In this edition of the News you will find:
Who's Making eTasks?
Maths At Home At School?
PD Is Back (14/07: Nope, but look at the link anyway)
Navigating Mathematics Centre
Get to Know a Cameo
... Red To Blue
... Pythagoras 1
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- Who's Making eTasks?
The most recent school to have started developing their own hands-on problem solving Task Library using the eTask Package is:
- St. Matthew's Primary School, Cornubia, Queensland
Congratulations on starting this adventure. We look forward to hearing about how you make use of your Task Library.
- Maths At Home At School?
If maths is back at school, is there any reason for Maths At Home?
Have been loving using these activities with the Grade 4s! Thank you!!
Kalliopi Geromanolis, Penleigh and Essendon Grammar School
- A maths at home resource for those who decide to opt out and continue home schooling?
- A homework source to partner machine learning or text book practice?
- An activity source for a school curriculum refreshed around learning to work like a mathematician?
- Hands-on professional learning material for schools, clusters, districts, systems, tertiary teacher training, professional associations?
- Something else?
- All of the above?
In preparation for the next two terms, which hopefully won't be as crazy as the last one, it might be time to take a second look at this public resource and find your own way of using it. It would be great to hear how it influences your teaching and your students' learning - just a little affirmation like Kalliopi's, or something more extensive with photos and comment from yourself and the kids.
Every activity has a Gallery section at the end. Think of it as a maths display board in the corridor, only it's available for the whole world to see. I bet the your learners would like to see their work on the web.
Every activity also involves the deliberate use of maths journals and a self-assessment section. This section sometimes expects students to evaluate themselves against the Working Mathematically process (see Link List below); sometimes to evaluate the content they have learnt and how they feel about it; and sometimes both.
There are now 52 activities spanning all year levels from K to 10 and each one has unfolding depth making it suitable for several levels. Highest Number (below) is a perfect example of how a combination of appropriate teaching craft choices and appropriate investigative questions leads to exactly the same game stimulating rich learning at 11 different year levels.
The most recent uploads are.
Incidentally, there are now four Maths At Home activities driven by the self-directed learning of a Picture Puzzle - Sphinx, Square Numbers, Garden Beds and the one above. Plenty of opportunity to explore this unique pedagogy before considering the other thirty-six available as a resource. See Link List below for the web address of both Maths At Home and Picture Puzzles.
- Rows, Rectangles and Multiplication (Years 4 - 8)
Building on the array model of multiplication and driven by a Picture Puzzle slide show, this activity moves from refreshing rows and arrays, to representing arrays as rectangles that gradually become more abstract, to tackling two digit multiplication by breaking the problem into smaller parts. The outcome is an algorithm (procedure) for multiplication that many think is more natural than that usually presented to learners. Another advantage is a direct link to the algebra of 'expanding brackets'. Although not mentioned directly in the activity, breaking an array into parts is the element common to both long multiplication and expanding brackets.
- Highest Number (Years K - 10)
Three activities in one and all built around the same game, which is simply rolling a dice and choosing whether the number it shows should be a hundreds, tens or ones digit. Once a dice number is used, it can't be used again until the next round. The aim is to make a higher number than your partner. Early Years Learners play with just tens and ones and make their own materials into bundles of ten before they start playing. Years 2 - 10 use playing cards to record their choice for a column and begin to think about strategy if the aim is to have the higher number after five rounds. Years 5 - 10 are provided with two additional Investigation Guides. One digs deeper into strategies in the game and the other investigates probability and statistics related to the game.
- PD Is Back
There has certainly been lots of important, intense and innovative professional learning in schools in recent months, albeit totally unexpected when the year began. And there still needs to be space and time to rebuild relationships, structures and routines in classrooms and across the school. However, there are people looking into next term and beyond with a view to supporting on-going staff development in teaching craft and curriculum content.
14/07: Mmm, nice idea, but unfortunately no longer actionable face to face due to Covid Isolation II. However, we are always available for a chat. Also, Maths At Home is a great way to include professional learning in the day to day work with your learners. I guarantee there is something in at least one MAH activity that you haven't thought of before.
You know our expertise is in face to face, practical, pedagogically sound workshops based around learning to work like a mathematician. If you recognise a need in your school, consider giving us a call, or sending an email, so we can chat through a delivery model that can work for you.
- Navigating Mathematics Centre
Mathematics Centre holds over 40 years of classroom success stories. Yes, from before the Interweb and even before personal computers right through to yesterday. We provide tools to help you find your way into the depth of the site and recently two major ones have been refreshed and updated.
- Big Picture is...
a page of easy to read bullet points covering the intent, context and content of every section of the site.
- Site Map is...
a table of contents hyperlinked to every section of the site.
If you are new to our site, or an old friend who is finding themselves returning to the same areas frequently, we suggest you take the time to explore in a new direction using either or both of these tools. See Link List below.
- Get to Know a Cameo
Task 132, Red To Blue
The work of a mathematician is the application of reasoning, not the practising of skills. The reasoning is stimulated by the challenge of an interesting problem. This problem is so interesting to students, in part because it seems to contain no maths, that they want to do it, even when they think they can't do maths. Ironically, in doing it they prove that they can do maths. And very well!
The cameo provides evidence from a Year 6 class and a Year 8 class to support this claim. However, the evidence will be far more convincing if you spend ten minutes trying the problem for yourself first.
Red To Blue seems easy enough. The tiles have a different colour on each side. All you have to do is start with them all red and turn them so they are all blue. The only rule is that all except one must be turned over on each move. When, or if, you can do it, what is the least number of moves? Can you explain why this is the least number? What happens if we change the number of tiles? What happens if we change the turning rule?
In the eTask Package this task is in the 'easy to make' set because it only needs about ten tiles or counters with a different colour or mark on each side.
Task 175, Pythagoras 1
Pythagoras' Theorem by talking, touching, manipulating and measuring. Not by being told a rule and getting on with calculations. The next focus is to find out what is special about where Perigal placed his cut lines. Students can also be encouraged to digger deeper into the shapes created by the dissection using the tools of transformation geometry.
This task is steeped in mathematical history. First the students are told the theorem attributed to the famous Pythagoras. Then they are challenged to check it using a dissection attributed to the less famous Henry Perigal who published it in 1891 when he was 90 years old. Perigal was a stockbroker by trade. For him mathematics was a hobby, but he was sufficiently serious about it to belong to the London Mathematical Society.
Throughout the task there is no mention of As or Bs or Cs. It's about words and interpreting them with squares, quadrilaterals and triangles. The students learn about
In the eTask Package this task is in the 'more work' set because apart from the task card, one additional card needs to be copied, laminated and cut into pieces. Better still of course if a craftsman can make the pieces from wood as in the photo.
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