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August 2023

In this edition of the News you will find:

Red Square  New eTask Schools

Red Square  Koala Capers

Red Square  Kids' Own Games

Red Square  Get to Know a Cameo
     ... Protons & Anti-Protons
     ... Change

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  • New eTask Schools

    Welcome to

    • Elimbah State School, Queensland
    • Revesby South Public School, New South Wales

    which both began building their own Task Library using the eTask Pack in the past month. After she received her pack, Nadine Paul, Assistant Principal at Revesby South wrote: I have downloaded all the files and excitedly begun searching through them all. Just amazing work, thanks for sharing.

    We're very pleased to have both schools on board and looking forward to them sharing their classroom stories with us in the future.

  • Koala Capers

    Koala Capers is the latest Video Book from Black Douglas (see Link List below to play the video from YouTube).

    Video Books unite the learning features of printed books, photos and video to create a re-imagined reading format that enriches content and context. A retired primary principal/consultant has described them as ...a fabulous aid to developing readers. They can be used by individuals, small groups or the whole class.

    Koala Capers is, in the first instance, about koalas and their relationship with their environment. As a text it is accessible to readers from about Year 2.

    The same colleague saw this title as ...a great way of encouraging new adult migrants and reluctant adult or secondary school remedial readers - even illiterates at any level in our correctional system - as the topic can be for any age. So, in the second instance it is a potential reading resource.

    It can also be a stimulus for mathematical learning.

    We've listed some of our initial thoughts here. If you also see mathematics learning potential in Koala Capers, it would be wonderful if you were able to explore your ideas and/or those below in the classroom and feed back with comments and photos. Integrated, cross discipline learning is something that is often successful with children. Perhaps there will be enough response for us to set up a page in Mathematics Centre as a record and reference.

    Maths Activities: Koala Capers
    These ideas will make more sense when you have read the Video Book. See Link List below.

    What's my timetable?
    The video tells us koalas sleep 18 to 22 hours each day. It also shows us other things they do in a day and we hear noises they sometimes make.
    • Make a list of all the things a koala might do.
    • Make a whole day timetable to show how one koala might fit in all or most of these things.

    How long does a teenager sleep?
    The video tells us that a koala sleeps longer each day than a human teenager. How long does a human teenager sleep? Perhaps the answer depends on whether it's a school night or a weekend night you are asking about.

    • Design and carry out a survey to find out how long teenagers sleep.
    • In your report, compare your results with the amount of sleep recommended for teenagers by health research, which is 8 to 10 hours.
    • Compare koala and teenager results to the time pets sleep.

    How much is half a kilogram of gum leaves?
    For homework children collect a small box of green gum leaves to bring to school on Nothing bigger than a shoe box; and no branches - koalas don't eat the branches.

    • Work together to estimate, then measure, the mass of eucalyptus leaves in the class.
    • If we were making half kilogram lunch packs for koalas, how many koalas would we be able to feed?
    • Work together to make the lunch packs and build a gum leaf takeaway shop for koalas.
    • While the lunch packs are in the classroom there is the opportunity to estimate and compare 500g of leaves to things in the room that are lighter, almost the same and heavier.

    Koala measurements 1
    A sequence in the video shows a koala climbing backwards down a branch to change trees.

    • How long do you think the branch is?
    • What else do you need to find out to be able to check your estimate?
      Find the information you need and check your estimate.
    • Estimate the distance the koala jumps.
      It begins the jump from something like a crouch position then jumps half-backwards to where it lands, Call this a koala jump.
      How far can you koala jump from a crouch position?
    • Make a class display of everyone's koala jump distance.

    Koala measurements 2
    The same sequence provides a good view of the branch from its base to where the koala began.

    • Work out the main angles along the branch compared to the horizontal branch.
    • Use newspaper and your decisions about length and angles of the branch to build a scale model of the branch.

    Thumb-thing to think about
    Ranger Rob was asked how many koalas there were on the bush reserve. She answered:

    You'll have to work that out for yourself, but I will tell you that altogether they have 244 thumbs with claws.
    • Invent other number stories using koalas.

    Koala statistics
    The video shows the total number of koalas killed for their fur between 1888 and 1927 and includes other statistics that will help you with these challenges.

    • Compare the total number with the population of your nearest capital city.
    • Which Australian capital city populations would you have to add together to be closest to the number of killed koalas.
    • Compare the number of koalas killed with the estimated human population of Australia in 1888 and 1927.
    • If the same number of koalas were killed each year through that time to make the total, estimate first, then calculate what the average number would be.
    • Compare this average number to the number of koalas estimated to be living in Australia today.
    • But the same number of koalas weren't killed each year.
      What fraction of all the koalas killed between 1888 and 1927 were killed in August 1927?
      Discuss why the number might have been so high in this month.
    • Investigate whether any animals are being hunted towards extinction today.
    • Prepare a report.

    Pack up your koalas
    When Douglas visited the koala sanctuary he bought a set of tiny toy koalas from the souvenir shop. He knew he could use them with his class to explore Task 230, Pack Up Your Bears, a number and pattern investigation. See Link List below.

    • Koalas aren't bears, they're marsupials, but that doesn't change the mathematics in the investigation. And model koalas don't have to look like koalas for the investigation either. They could be Poly Plug or wooden blocks.

  • Kids' Own Games

    The yellow plug acts like a chess queen, protecting all the spaces shown by arrows.
    Kids' Own Games is a collection of Poly Plug activities in the Free Tour section of Calculating Changes. They have been contributed by several teachers. Queenie, as in the diagram, is an example. The children's first challenge to us is to discover the smallest number of queens necessary to protect every space on the board.

    Perhaps they have modified another well known problem and, as with others in the collection, it may not be directly related to learning mathematical skills, but the reasoning, justification and communication skills required to design, trial and modify your own game are the core work of a mathematician and support the development of literacy.

    Another example is Poly Plug Battleships. In this case there is a clear link to mathematical skill learning, namely, locating points in two dimensions using a grid. And yes, this problem has been around forever, but NRICH (Cambridge University) acknowledges that it inspired them to design their interactive on-screen activity called Poly Plug Rectangles, which is also included in one of their videos.

    There are four such activities in the collection plus a 'Game Suite' of another six from one school where the children not only designed their own games but also coded their own web pages to publish them. Their code has been preserved in the Suite. Publishing for others to understand is a vital element of a mathematician's work.

    We would be happy to add photos, comments, journal entries and so on from your classroom to the Kids' Own Games collection, or to extend the collection with new games from your students.

  • Get to Know a Cameo

    Task 130, Protons & Anti-Protons
    The model used in this investigation is based on a simplified version of particle physics. Two different types of matter are represented by two different colours of counter. Things get interesting when numbers of each type come together. It's always the case that equal numbers of Protons and Anti-Protons combine to have zero effect on the total present. The task involves making collections to explore this principle, adding to collections and subtracting from collections. There are some situations in which taking something away actually produces more of what is left behind. Fascinating. The challenge on the card puts the students' understanding of the model to the test and is self-correcting.

    The focus of the card is on making, drawing and calculating with the model. However, with sufficient practice, it is only small step to introduce positive and negative charges as a property of the particles and thereby create a model for integer arithmetic that has the identity element for addition built in.

    In the eTask Package this task is in the easy to make set because it only needs counters in two colours.

    Task 165, Change
    This task is about finding at first one way, then ten ways, then all the ways to make $2 with Australian coins. Students might move from using the coins to using pencil and paper. Some might use pencil and paper from the start. No problem. But if the coins weren't available, some students might not be able to begin the task at all.

    Within its expanding complexity students will be actively using substitution (We can use two 20 and one 10 instead of 50.) and applying strategies such as breaking the problem into parts and trying every possible case. All this in a real life context.

    The cameo gives searching for all possible ways a kick start with an organised list showing those using $1 and $2 coins. (Would you believe 50?) It also suggests an extension based on the fact that the largest value of silver coins an Australian merchant is obliged to accept is $5. Further, it suggests a way of running a whole class lesson using just the one set of coins from the task.

    In the eTask Package this task is in the 'special' set because it needs a particular collection of play money. If you happen to have play money in the school, then the task automatically becomes easy to prepare.

Keep smiling,
Green Line

Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. Professional development: it's what we do.
    2. Red Plug Hunting
    3. Get to Know a Cameo
      ... Latin Squares, Pentominoes

Did You Know?

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