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May 2021

In this edition of the News you will find:

Red Square  Do Your Bit For Vaccing

Red Square  Corresponding With Danielle

Red Square  Maths At Home Update

Red Square  Get to Know a Cameo
     ... Soma Cube 2
     ... Eureka

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  • Do Your Bit For Vaccing

    Our first article this year was titled International Year of Vaccination. Given the higher than desirable rate of vaccination resistance in the community at the moment, it's time to read it again. See Link List below.

    The article highlights the vaccination component of the free Working Mathematically with Viruses resource which includes video, spreadsheet software, self-directed learning, challenge and written reporting in context - all sound teaching craft. The mathematical content, in this section of the activity, includes percentages and interpreting graphs built on number patterns, multiplication and powers that have been exposed in early sections of the activity. The software is designed for students to set the parameters and investigate various scenarios. The one thing that is unchangeable is that all outbreaks start with 1 case. For example:

    What is happening in the first week of this situation?

    Students now predict and then run the model for up to 20 weeks
    to reveal a representation of what would happen in the community.

    This can be compared with a second experiment such as this one,
    which changes only one parameter in the model.

    Where have the dotted lines gone? ... Oh they are there. ... Under the solid lines.
    Mmm this isn't starting out well.

    Another feature of the software is that at any time in the 20 weeks students can change the percentage to reflect an on-going vaccination roll-out.

    • Secondary teachers can immediately make use of the resource.
    • Primary teachers - from Year 4? - may need to make adaptations.

    The activity has the potential to get students talking - at home - about the value and importance of universal vaccination. And because the activity is publicly available on the web, they can show their parents what they are talking about. Of course teachers can also set part of the activity as a homework assignment to encourage the family discussion.

    Maths teachers are in a unique position to help educate the community about this life and life-style changing opportunity. Perhaps 'the community' might include a general staff meeting, or a parent information night.

  • Corresponding With Danielle
    I am a math teacher in the US and I am very interested in your Maths With Attitude series.  I am returning to high school public education after being away for 14 years.  Before I left public education, I had quite an extensive collection of tasks.  However, over the years, things have been lost.  I am looking to get my hands on some more task ideas to jump start my teaching career again.  This would be something I would be purchasing, not a school.  Can that be done?  Does the Maths With Attitude series contain specific task ideas?  I can get materials.  I just need the ideas.
    Thank you,
    enthusiasm ... a teacher from outside Australia ... returning to teaching
    wanting to build on previous successes with tasks ... willing to create tasks with own materials
    See Link List below for links mentioned in this response.
    G'day Danielle,
    I am very excited that you want to restart your career by creating it around tasks, which, in effect, means that you want to build a curriculum around learning to work like a mathematician, rather than just learning maths. The concept of learning to work like a mathematician is the clear and present core of all the work we do, regardless of which of our resources you choose to use.
    Let's work first with your words 'specific task ideas'. There is a heap of freely available task ideas if you begin with our Task Library:

    You will recognise many of the 241 tasks shown on this page as photographs. Click on any photo and it will link to the teaching notes for that task, which we call its Task Cameo. Each Cameo is built around the 3 possible lives of a task:

    • as designed as an invitation for two students try out working like a mathematician together.
    • as a framework for a whole class investigation guided by the teacher to model how to work like a mathematician.
    • in either case extended by an Investigation Guide leading the students deeper into the iceberg of the task.

    Investigation Guides provided by teachers are included in some Cameos and some have a From The Classroom section which teachers have provided to show how the task has been used with their students.

    Another way to approach Cameos is through the Task Cameo Content Finder:

    It explains on that page how to use it. There are two ways. Either way, you are using a need you may have to focus teaching around particular content, to select tasks to address that content. You might be happy to find one task and use it in its whole class investigation life, or you might find (usually, will find) a collection of tasks that address that content, which immediately offers opportunity to create unit plans using various models. Several such models are described at this link:

    From here you can look at spending money if you still need to. Firstly, you know what a set of tasks is and you say you can get materials. Over time therefore you can create your own physical Task Library using the eTask Package. Read about it here, if you haven't already:

    Maths With Attitude is something you have already looked at purchasing. It is an extensive set of unit plans providing a core curriculum built around learning to work like a mathematician. Each year level set of MWA Manuals provides 20 weeks of Working Mathematically planning. There's more about MWA at this link:

    MWA is written assuming teachers have access to both a set of Tasks and Maths300, which some years ago we passed to the Australian Association of Mathematics Teachers to manage:

    MWA is a unique planning resource which can provide rich outcomes using either Tasks or Maths300 on their own, or better still together. This flexibility is because of the way it is written and the depth of the Task Cameos.

    I hope all this is helpful for you. I look forward to continuing this conversation.
    Keep smiling,
    Doug. Williams

    This is wonderful!!  Thank you so much for all of this information.  I truly appreciate it.  It is more than I could have hoped for...I am very excited!!  I will spend some time looking over the resources you directed me towards and then I will reach out again if I have further questions.  I am also going to look some more at the Maths With Attitude series.  It may be helpful to have in my room.  I am familiar with Maths300, but I need to refresh my memory on the details.  I know the program works and have seen it first hand.  I am very excited to jump back in.

    Thank you again!

    Correspondence published with Danielle's permission.

  • Maths At Home Update

    If you are registered at our Maths At Home site you have already received the following information. If not, then please take a look. Both activities and the Gallery contribution offer something new and refreshing.

    • Money Charts (2-8)
      Text book exercises on adding and subtracting money come to life in this hands-on logic challenge presented as an addition chart. Convention decrees that the value in any box must be the sum of the term at the left end of its row and the term at the top end of its column. The emphasis is on encouraging patient application of if-then reasoning and working backwards, which are effective tools in many problem solving situations. Using coins rather than written amounts aids reasoning, supports familiarity with coins and, importantly, provides additional information which allows students to self-check their finished chart.
    • Protons & Anti-Protons (4-10)
      Protons and Anti-Protons are particles with the interesting property that equal numbers of them annihilate each other. Therefore when equal numbers of them are present they have a net zero effect. This is a simplified version of an aspect of particle physics, but sufficiently accurate to be worth exploring further.
      • What happens if we add more particles to a collection?
      • What happens if we subtract some particles from a collection?
      Investigating these questions, using objects as the particles, leads to a model for 'Proton Arithmetic' which is just one small step away from the arithmetic of positive and negative numbers. At the end of the activity the door to that step is tantalizingly opened.

      See Link List below for Maths At Home, then take the Learners link for the activity library. Remember, if you register you will know about new activities the moment they are published.

  • Get to Know a Cameo

    Task 161, Soma Cube 2
    Soma Cube is a classic spatial problem solving challenge. It is a 3D jigsaw which has challenged people of all ages since its invention in 1927 by Piet Hein. A cube is created by fitting the seven pieces together. Students of all ages like to try it and are often amazed by the number of solutions. Once students are confident with a solution they record it on isometric paper. Then the task offers them an opportunity to challenge each other with a speed test. The Cameo also offers additional object building puzzles using the same pieces.

    In the eTask Package this task is in the 'easy to make' set because most schools have collections of cubes, or can easily have them made from square section timber. Some will have a commercial Soma Cube. The task Soma Cube 1, see Link List below, shows how the seven pieces are made.

    Task 163, Eureka
    This task offers success to everyone who tries it because there are so many solutions. The story shell about three prospectors finding gold nuggets stirs the imagination and is enhanced by the yellow counters. The observations made about the collection of nuggets - which are the conditions of the problem - are easy to understand and students quickly find themselves absorbed in a delightful number puzzle. Finding one solution is satisfying but of course the challenges are:
    • How many solutions are there?
    • How do you know when you have found them all?
    The cameo offers clear guidance in how to tackle those questions.

    In the eTask Package this task is in the 'easy to make' set because it only requires twelve yellow counters or similar.

Keep smiling,
Green Line

Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. New Cube Tube Videos
    2. Maths At Home Update
    3. Get to Know a Cameo
      ... Row Points, Koala Karts

Did You Know?

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