News

April 2023 In this edition of the News you will find:   DIY Workshop: A School Without Books   Uncover Counting   Get to Know a Cameo      ... Heads & Legs      ... Fraction Estimation Please feel free to distribute this information. Email News Services If you would like to subscribe please send an email request to: doug@blackdouglas.com.au: In the subject line write Subscribe Maths. Add your name and preferred email address. Update messages are sent from Mathematics Centre monthly through the school year. Working with Mathematics Centre will help you find your way around our site. Browsing Hint Use the View/Zoom options of your browser to 'move' the page closer or further away. Ctrl +, Ctrl - and Ctrl 0. DIY Workshop: A School Without Books We provide the workshop content through the video. You provide the local leader to organise, facilitate and follow up the session. A teacher once commented in a workshop that: A school without tasks is like a school without books. A school without books?? Not possible! A school without books would have an impoverished curriculum. Books are chosen by students for fun and lead to literacy and literary adventures. Books are chosen by teachers for small group and whole class literacy and literary adventures. It's the same with maths tasks. Chosen by students for fun and leading to skill development and reasoning adventures. Chosen by teachers for small group or whole class adventures leading to skill development and reasoning adventures. And they are the only problem solving resource that integrates the use of concrete materials. Just one of the many teaching craft features highlighted in this workshop that encourages you to identify reasons why the teacher might have made that comment. See Link List below for more details.

• Uncover Counting

  If I ever had to give just one reason to justify the invention of Poly Plug it would be this activity. It is so rich with pedagogy, mathematical content and reasoning and there is no other concrete way to do it efficiently and fascinate, captivate and absorb so many learners. The activity started long before these photos when each child was asked to turn over rows of three blue plugs in their own board. That's one sentence. How many teaching craft points - 'their own', colour to encourage visual learning, texture to encourage kinaesthetic learning, more with the turning over, pattern, learning in community, talking with each other as they do it, the almost natural urge to count as you turn and the pattern develops ... any more?

  Check with your neighbours that we all have rows of three? Yes?
  Agreed? Okay, now bring them out here and arrange them on the floor so that together we make rows of six.
  Remember, rows go across your tummy.

  Three more sentences. Any more teaching craft (pedagogical) features?

  Now I am going to cover all of your Poly Plug with this cloth.

  Is mystery a recognised pedagogical technique?

  How many blue plugs are showing?
  - Duuh. None.
  How do you know?
  - Because we can't see any?
  Okay, what's the number name for none?
  

  It doesn't matter what answer you get, as long as it is means zero. Start a board list. It might even include words from other languages and sport ... such as love ... everyone knows that love means nothing. (Sorry just checking you are still reading.) But don't get too carried away with this step or you might get nothing else done.

  Every number has more than one name. Even zero. Let's explore other numbers.
  In a moment I will pull the cloth back one row of blue plugs. Whisper to the person next to you and tell them how many blue plugs we will see.
  What you whispered is your hypothesis - your intelligent guess. How can we check your hypothesis?
  - Pull the cloth back.
  Okay I will ... and if your hypothesis was correct you are allowed to go 'Yessss!'.

  Pause: Teaching craft check. Anything else been happening likely to fascinate, captivate and absorb the learners?

  So, what number of blue plugs can you see?
  - Six.
  How do you know?
  Can you check it another way?

  And now the teacher manages a learner-led 'show and tell' and/or board record of various ways we can convince each other that there are six blue plugs showing. Look back at the photos and pretend you can only see the first row. Make a list of at least six different ways to be convinced there are 6 showing.

  And so the journey continued in this class, their first with Uncover Counting, to the point you see in the photos.

  Over time many variations can be introduced (but don't be in a hurry to do that). Here's two:

  • The class can count by any group. You only have to tell them a different way to turn over plugs, e.g. Girls make rows of 4 and boys make rows of 3. Put them on the floor to make rows of 7.
  • A calculator can be used to keep a running record and show the hypothesis to the neighbour instead of whispering, just as in Predict A Count (see July 22 News in Link List below).

  If you are a member of Calculating Changes you can find out more about Uncover Counting from your web site.
  If not, or if you don't have Poly Plug, explore the Maths At Home activity titled Exploring Times Tables which provides a visual times tables chart (no numerals anywhere) and use it in conjunction with the Picture Puzzles Teaching Notes for the Number & Computation A menu. See Link List below.

• Get to Know a Cameo

  Task 14, Heads & Legs
  

  This well known investigation eases learners in through a story shell with props - the farmyard and the animal cards - and guaranteed success with the first question, because they make the problem themselves and count what can be seen in order to answer. They know how many animals of each type there are in the farmyard and count the heads and legs on the cards. But what happens if I tell you the number of heads and legs and ask you to find the number of each animal in the farmyard?

  This backwards question is central to the rest of the challenges on the card. The cameo details several ways learners have reasoned their way through such problems.

  The cameo also offers a thorough report from Bayswater Primary School explaining how they used the problem at every level K to 6 as a professional learning experience in developing common assessment tasks. Within its seven pages it includes student work and teacher created rubrics. A must read for anyone exploring how to gather assessment information in a curriculum built around learning to work like a mathematician.

  In the eTask Package this task is in the 'more work' set because of the extra work involved in printing, laminating and cutting the animal cards.

  Task 205, Fraction Estimation ... formerly titled Peg & Tape Fractions
  

  The name of this task changed in the production of the eTask Package so that it matched the title of its partner lesson in Maths300. Both task and lesson are excellent on their own, but in combination they are brilliant, largely because of the software component added by Maths300. As a task, students are given a length of non-stretchable cloth such as herringbone tape, a peg each and a fraction challenge, which in the first question on the card is two fifths. They lay out the whole (length of tape) across the floor, choose the starting end and place their peg where they estimate the given fraction would be. Now they want to

  know which person is closer and that's the real challenge of the task. To create at least one way to check. They can use a ruler if they wish (although interestingly this is not the first choice of most learners). However the next teacher question, after being shown the ruler solution, would be What happens if you don't have a ruler?.

  The Cameo offers three ways and there may be more. It also offers an extension that involves relating fractions to decimals using two identical lengths of tape. As a bonus there is a From The Classroom section in which Nichola Brandon describes in great detail, and with lots of photos, how she integrated Fraction Estimation into an extensive fraction unit in Year 4. She concludes her contribution with:

  My practice has changed immensely! ... My low level students are now loving maths because they can get involved and can achieve! And my high flyers remain engaged because they can take the activity as far as they want to! ... I have changed my practice because it works!

  In the eTask Package this task are in the 'easy' set because it only needs herringbone tape and clothes pegs.

Link List Video: A School Without Books eTask Package Calculating Changes July 2022 News: Predict A Count Uncover Counting (Calculating Changes Members) Maths At Home: Exploring Times Tables Picture Puzzles Teaching Notes: Number & Computation A Heads & Legs Fraction Estimation Task Library Task Cameo Library Task Cameo Content Finder Calculating Changes Content Finder Calculating Changes Year Level Finder Working Mathematically with Infants Maths At Home Activity Library Order Form Did you miss the Previous News? If so you missed information about: New eTask Schools School Mathematics Is... Poly Plug, Proportion & Percent Get to Know a Cameo ... Rectangle of Squares, Soft Drink Crates

Did You Know? You can Search Mathematics Centre. Our Site Map acts as a Table of Contents to help you find what you need in Mathematics Centre. You can find photos of every task using the Task Library. You can find tasks by content using the Task Cameo Content Finder. You can create your own Task Library in a professional learning context with the eTask Package. Calculating Changes offers Content Finder & Year Level Finder tools. You can find tasks coded by Year Level and Curriculum Strand in the Task Centre Catalogue. (PDF file) You can search for lessons by Year Level, Curriculum Strand, Lesson Features & Keyword at Maths300. You can connect Tasks to their Maths300 companion lesson using Tasks & Maths300. (PDF file) Excel version provided by Pymble Ladies' College also links each Task to its Maths With Attitude content strand. All these links, and more, appear in Working with Mathematics Centre. (PDF file)