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News

Best wishes to you all
for a peaceful family Christmas, a happy
New Year celebration and a great holiday!

December 2019

In this edition of the News you will find:

Red Square  Fractions, Algebra, Measurement & More

Red Square  Planning Units of Work

Red Square  What's The Chances With Coke?

Red Square  Get to Know a Cameo
     ... Scale Drawing
     ... Crossing The River 2

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  • Fractions, Algebra, Measurement & More

    This was the content involved across the workshop sessions (each one hour) that we offered at the December Conference of the MAV. The 'more' included introducing Algebra Through Geometry (see Link List below) and using rectangles and squares to develop the multiplication concept, times tables, long multiplication, algebra rules such as expansion of two binomials, (a + b)2 and a2 - b2 and even how to calculate the area of a circle using a square.

    All sessions were centred in learning to work like a mathematician and the teaching craft that fascinates, captivates and absorbs learners. These photos from a couple of the sessions show teachers embracing various pedagogical techniques designed to bring this about. The shift through concrete and visual to abstract, with additional input from challenge, technology, working in pairs, recording and whole class and small group discussion is particularly evident in the algebra set.

    Learning Algebra with Picture Puzzles

    The session began with physical involvement to explore Task 11, Lining Up (see Link List below). A group in a line at the front -- which actually wasn't that easy to arrange in a tutorial room crowded with lecture chairs.

    • How many in the line?
    • What's your place in the line from that end?
    • From the other end?
    • Does anyone have a special place?
    • Imagine I tell you that you are ... from this end and ... from that end. How many in the line?

    Return to your seats. Make a model that shows 'you' and explain to your partner how to work out questions like these.

    Use your internet device to explore the Lining Up Picture Puzzle. (See Link List below.)


    Here's me 11th from each end.

    But that counts me twice, so...


    Choose your own algebra investigation from the Pattern & Algebra B menu. Garden Beds (see Link List below).

    One screen, two learners, concrete materials and a challenge. Match Triangles (see Link List below).


    Can we check it another way?

    A journal is essential for a mathematician.

    Luke's Fraction Game and a Practical Fraction Unit

    Nichola Brandon created this unit of work within a professional development sequence in response to a request for classroom trialling. Nichola has provided her plan, with slide shows of her class in action and links to activity sources. See Link List below.

    Nichola began with Luke's Game and so did we. Then teachers could choose from her unit to explore as many of the activities as time would allow.

    These two teachers are beginning Peg & Tape Fractions.


    This pair began by exploring the Chocolate Cake activity from Maths300.

    Later they explored Fractions, Plugs & a Calculator from Calculating Changes

  • Planning Units of Work

    A key to the success of Nichola's unit was the use of Threading. This is a teaching model which has been developed by our Calculating Changes network to help engineer 'aha' moments in number. Sometime between now and the beginning of the 2020 school year you are likely to be planning a unit of work. If you are looking for a fresh approach you could explore the Models & Structures link in the Link List below. It includes 12 models that can be instituted for one lesson through to three or more weeks.

  • What's The Chances With Coke?

    Just in case you don't recognise it, that's my name.

    A friend was walking through Eastland and spied a random fridge with these two bottles stacked in the front. She sent me the photo.

    • What's the chance of that??

    Probably an impossible question to answer because there's too many variables, but surely there's a lesson or two somewhere in Coke's current crazy promotion. It's that time of year where you might feel free to experiment a little with your class, so take look at the news report in the Link List below and see what comes to mind.

    They have apparently produced thousands of names - first names and family names - so it might be a good idea to cut the sample space down a bit to develop investigation questions. Perhaps a starting point might be something like suppose Coke produced bottles with 100 different first names and 50 different family names, how many first and family name arrangements are possible?

    Suppose they only produced 50 first names and 25 family names, would the number of arrangements be halved?

    After the summer break a Fermi problem investigation might be:

    • How many Year 7 families shared a family Coke since the end of school last year?

    Note: I do realise that my success is a combination of two family names (according to Coke), but hey, you take what infamy you can get.

  • Get to Know a Cameo

    Task 41, Scale Drawing
    Whether you are developing measurement and number skills, or properties of similarity and ratio and proportion this task is a non-threatening problem solving situation you could include in the unit. Perhaps it's the starting point.

    The first challenge is to copy a cartoon-like house drawing produced on a large grid onto a smaller grid. Extension questions suggested in the cameo develop an understanding that if the side lengths of a shape are changed by a factor of m, then area is is changed by a factor of m2. Also, in similar shapes (ones whose side lengths are related by a factor in this way) angle sizes remain the same.

    Challenges continue with encouragement to create their own drawing and scale it, suggestion to investigate scales on maps, asking what happens if the rescaling operates in one direction (say horizontally) but not the other and what happens if a grid of equilateral triangles is used instead of a grid of squares.

    Guidance and print resources are supplied to support a whole class investigation.

    In the eTask Package this task is in the 'easy to make' set because it only needs one additional laminated board, a marker pen and a wiping cloth. [Note: The laminated board was omitted from all eTask Packages purchased before the end of December 2019. This is now freely available through the link below and can be printed and laminated to include in your Task Library.]

    Task 106, Crossing The River 2
    Probably the best thing about this task is that it doesn't require any mathematical content at all! So, regardless of any child's perceived 'textbook capabilities' you can focus on the higher order reasoning, questioning, problem solving and communication skills which are the core of a mathematician's work, regardless of the content area in which they operate best. School mathematics is learning to work like a mathematician, so this investigation should surely appear somewhere in primary school and again in secondary school. Further, 'in the old days', this problem was frequently used when training computer programmers, so it has a historic importance and, through that, a doorway into teaching flow charts.

    The rules are simple:

    • 1 row boat that can only carry 2 people.
    • 3 adults (all of whom can row) and 3 children (only one of whom can row).
    • At no stage can the number of adults be more than the number of children.

      The objective is for all six people to get from one side of a river to the other.

    One solution is shown in the cameo, but don't expect it (or any other) to develop in 'five minutes'. When a solution is found, the task shifts to being able to record and then communicate the reasoning and the solution. A critical part of a mathematician's work. This could involve using software, or photographs or drawings (a comic strip perhaps) and text.

    It is easy to create a whole class lesson from the task - especially if you have Poly Plug - and suggestions for this in the cameo draw on teaching craft techniques including physical involvement, concrete and visual learning, discussion and recording and working in community.

    In the eTask Package this task is in the 'easy to make' set because it only needs 6 cubes (or other objects) in three colours (ratio 1:2:3).

Keep smiling,
Doug.
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. December Conference Workshops
    2. Get to Know a Cameo
      ... Cars In A Garage, Rod Mats & Make The Whole
    3. ...and more...

Did You Know?

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