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June 2022 In this edition of the News you will find:   Learning to Write a Maths Report   Flash & Show   Get to Know a Cameo      ... Planets      ... Cube Numbers Please feel free to distribute this information.

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• Learning to Write a Maths Report
  

  School mathematics is learning to work like a mathematician. A mathematician's work begins with an interesting problem. Somewhere further along the investigation journey, a mathematician uses their journal notes to prepare a report for the information of peers. Obviously preparing maths reports is part of a Working Mathematically curriculum, so teaching how to do that is equally obviously part of the curriculum. These lessons, perhaps 2 or 3 times a year, are as important as any other. They also offer opportunity to build literacy / numeracy / technology links.

  Our short article Learning to Write a Maths Report (see Link List below) offers further background and a lesson plan for one way to develop this skill. It offers several examples, including some in which students from several levels use posters, slide shows or video to present the information, rather than assuming 'writing a report' must mean in a form similar to the photo.

• Flash & Show

  This teacher is using the Poly Plug board as a flash card in this class of 5 year olds. You can see more 'cards' stacked on the floor beside the chair. Perhaps the teacher has just finished showing the board for 5 seconds and is about to hide it, then ask: Put your hand up if you can tell me the number of blues. or Everyone tell me the number of blues you saw. Perhaps that will be followed by: How do you know it's two? and Can we check that another way?. But what happens if the teacher flashes the board then asks the children to: Show the number of blues with your calculator?. or Find this number of things in the room and bring them back to sit with you. or both. Poly Plug and calculators are assumed materials in Calculating Changes classrooms, which is the source of these variations on a traditional activity that often requires teachers to cut cards, make sticky dot patterns then laminate the cards.

  Often children will be asked to return to their seats and draw a picture of ...what we did in Flash and Show today.

  Teachers also reverse the process and flash either the calculator number (using the calculator app of their computer connected to the class display screen), or flash a collection of objects. Children then show with their Poly Plug and whichever other way the teachers hasn't used. Flashing objects works well with magnetic objects on the whiteboard covered by a tea towel, or similar, that can be flipped up.

  Let's play Flash and Show in groups today. One of you will be the teacher.

  Flash & Show is a recommended activity in Working Mathematically with Infants (see Link List below). Calculating Changes Members can access the full text of the activity through Link List below. Others can explore more activities from the Calculating Changes Free Tour in Link List below.

• Get to Know a Cameo

  Task 126, Planets
  

  There are patterns in the solar system and Planets helps students to uncover them. They build a model of the solar system at a point in time where the planets are aligned (very rare, but possible) using a piece of string to represent the alignment. Cards, one for each planet, are placed along the line to represent the distance of each from the sun. The length of the string provided has been chosen to clearly relate mathematically to the longest distance involved. The task relies on estimation in the first instance and then proportional reasoning. Measurements are provided as a guide, but are used as a check by calculating and measuring.

  In the eTask Package this task is in the 'more work' set because of the extra laminating and cutting required to make the planet cards.

  Task 208, Cube Numbers
  

  Cube Numbers is rich with mathematics for middle and senior years of secondary school, but can be easily entered by students from Year 6. It is really only making cube 'buildings' from unit cubes, then finding a process for taking them apart to reveal the cube one size smaller. The key word on the card is 'slice'. It's not about pulling a cube apart willy-nilly. It is about finding a way to interpret the word slice (which may be horizontal or vertical), so that the process to find the cube one size smaller is the same regardless of the starting cube size. At first students have the materials to actually do this. Gradually they are challenged to turn the physical experiences into a mind experiment to conceive it working with larger and larger cubes.

  Generalising to any starting size leads to a special case of the difference between two cubes rule. This begs the question What happens if the cubes are any size apart?, which leads to the general result for a³ - b³. A What happens if...? question from there leads to the related rule for (a + b)³.

  The cameo links to Task 160, Painted Cubes, which includes a From The Classroom section that shows one senior student's journal record of 'discovering' a rule for calculating the difference between two cubes.

  In the eTask Package this task is in the 'easy' set because it only needs a given number of cubes in each of three colours. Wooden cubes or plastic linking cubes are common in primary and secondary schools.

Link List Learning to Write a Maths Report Working Like A Mathematician Flash & Show (Members) Calculating Changes Free Tour Working Mathematically with Infants Planets Cube Numbers Task Library Task Cameo Content Finder Calculating Changes Content Finder Calculating Changes Year Level Finder Order Form Did you miss the Previous News? If so you missed information about: Developing and Sustaining Corporate Memory Free Play to Start the Day Get to Know a Cameo ... Mirror Patterns 2, Area Of A Triangle

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)