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August 2021

In this edition of the News you will find:

Red Square  eTasks Valued

Red Square  Maths At Home Update

Red Square  New Cube Tube Videos

Red Square  John Hibbs on Times Tables

Red Square  80% Vaccinated?

Red Square  Get to Know a Cameo
     ... Tetrahedron Triangles
     ... Take Away Tiles

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  • eTasks Valued

    Welcome to the new teachers and schools who received their eTask Pack in the past month or so.

    Lisa from Grass Lakes Community Schools, Michigan, purchased hers at the end of July - still summer holidays in the States - and responded with:

    I am all set with the files. I have been so excited to be putting many of these tasks together already! Thank you for the amazing resources!
    We're excited too Lisa, but hope you had a bit of a holiday as well.

    Ben from Collingwood College, Victoria, is planning to begin by putting his tasks together based on the lists in our Maths Around The Kitchen Table link (see Link List below). Why? He wants to create take home mathematics packs to reach out to his students learning from home during lockdown - especially those who are device disadvantaged. He can easily include extension and support notes by copying, editing and pasting from the cameos of the tasks he chooses. (See Link List below for the Task Cameo Library.)

    Within a day or two of receiving her eTask pack, Carla from St. Clare's Primary School, Victoria, wrote back:

    The eTask package is extremely comprehensive. Thank you for your time and knowledge! My colleague and I are very excited about getting it started, we are currently working our way through the package and eManual. 

  • Maths At Home Update

    If you are registered at our Maths At Home site you have already received, and possibly already acted on, the following information. If not, then please take a look. These activities are designed for learning from home and are readily adaptable to the face to face teaching. Three new activities this month so there are now 69 activities in the learners' library, and among them, something for everyone.

    • What Can You Do With The Sunday Paper? (K-8)
      ... Don't throw the Sunday paper in the recycle bin. Save it for maths activities with the whole family. The first job is to roll newspaper sheets into tubes and joiners. Some can roll, one can tear off bits of masking tape and one can use the tape to stop the tubes unrolling. You will be amazed at what shapes and objects you can make with just one Sunday paper. But building stuff is only the start. This is really three activities in one. There is also pattern work with shape and number and money calculation? Dive in. A rainy Sunday afternoon is a great time to get started.
    • Calculator Walk (K-1/2)
      ... This activity is for the youngest learners. It combines everything good in learning at home - playing with a 'new machine', learning maths informally with a close older family member, learning what the learner already knows and ... going for a walk. The parent gives the child a calculator, hopefully as a gift they can 'keep forever'. They explore it, discuss it, learn how to write on its screen and take it with them on a number hunt around the house, the yard, the street, ... On return a favourite number is recorded in their journal along with information about where it was found and why it is special. Interest in the calculator itself is also harnessed for creative endeavours.
    • Times Tables Torture (2-10)
      ... Memorising times tables is torture for some kids! But why should they have all the fun. Now it can be torture for everyone! The activity provides slides of every times table children need to know. They create their own slide show of 20 slides which challenges them to write each answer against the clock. They also choose the seconds for which each slide shows. A partner controls the timing, at the end work is corrected with a calculator, then the swap roles and repeat. See it ... Write it. Students are encouraged to continually improve their personal best. Conceptual support for how tables derive from multiplication is provided through the linked activity Exploring Times Tables. Learners are encouraged to use the activity for just 10 minutes a day, 4 days a week until they reach a high level of speed and accuracy.

    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.

  • New Cube Tube Videos

    These two videos were produced as part of Maths At Home during August. Both are integrated into the relevant activity listed above. The first was created as an example of a Times Tables Torture slide show. The second is a contribution from a home learning student to which we have simple added music and titles. See Cube Tube in Link List below or access in context through the relevant Maths At Home activity.

    The video demonstrates how to use the Times Tables slides provided in the activity to create your own slide show or video. This could be the scariest way of practising times tables that has ever been invented. In the end it is entirely up to the learner to remember these useful number facts and the activity, the tongue-in-cheek torture context and the video work together to encourage the learner to take responsibility for doing exactly that.

    The viewer is expected to learn by taking a taking a Times Tables Torture Test themselves. Are you game?

    Jojo, Year 6, was doing school at home. Her screen presented questions about line symmetry of polygon shapes. She decided to make them from newspaper tubes (as in the Maths At Home activity What Can You Do With The Sunday Paper?) ... then she sent us a video. It's wonderful. We added a little music and titles and included it in the activity notes.

  • John Hibbs on Times Tables

    Through the years John Hibbs, retired teacher and inspector of schools from UK, has contributed to our site by sharing notes from the journals he has kept throughout his career. See Notes from and Inspector's Notebook in Link List below.

    John keeps up a strong interest in mathematics education, for example, contributing regularly at the Association of Teachers of Mathematics (ATM) annual conference, and registered for our Maths At Home update as soon as they began with Lockdown 2020.

    Our update on Times Tables Torture drew him back to his first year teaching - Year 7 in a London school in 1964. His journal pages about his approach to encouraging and supporting kids to 'learn their tables', which shares features with the Maths At Home activity, and accompanying emails have been included in our latest of his 'Notes'.

    See Link List below because:

    • Mathematicians keep journals of their investigations.
    • John will convince you that there are only 36 times tables to remember and about a quarter of those are the '2 times'.
    • The way John prepared his flash cards is unique and more than 50 years on is something you might want to do.
    • There is a number pattern surprise waiting for you.

  • 80% Vaccinated?

    They say that the Delta variant of C19 is at least twice as virulent as the 2020 strain, which had an R value of somewhere between 2 and 3. So, let's do a Delta investigation with R = 5 to find out what we might expect if the population fulfils the national political expectation of becoming 70-80% vaccinated.

    The software is freely available for home or school use in Working Mathematically with Viruses from Maths At Home (see Link List below).

    Step 1
    We begin with one case, R = 5 and 0% of the population vaccinated.

    Step 2
    After 2 weeks there are 25 new cases and 30 active cases.
    The original case has either recovered, or is dead, assuming a 14 day infectious period.

    Step 3
    This is worrying so we instantly vaccinate 80% of the population.

    Step 4
    At Week 10 a pattern is emerging, but the virus is not eradicated.
    Will we have to live with 25 new cases every week as well as simultaneously caring for the other 25 active cases which have accumulated from the previous 14 days?

    Step 5
    By Week 20 the pattern is clear.
    Assuming no further steps are taken, we will have to live forever with 25 new cases every week plus simultaneously caring for the other 25 active cases?

    Potentially that's as many as 50 hospital beds across the geography of the population that will not be available for any other form of health need. Perhaps as many as one third of those will need to be ICU beds.

    Each of these experiments with take about 3 minutes.

    • Repeat the experiment for 70% vaccination and report.
    • Repeat the experiment for 90% vaccination and report.
    • Using Option 5, repeat the experiment again for all three percentages to compare no vaccination with vaccination at the chosen rate.


    • Vaccinating 80% of the population overnight is clearly a best case scenario. Try growing the vaccinated percentage each week which is more in line with what is currently being promoted as success in the daily media.
    • There are assumptions in our model. They are clearly listed in the activity plan.
    • There are assumptions in the official models.
    • Our model accurately reflects the general trends in the official model(s) because both are underpinned by the same source mathematics.
    • Viruses can't do mathematics - they are only a chemical compound - but, in the same way as a sunflower can't escape the Golden Ratio, a virus cannot escape the Powers that govern its replication.
    • Our model is accessible to and operable by students.

  • Get to Know a Cameo

    Task 186, Tetrahedron Triangles
    This stunning task addresses multiple mathematical outcomes across the broad areas of space, number and algebra. In its best form it is dependent on using click together plastic triangles like 3d Geoshapes or Mini-Geofix. The task begins with the net of a Size 1 tetrahedron, something children as young as six or seven do quite naturally. They also usually fold it up to make a tetrahedron. Students using the task are then challenged to explore Size 2, Size 3, and so on with a view to being able to predict the number of triangles needed to make a tetrahedron of any size. That's where it enters, the number pattern, generalisation, algebraic symbolism world. There are several extensions in the cameo, one of which lifts this investigation into the realm of senior high school mathematics.

    Of course this could be a text book problem but should students be denied the opportunity to make the physical objects?
    Or should their experience with 3D geometry be limited to the 2D world of a screen with programmed optical trickery?

    In the eTask Package this task is in the 'special' set because the Geoshapes or Geofix or equivalent are essential.

    Task 215, Take Away Tiles
    This is probably the most difficult of a family of similar number puzzles. Or is that because it involves subtraction, with students might be less confident? Ten digits have to be placed on the ten spaces so that the equation on the card is true. How many solutions are there? How do you know when you have found them all? They're the big questions, but just finding one solution might be a big success depending on the age or experience of your students.

    The cameo gives lots of support for framing questions which can lead the students from random guessing, to collecting data, to noticing unstated conditions, to making

    and testing hypotheses and to breaking the problem into parts based on what has been discovered. All of which is the work of a mathematician.

    In the eTask Package this task is in the 'easy' set because, it only needs ten numbered tiles that fit the grid.

Keep smiling,
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. I Moved The Decimal Point
    2. Maths Mat Continues To Matter
    3. Maths At Home Update
    4. Get to Know a Cameo
      ... Farmyard Friends, Knight Protectors

Did You Know?

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