordinates of the next corner at either end of the first quadrant.
    • Explain whether or not you expect these points to lie on the curve: (0, m) ... (n, 0)
    • Derive the equation of the curve. Perhaps a graphing calculator would help.
    • There appears to be a curve in each of the four quadrants. Do you need 4 equations, 2 equations or 1 equation?
    • Anita said the top half of the black is like the curves for growth and decline of COVID cases. In what ways is she correct? In what ways is she not correct?

    Photos and stories of anything you
    do develop around Rhonda's
    Quilt would be welcome.

    Click the image to reveal and save a high resolution version for display or printing,

  • Those B___y Times Tables

    Following his contribution last month connecting his early teaching days with Times Tables Torture from Maths At Home, John wrote a short article with this title to provide background to his early experiences. John's direct, no nonsense writing style is easy reading. We have added this to the Working Mathematically section of the site. You can read it directly from the Link List below. If you haven't yet read his first contribution, that is also linked again below.

  • Get to Know a Cameo

    Task 206, Intersections
    The big problem embodied in this investigation - if I drop 100 sticks randomly, what's the maximum number of possible intersections - seems impossible, or ridiculously tedious at first sight. However, perhaps the best thing about this problem is the simple, elegant way it succumbs to breaking into smaller parts, trying each case, recording in a table and seeking a pattern. The outcome is Triangle Numbers and all their attendant algebra potential (substitution & solution of equations, ordered pairs, graphing, equations to curves and more) and yet the problem can be cracked from around Year 4.

    In the eTask Package this task is in the 'easy' set because it only needs a collection of sticks such as kebab skewers with their ends cut off.

    Task 233, Money Money Money
    The starting point of this task is a story about a day dreaming bank teller who makes up problems to pass the time. Add to that the opportunity to handle 'big money' and the students are hooked. The task includes three levels of challenge which progress from essentially content free reasoning through to simultaneous equations (and even a little on inequations).

    The extension challenges students to create a problem of their own as if they were the bank teller. This is definitely not a trivial exercise.

    In the eTask Package this task is in the 'special' set because it must have a specific collection of paper money. Excellent Australian play money can be sourced at: http://www.geoaustralia.com/english/PlayMoney/index.html
    An alternative is to design a set of rectangles showing the relevant values and print 'money' as required.

Keep smiling,
Doug.
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. eTasks Valued
    2. Maths At Home Update
    3. New Cube Tube Videos
    4. John Hibbs on Times Tables
    5. 80% Vaccinated?
    6. Get to Know a Cameo
      ... Tetrahedron Triangles, Take Away Tiles

Did You Know?

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