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News

Current News

In this edition of the News you will find:

Red Square  A Little Feedback

Red Square  Maths At Home Update

Red Square  Get to Know a Cameo
     ... Staircase
     ... Pyramid Puzzle

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  • A Little Feedback

    Thanks to these teachers who found time last month to send a short message. Often it is personal comment from a colleague that is an important stimulus for change in another's teaching, so I am including the messages here (with permission) because on this occasion you might be the one influenced.

    Thank you so much for sending me your wonderful newsletters over the years. The time has now come for me to unsubscribe as I am no longer in a position to actively use your ideas.
    Sidney
    We are very excited to begin our Maths Task journey. The ePackage was easy to download, which is fantastic, and we look forward to receiving our Poly Plugs and Rotagrams.
    Marie Martin, Yarra Glen Primary School
    Although I've had heaps of fun with your excellent ideas over the years, I've now retired, so please unsubscribe me from the mailing list.
    Many, many thanks for the inspiration :)

    Lucy Browne, UK

  • Maths At Home Update

    Two new activities during October so there are now 74 activities in the learners' library - something for everyone K to 10. Originally Maths At Home was designed to support you in providing home learning during school closure, but now eye contact learning is returning the content, teaching craft and structure of the activity notes are easily adapted to the whole class setting or homework projects. This opportunity was taken up by several schools between lockdowns. MAH is now a resource you might look at more closely as you begin your planning for 2022. It is totally public.

    MAH has now been used in at least these three additional ways:

    • As a self-directed project carried out at home, perhaps with a localised guidance sheet from the teacher.
    • As a self-directed project in school, individually or in small groups, to help the teacher differentiate learning in the classroom.
    • As the framework of a whole class investigation - in essence, a lesson plan created for the teacher.

    • Toss Up (1/2-6)
      ... A simple game to prepare and play. Print some pages and collect five objects. For instance, caps from bottles of water or milk are easy to find at home. The game is about tossing or dropping the caps on the playing boards, which are all designed the same way but each one uses different numbers. A bit of competitive fun, lots of mental arithmetic (supported by a calculator if chosen) an unspoken comparison between our base 10 place value system and calculation in other bases, and confirmation of how elegant our system is for recording numbers. A few extra challenges are included to extend thinking beyond mere calculation.

    • Letters & Numbers (3-7)
      ... Calculations are obviously an important part of a mathematician's work. Equally important though are the related skills of estimating number and being able to calculate an answer in more than one way in order to check it. Estimating, calculating and checking another way are central to this activity. The context is one of giving value to each letter of the alphabet so that the values of words can be estimated, calculated, checked and compared. In the early part of the activity, there are only 2 basic values - $10 for vowels and $5 for consonants and the focus is Pets. Later every letter gets its own value, based on its position in the alphabet and the focus becomes first names in the family. The activity rounds off with a game making words from randomly chosen letters (similar to Scrabble or the TV game Letters & Numbers). A print sheet of alphabet tiles with associated values is available in the activity.

    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.

  • Get to Know a Cameo

    Task 51, Staircase
    Students build towers of blocks so that each tower is one block higher than the previous. Placed side by side, they make a staircase. The first staircase is one step and uses one block, the next is two steps and uses three blocks and so on. Students are asked to continue the sequence and record in a table. Everyone can make a start. Predicting a little further ahead and checking predictions follow, up to a Size 10 staircase. Again, everyone is likely achieve this and the young mathematicians are asked to write a report about what they have discovered so far. Many extra challenges are suggested in the cameo including the tantalising "If I tell you a staircase of any number of steps, can you tell me how many blocks are needed to make it?"; graphing the ordered pairs and discovering that not all graphs are straight lines; and just about every other aspect of a text based algebra course.

    In the eTask Package this task is in the 'easy' set because it only needs a small number of click together cubes, which we expect are in every maths storeroom.

    Task 101, Pyramid Puzzle
    The card shows the four pieces of the puzzle. There are only two different pieces but one puzzle needs two of each of them. All four pieces are essentially 2 dimensional, yet it is possible to build them into a 3 dimensional pyramid (tetrahedron). This is not as easy as you might think.

    Achieving the construction challenge reveals a pattern in the number of spheres at each level and with a deeper look reveals a pattern in the total number of spheres needed to make pyramids of size 1, 2, 3, 4. Of course the patterns suggest predicting and checking the next level and the next and so on.

    Eventually this spatial puzzle, which was a challenge in itself, leads to Year 12 algebra (and higher) through summing Natural Numbers, Triangle Numbers and Square Numbers and Mathematical Induction as a tool for proving hypotheses about what these sums might be. When those are sorted there is of course the question: "What happens if I try to sum the Cube Numbers?"

    If you teach Years 10, 11 or 12, please take time to look at this cameo and read through to the Classroom Contribution from Damian Howison. Stimulated by the Christmas song Twelve Days of Christmas he has developed the proposition that any size tetrahedron can be built from spheres connected like those in the puzzle. The photographic examples of Year 10 students' work which he provides as evidence are priceless.

    In the eTask Package this task is in the 'special' set because it must have the same design pieces as the puzzle that gave birth to the task. This design might be found in a puzzle shop. (There other designs of Pyramid Puzzle but you want this one so it matches the card.) An alternative is to use foam spheres from craft shops, thin skewers and the appropriate glue. Examples are in the photos mentioned in the paragraph above.

Keep smiling,
Doug.
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Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. Maths At Home Update
    2. Rhonda's Quilt
    3. Those B__y Times Tables
    4. Get to Know a Cameo
      ... Intersections, Money Money Money

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