News

November 2022 In this edition of the News you will find:   New eTask Schools   New Cube Tube Video   Bridging 10   Get to Know a Cameo      ... Consecutive Sums      ... Making Fractions 1, 2 & 3 Please feel free to distribute this information.

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• New eTask Schools

  Welcome to

  • Chairo Christian School, Pakenham Campus

  which began building their own Task Library using the eTask Pack this month. Given they also asked for the Maths With Attitude Year 9/10 manuals it looks like their starting point will be making tasks for this level. Best wishes for using tasks to help your students learn to work like a mathematician. We hope to hear from your classrooms in the future.

• New Cube Tube Video

  The Frog Pond investigation has been successfully used in classes from K to 8 to develop appropriate chance and data learning for the level. Sometimes it is used as a task card (Task 13) by a pair of students; sometimes as a whole class lesson which includes pairs gathering data for class discussion. This video is a workshop starter. Perhaps for a faculty meeting to generate a refreshing discussion about learning features and what you value in mathematics teaching; perhaps as a component in a professional development day. Teachers are the intended audience, but your discussion might lead you to use parts of it with your students.

  The best way to access any Cube Tube Video the first time is through its record on our Cube Tube page. This provides background information for the video, resources you will need (if it is a workshop video) and a link to its teaching notes (if the video includes tasks or activities from Mathematics Centre). See Link List below to access The Frog Pond video this way.

  After the first time you can easily access any Cube Tube video from our channel using our You Tube handle. Our channel is at:

  • https://www.youtube.com/@cubetubemaths

  Copy and paste this into the URL line of your browser, then when you arrive add the site to your bookmarks.

• Bridging 10

  Calculating Changes is on-line professional development for primary teachers who are interested in engineering 'aha' moments in number more often. Activities have been developed by teachers for teachers and almost all use the teaching technique of Threading. (See Link List below.)

  Markus Bucher, Kingston Primary School, introduces Bridging 10 in this way:

  Following a workshop on Early Years Numeracy I realised that Ten Friends could be readily adapted to encourage 'aha' moments related to bridging 10 - that first important step in understanding Place Value. Ten Friends (see Link List below) uses one red board ten frame between two players. Bridging 10 uses one red board with two ten frames - one for each player. One plugs their frame with blue plugs, the other with yellow. They are working together to make a combined total of ten or more plugs. They stop playing and start recording when that is achieved. Players take turns to roll the (spot) dice or draw numeral cards and add plugs to their frame. In the example, the blue player must have had at least two rolls, the yellow player might have had only one. That detail doesn't matter.

  What does matter is that the players have stopped here because they know their combined total is ten or more.
  Perhaps the activity should be called Have we got 10 or more yet?.

  Now they:

  1. Say what they have made. In the example: Stop. We have made seven plus five equals twelve. That's more than 10.
  2. Shift plugs from one frame to the other to make a 10 and check their hypothesis.
  3. Write their spoken equation on their calculator and compare the screen answer to their model.
  4. Discuss and record what they have done/learnt.

  The 'aha' moment will eventually come.

  Calculating Changes members can find more about Bridging 10 in the Link List below, which includes how it was used in a Year 4 class.

• Get to Know a Cameo

  Task 7, Consecutive Sums
  

  The critical element in this task is that the addends in any equation and its answer must be among the discs numbered 0 to 25. The second important element is to solve the equation using consecutive addends each time. The first question on the card is designed to ensure students are clear about these parameters. For example, this is not a task about finding all the two addend equations that equal 25. Only those that can be made with consecutive addends, which can only be 12 and 13. But what happens if the solution is 24 instead of 25?

  The process of placing discs helps to clarify the problem. It is also common that once understood, students drift to a written approach. As the problem grows into three and four addends, the discs remain available as a way of checking. There is considerable reasoning and explanation involved as the students find more and more solutions for each question. Patterns start to develop and hypotheses are made and tested. The cameo offers several iceberg questions and suggests how the card questions might be generalised in both words and symbols.

  In the eTask Package this task is in the 'easy' set because it only requires 26 counters.

  Tasks 177, 199 & 222, Making Fractions 2, 3 & 1
  

  These three tasks have the same structure. Blocks which have a geometric relationship to each other are used to explore fractions. The exploration is through value relations, where one block in the set is given the value 1 (and becomes the whole) and the value of each of the other blocks has to be calculated. Further every type of block in the set is given its turn to be the whole and the values of the other blocks are recalculated. The results are recorded in a table. There are patterns to find in the table. The blocks are different from task to task. Task 177, Making Fractions 2, is based on halves, quarters, eighths and sixteenths. It is the easiest because the whole is included and the fractions are straightforward for most students. Task 199, Making Fractions 3, is based on halves, thirds, quarters, sixths and twelfths. It is more difficult than 177. The whole isn't actually included but can be easily created from each of the subsets of congruent shapes. Calculating values in this case requires a little more reasoning. Task 222, Making Fractions 1, is based on quarters, fifths, eighths and ninths of the largest square. It is the most difficult. The whole is present, but direct relationships between the blocks are limited. A higher level of proportional reasoning is involved. Each task cameo has similar general information and information specific to its blocks. The Making Fractions 3 cameo also includes a teacher's slide show illustrating how the related Maths300 lesson, Chocolate Cake, worked in her class, and reviews of the task by another teacher and some students.

  In the eTask Package these tasks are in the 'special' set because each needs additional printing, laminating and cutting of a template of its blocks.

Link List eTask Package Working Mathematically (PDF) New Cube Tube Video Calculating Changes Threading Ten Friends Bridging 10 (Members) Consecutive Sums Making Fractions 2 Making Fractions 3 Making Fractions 1 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 A Different Angle on Angles Trial, Record & Improve Get to Know a Cameo ... Rectangle Nightmare, What's In The Bag?

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)